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6 Commits
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main
| Author | SHA1 | Date | |
|---|---|---|---|
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ce60263c6e |
5
.obsidian/app.json
vendored
5
.obsidian/app.json
vendored
@@ -1,13 +1,14 @@
|
||||
{
|
||||
"showInlineTitle": true,
|
||||
"useMarkdownLinks": true,
|
||||
"promptDelete": true,
|
||||
"promptDelete": false,
|
||||
"showLineNumber": true,
|
||||
"attachmentFolderPath": "images",
|
||||
"pdfExportSettings": {
|
||||
"includeName": true,
|
||||
"pageSize": "A4",
|
||||
"landscape": false,
|
||||
"margin": "0",
|
||||
"margin": "2",
|
||||
"downscalePercent": 64
|
||||
},
|
||||
"readableLineLength": false,
|
||||
|
||||
6
.obsidian/appearance.json
vendored
6
.obsidian/appearance.json
vendored
@@ -1,11 +1,11 @@
|
||||
{
|
||||
"accentColor": "",
|
||||
"theme": "system",
|
||||
"theme": "moonstone",
|
||||
"cssTheme": "Tokyo Night",
|
||||
"nativeMenus": true,
|
||||
"baseFontSize": 14,
|
||||
"interfaceFontFamily": "AppleGothic,Inter",
|
||||
"textFontFamily": "AppleGothic,Inter",
|
||||
"interfaceFontFamily": "AppleGothic,Ubuntu Mono",
|
||||
"textFontFamily": "AppleGothic,DejaVu Math TeX Gyre",
|
||||
"monospaceFontFamily": "PT Mono,Andale Mono",
|
||||
"baseFontSizeAction": false,
|
||||
"translucency": true
|
||||
|
||||
3
.obsidian/community-plugins.json
vendored
3
.obsidian/community-plugins.json
vendored
@@ -7,5 +7,6 @@
|
||||
"obsidian-style-settings",
|
||||
"url-into-selection",
|
||||
"obsidian-csv-table",
|
||||
"mermaid-tools"
|
||||
"mermaid-tools",
|
||||
"obsidian-latex"
|
||||
]
|
||||
30
.obsidian/plugins/obsidian-latex-suite/data.json
vendored
Executable file
30
.obsidian/plugins/obsidian-latex-suite/data.json
vendored
Executable file
File diff suppressed because one or more lines are too long
15605
.obsidian/plugins/obsidian-latex-suite/main.js
vendored
Executable file
15605
.obsidian/plugins/obsidian-latex-suite/main.js
vendored
Executable file
File diff suppressed because one or more lines are too long
11
.obsidian/plugins/obsidian-latex-suite/manifest.json
vendored
Executable file
11
.obsidian/plugins/obsidian-latex-suite/manifest.json
vendored
Executable file
@@ -0,0 +1,11 @@
|
||||
{
|
||||
"id": "obsidian-latex-suite",
|
||||
"name": "Latex Suite",
|
||||
"version": "1.9.8",
|
||||
"minAppVersion": "1.0.0",
|
||||
"description": "Make typesetting LaTeX math as fast as handwriting through snippets, text expansion, and editor enhancements",
|
||||
"author": "artisticat",
|
||||
"authorUrl": "https://github.com/artisticat1",
|
||||
"fundingUrl": "https://ko-fi.com/artisticat",
|
||||
"isDesktopOnly": false
|
||||
}
|
||||
235
.obsidian/plugins/obsidian-latex-suite/styles.css
vendored
Executable file
235
.obsidian/plugins/obsidian-latex-suite/styles.css
vendored
Executable file
@@ -0,0 +1,235 @@
|
||||
/* Settings panel */
|
||||
|
||||
.setting-item.hidden {
|
||||
display: none;
|
||||
}
|
||||
|
||||
.setting-item.setting-item-heading .latex-suite-settings-icon {
|
||||
margin-right: var(--size-4-2);
|
||||
display: inline-flex;
|
||||
}
|
||||
|
||||
.setting-item.setting-item-heading:has(.latex-suite-settings-icon) {
|
||||
border-bottom: 1px solid var(--background-modifier-border);
|
||||
}
|
||||
|
||||
.setting-item.setting-item-heading:has(.latex-suite-settings-icon) + .setting-item {
|
||||
border-top: none;
|
||||
}
|
||||
|
||||
.setting-item.setting-item-heading:has(.latex-suite-settings-icon) ~ .setting-item:not(.setting-item-heading), .latex-suite-snippet-variables-setting + .setting-item-control {
|
||||
width: calc(100% - 26px);
|
||||
margin-left: 26px;
|
||||
}
|
||||
|
||||
.latex-suite-snippet-variables-setting .setting-item-control {
|
||||
height: 120px;
|
||||
}
|
||||
|
||||
.latex-suite-snippet-variables-setting .setting-item-control textarea {
|
||||
width: 100%;
|
||||
height: 100%;
|
||||
}
|
||||
|
||||
.snippets-text-area, .latex-suite-snippet-variables-setting {
|
||||
display: inline-block;
|
||||
}
|
||||
|
||||
.snippets-text-area .setting-item-info, .latex-suite-snippet-variables-setting .setting-item-info {
|
||||
margin-bottom: 0.75rem;
|
||||
}
|
||||
|
||||
.snippets-text-area .setting-item-control {
|
||||
flex-direction: column;
|
||||
align-items: flex-end;
|
||||
}
|
||||
|
||||
.snippets-editor-wrapper {
|
||||
width: 100%;
|
||||
margin-bottom: 0.75rem;
|
||||
}
|
||||
|
||||
.snippets-editor-wrapper .cm-editor {
|
||||
border: 1px solid var(--background-modifier-border);
|
||||
border-radius: 4px;
|
||||
font-size: var(--font-inputs);
|
||||
height: 20em;
|
||||
outline: none !important;
|
||||
text-align: left;
|
||||
}
|
||||
|
||||
.snippets-editor-wrapper .cm-line, .snippets-editor-wrapper .cm-lineNumbers {
|
||||
font-family: var(--font-monospace);
|
||||
}
|
||||
|
||||
.snippets-footer {
|
||||
width: 100%;
|
||||
display: flex;
|
||||
align-items: center;
|
||||
justify-content: space-between;
|
||||
}
|
||||
|
||||
.snippets-editor-validity {
|
||||
display: flex;
|
||||
align-items: center;
|
||||
}
|
||||
|
||||
.snippets-editor-validity-indicator {
|
||||
color: white;
|
||||
display: inline-block;
|
||||
border-radius: 1em;
|
||||
margin-right: 10px;
|
||||
cursor: default;
|
||||
visibility: hidden;
|
||||
}
|
||||
|
||||
.snippets-editor-validity-indicator svg {
|
||||
width: 16px !important;
|
||||
height: 16px !important;
|
||||
}
|
||||
|
||||
.snippets-editor-validity-indicator:hover {
|
||||
color: white;
|
||||
}
|
||||
|
||||
.snippets-editor-validity-indicator.valid {
|
||||
background-color: var(--color-green);
|
||||
visibility: visible;
|
||||
}
|
||||
|
||||
.snippets-editor-validity-indicator.invalid {
|
||||
background-color: var(--color-red);
|
||||
visibility: visible;
|
||||
}
|
||||
|
||||
.snippets-editor-buttons {
|
||||
display: flex;
|
||||
flex-direction: row;
|
||||
}
|
||||
|
||||
.latex-suite-confirmation-modal .setting-item {
|
||||
border: none;
|
||||
}
|
||||
|
||||
.search-input-container input.latex-suite-location-input-el {
|
||||
width: initial;
|
||||
}
|
||||
|
||||
/*
|
||||
Snippet color classes.
|
||||
*/
|
||||
|
||||
/* These extra selectors enforce their color on all children, because CodeMirror does weird nesting of spans when
|
||||
nesting multiple decorations. */
|
||||
|
||||
.latex-suite-snippet-placeholder {
|
||||
border-radius: 2px;
|
||||
background-color: var(--placeholder-bg);
|
||||
outline: var(--placeholder-outline) solid 1px;
|
||||
}
|
||||
|
||||
.latex-suite-snippet-placeholder-0, span.latex-suite-snippet-placeholder-0 span {
|
||||
--placeholder-bg: #87cefa2e;
|
||||
--placeholder-outline: #87cefa6e;
|
||||
}
|
||||
|
||||
.theme-dark .latex-suite-snippet-placeholder-0, span.latex-suite-snippet-placeholder-0 span {
|
||||
--placeholder-outline: #87cefa43;
|
||||
}
|
||||
|
||||
.latex-suite-snippet-placeholder-1, span.latex-suite-snippet-placeholder-1 span {
|
||||
--placeholder-bg: #ffa50033;
|
||||
--placeholder-outline: #ffa5006b;
|
||||
}
|
||||
|
||||
.theme-dark .latex-suite-snippet-placeholder-1, span.latex-suite-snippet-placeholder-1 span {
|
||||
--placeholder-outline: #ffa5004d;
|
||||
}
|
||||
|
||||
.latex-suite-snippet-placeholder-2, span.latex-suite-snippet-placeholder-2 span {
|
||||
--placeholder-bg: #00ff0022;
|
||||
--placeholder-outline: #00ff0060;
|
||||
}
|
||||
|
||||
.theme-dark .latex-suite-snippet-placeholder-2, span.latex-suite-snippet-placeholder-2 span {
|
||||
--placeholder-outline: #00ff003d;
|
||||
}
|
||||
|
||||
|
||||
/* Conceal */
|
||||
|
||||
span.cm-math.cm-concealed-bold {
|
||||
font-weight: bold;
|
||||
}
|
||||
|
||||
span.cm-math.cm-concealed-underline {
|
||||
text-decoration: underline;
|
||||
}
|
||||
|
||||
span.cm-math.cm-concealed-mathrm, sub.cm-math.cm-concealed-mathrm {
|
||||
font-style: normal;
|
||||
}
|
||||
|
||||
|
||||
/* Conceal superscripts without changing line height */
|
||||
sup.cm-math {
|
||||
line-height: 0;
|
||||
}
|
||||
|
||||
sup.cm-math, sub.cm-math {
|
||||
font-style: italic;
|
||||
}
|
||||
|
||||
|
||||
/* Inline math tooltip styling */
|
||||
|
||||
.theme-light .cm-tooltip.cm-tooltip-cursor {
|
||||
box-shadow: 0px 1px 2px rgba(0, 0, 0, 0.028), 0px 3.4px 6.7px rgba(0, 0, 0, .042), 0px 5px 20px rgba(0, 0, 0, .07);
|
||||
}
|
||||
|
||||
.theme-dark .cm-tooltip.cm-tooltip-cursor {
|
||||
box-shadow: 0px 1px 2px rgba(0, 0, 0, 0.1),
|
||||
0px 3.4px 6.7px rgba(0, 0, 0, 0.15),
|
||||
0px 0px 30px rgba(0, 0, 0, 0.27);
|
||||
}
|
||||
|
||||
|
||||
/* Highlight brackets */
|
||||
.theme-light .latex-suite-highlighted-bracket, .theme-light .latex-suite-highlighted-bracket [class^="latex-suite-color-bracket-"] {
|
||||
background-color: hsl(var(--accent-h), var(--accent-s), 40%, 0.3);
|
||||
}
|
||||
|
||||
.theme-dark .latex-suite-highlighted-bracket, .theme-dark .latex-suite-highlighted-bracket [class^="latex-suite-color-bracket-"] {
|
||||
background-color: hsl(var(--accent-h), var(--accent-s), 70%, 0.6);
|
||||
}
|
||||
|
||||
|
||||
/* Color matching brackets */
|
||||
|
||||
.theme-light .latex-suite-color-bracket-0, .theme-light .latex-suite-color-bracket-0 .cm-bracket {
|
||||
color: #527aff;
|
||||
}
|
||||
|
||||
.theme-dark .latex-suite-color-bracket-0, .theme-dark .latex-suite-color-bracket-0 .cm-bracket {
|
||||
color: #47b8ff;
|
||||
}
|
||||
|
||||
.theme-light .latex-suite-color-bracket-1, .theme-light .latex-suite-color-bracket-1 .cm-bracket {
|
||||
color: #ff50b7;
|
||||
}
|
||||
|
||||
.theme-dark .latex-suite-color-bracket-1, .theme-dark .latex-suite-color-bracket-1 .cm-bracket {
|
||||
color: #ff55cd;
|
||||
}
|
||||
|
||||
.theme-light .latex-suite-color-bracket-2, .theme-light .latex-suite-color-bracket-2 .cm-bracket {
|
||||
color: #69ba00;
|
||||
}
|
||||
|
||||
.theme-dark .latex-suite-color-bracket-2, .theme-dark .latex-suite-color-bracket-2 .cm-bracket {
|
||||
color: #73ff63;
|
||||
}
|
||||
|
||||
/* .latex-suite-color-bracket-3 {
|
||||
color: #8de15c;
|
||||
} */
|
||||
206
.obsidian/plugins/obsidian-latex/main.js
vendored
Executable file
206
.obsidian/plugins/obsidian-latex/main.js
vendored
Executable file
@@ -0,0 +1,206 @@
|
||||
'use strict';
|
||||
|
||||
var obsidian = require('obsidian');
|
||||
|
||||
/*! *****************************************************************************
|
||||
Copyright (c) Microsoft Corporation.
|
||||
|
||||
Permission to use, copy, modify, and/or distribute this software for any
|
||||
purpose with or without fee is hereby granted.
|
||||
|
||||
THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
|
||||
REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY
|
||||
AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
|
||||
INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM
|
||||
LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR
|
||||
OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR
|
||||
PERFORMANCE OF THIS SOFTWARE.
|
||||
***************************************************************************** */
|
||||
/* global Reflect, Promise */
|
||||
|
||||
var extendStatics = function(d, b) {
|
||||
extendStatics = Object.setPrototypeOf ||
|
||||
({ __proto__: [] } instanceof Array && function (d, b) { d.__proto__ = b; }) ||
|
||||
function (d, b) { for (var p in b) if (Object.prototype.hasOwnProperty.call(b, p)) d[p] = b[p]; };
|
||||
return extendStatics(d, b);
|
||||
};
|
||||
|
||||
function __extends(d, b) {
|
||||
if (typeof b !== "function" && b !== null)
|
||||
throw new TypeError("Class extends value " + String(b) + " is not a constructor or null");
|
||||
extendStatics(d, b);
|
||||
function __() { this.constructor = d; }
|
||||
d.prototype = b === null ? Object.create(b) : (__.prototype = b.prototype, new __());
|
||||
}
|
||||
|
||||
function __awaiter(thisArg, _arguments, P, generator) {
|
||||
function adopt(value) { return value instanceof P ? value : new P(function (resolve) { resolve(value); }); }
|
||||
return new (P || (P = Promise))(function (resolve, reject) {
|
||||
function fulfilled(value) { try { step(generator.next(value)); } catch (e) { reject(e); } }
|
||||
function rejected(value) { try { step(generator["throw"](value)); } catch (e) { reject(e); } }
|
||||
function step(result) { result.done ? resolve(result.value) : adopt(result.value).then(fulfilled, rejected); }
|
||||
step((generator = generator.apply(thisArg, _arguments || [])).next());
|
||||
});
|
||||
}
|
||||
|
||||
function __generator(thisArg, body) {
|
||||
var _ = { label: 0, sent: function() { if (t[0] & 1) throw t[1]; return t[1]; }, trys: [], ops: [] }, f, y, t, g;
|
||||
return g = { next: verb(0), "throw": verb(1), "return": verb(2) }, typeof Symbol === "function" && (g[Symbol.iterator] = function() { return this; }), g;
|
||||
function verb(n) { return function (v) { return step([n, v]); }; }
|
||||
function step(op) {
|
||||
if (f) throw new TypeError("Generator is already executing.");
|
||||
while (_) try {
|
||||
if (f = 1, y && (t = op[0] & 2 ? y["return"] : op[0] ? y["throw"] || ((t = y["return"]) && t.call(y), 0) : y.next) && !(t = t.call(y, op[1])).done) return t;
|
||||
if (y = 0, t) op = [op[0] & 2, t.value];
|
||||
switch (op[0]) {
|
||||
case 0: case 1: t = op; break;
|
||||
case 4: _.label++; return { value: op[1], done: false };
|
||||
case 5: _.label++; y = op[1]; op = [0]; continue;
|
||||
case 7: op = _.ops.pop(); _.trys.pop(); continue;
|
||||
default:
|
||||
if (!(t = _.trys, t = t.length > 0 && t[t.length - 1]) && (op[0] === 6 || op[0] === 2)) { _ = 0; continue; }
|
||||
if (op[0] === 3 && (!t || (op[1] > t[0] && op[1] < t[3]))) { _.label = op[1]; break; }
|
||||
if (op[0] === 6 && _.label < t[1]) { _.label = t[1]; t = op; break; }
|
||||
if (t && _.label < t[2]) { _.label = t[2]; _.ops.push(op); break; }
|
||||
if (t[2]) _.ops.pop();
|
||||
_.trys.pop(); continue;
|
||||
}
|
||||
op = body.call(thisArg, _);
|
||||
} catch (e) { op = [6, e]; y = 0; } finally { f = t = 0; }
|
||||
if (op[0] & 5) throw op[1]; return { value: op[0] ? op[1] : void 0, done: true };
|
||||
}
|
||||
}
|
||||
|
||||
var DEFAULT_SETTINGS = {
|
||||
preamblePath: "preamble.sty",
|
||||
};
|
||||
var JaxPlugin = /** @class */ (function (_super) {
|
||||
__extends(JaxPlugin, _super);
|
||||
function JaxPlugin(app, manifest) {
|
||||
var _this = _super.call(this, app, manifest) || this;
|
||||
_this.app = app;
|
||||
_this.settings = DEFAULT_SETTINGS;
|
||||
return _this;
|
||||
}
|
||||
JaxPlugin.prototype.loadPreamble = function () {
|
||||
return __awaiter(this, void 0, void 0, function () {
|
||||
var preamble;
|
||||
return __generator(this, function (_a) {
|
||||
switch (_a.label) {
|
||||
case 0: return [4 /*yield*/, this.app.vault.adapter.read(this.settings.preamblePath)];
|
||||
case 1:
|
||||
preamble = _a.sent();
|
||||
if (MathJax.tex2chtml == undefined) {
|
||||
MathJax.startup.ready = function () {
|
||||
MathJax.startup.defaultReady();
|
||||
MathJax.tex2chtml(preamble);
|
||||
};
|
||||
}
|
||||
else {
|
||||
MathJax.tex2chtml(preamble);
|
||||
}
|
||||
return [2 /*return*/];
|
||||
}
|
||||
});
|
||||
});
|
||||
};
|
||||
JaxPlugin.prototype.loadSettings = function () {
|
||||
return __awaiter(this, void 0, void 0, function () {
|
||||
var _a, _b, _c, _d;
|
||||
return __generator(this, function (_e) {
|
||||
switch (_e.label) {
|
||||
case 0:
|
||||
_a = this;
|
||||
_c = (_b = Object).assign;
|
||||
_d = [{}, DEFAULT_SETTINGS];
|
||||
return [4 /*yield*/, this.loadData()];
|
||||
case 1:
|
||||
_a.settings = _c.apply(_b, _d.concat([_e.sent()]));
|
||||
return [2 /*return*/];
|
||||
}
|
||||
});
|
||||
});
|
||||
};
|
||||
JaxPlugin.prototype.saveSettings = function () {
|
||||
return __awaiter(this, void 0, void 0, function () {
|
||||
return __generator(this, function (_a) {
|
||||
switch (_a.label) {
|
||||
case 0: return [4 /*yield*/, this.saveData(this.settings)];
|
||||
case 1:
|
||||
_a.sent();
|
||||
return [2 /*return*/];
|
||||
}
|
||||
});
|
||||
});
|
||||
};
|
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@00677611 \\ \hline
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l.14 User ID &&
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CHC119 \\ \hline
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AI Coursework \\ \hline
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Artificial Intelligence and Data Mining \\ \hline
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|
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34123\\ \hline
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\documentclass{beamer}
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\title{My Presentation}
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\subtitle{Using Beamer}
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\author{George Wilkinson}
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\institute{University of Salford}
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\date{\today}
|
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\begin{document}
|
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\begin{tabular}{|l|r|}
|
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\hline
|
||||
Student Roll Number && @00677611 \\ \hline
|
||||
User ID && CHC119 \\ \hline
|
||||
Assessment Title && AI Coursework \\ \hline
|
||||
Module Title && Artificial Intelligence and Data Mining \\ \hline
|
||||
CRN && 34123\\ \hline
|
||||
\end{tabular}
|
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\end{document}
|
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AI & Data Mining/Assessment/Coursework Prep Notes.md
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||||
Lectures 5,6,7,8,9,10,11,12
|
||||
Chapters 20,21,22,23
|
||||
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texlive-recommended
|
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texlive-luatex
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texlive-fonts-recommended
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@@ -1,4 +1,5 @@
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# 1R: (AV)CTARs
|
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|
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(foreach) Attribute
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||||
(foreach) Value
|
||||
Count (class)
|
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@@ -8,6 +9,7 @@
|
||||
Smallest (error rate)
|
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|
||||
# Missing Values: Ma $\Delta$D CPS
|
||||
|
||||
Malfunctioning Equipment
|
||||
Change in Design
|
||||
Collation of Datasets
|
||||
|
||||
@@ -1,11 +1,15 @@
|
||||
# 1R
|
||||
|
||||
### (AV)CTARs
|
||||
|
||||
Simple
|
||||
Classification
|
||||
One-Level tree
|
||||
|
||||
Tie, make arbitrary choice
|
||||
|
||||
## Issue with Numerics
|
||||
|
||||
- Discretise
|
||||
- List values of attribute
|
||||
- Sort asc
|
||||
@@ -13,11 +17,15 @@ Tie, make arbitrary choice
|
||||
- Breakpoints between change in class
|
||||
- Interval assigned to majority class
|
||||
- Enforce bucket size, if adjacent interval has same class, merge.
|
||||
|
||||
## Issue with Missing Values
|
||||
|
||||
- Assign "missing" as a value
|
||||
- Treat normally
|
||||
|
||||
## Issue with Overfitting
|
||||
|
||||
- Bucket Enforcement
|
||||
- Ensure attribute tested is applicable
|
||||
|
||||
# PRISM
|
||||
# PRISM
|
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||||
@@ -8,4 +8,4 @@
|
||||
2. Search Engines recognise language
|
||||
3. Telephone menus recognise language and can "hear"
|
||||
4. Dynamic routing algorithms utilise machine learning
|
||||
7. Following the principles defined by the turing test, AI should classify as both science and engineering. The concepts and programming are scientific, however robotics and hardware are engineering.
|
||||
7. Following the principles defined by the turing test, AI should classify as both science and engineering. The concepts and programming are scientific, however robotics and hardware are engineering.
|
||||
|
||||
@@ -134,7 +134,7 @@ Limited rationality means acting appropriately when there is not enough time to
|
||||
|
||||
Perfect rationality remains a good starting point for theoretical analysis.
|
||||
|
||||
#### Value Alignment Problem
|
||||
#### Value Alignment Problem
|
||||
|
||||
A problem with perfect rationality is that it would assume a fully specified objective given to the machine.
|
||||
Artificially defined problems such as chess, come with an objective.
|
||||
@@ -147,7 +147,8 @@ Problem of achieving this is called the value alignment problem
|
||||
|
||||
### Bad Behaviour
|
||||
|
||||
If a machine is intelligent enough to reason and act, such a machine may attemt to increase chances of winning by immoral means:
|
||||
If a machine is intelligent enough to reason and act, such a machine may attempt to increase chances of winning by immoral means:
|
||||
|
||||
- Blackmail
|
||||
- Bribery
|
||||
- Grabbing additional computing resources for itself
|
||||
@@ -157,5 +158,5 @@ These behaviours are rational, and are logical for success, however immoral.
|
||||
|
||||
We do not want machines that are intelligent in the sense of pursuing their objectives.
|
||||
We want them to pursue our objectives.
|
||||
If we cannot transfer our objectives perfectly to the machine, we need the machine to know that is does not know the complete objective and have the incentive to act cautiously, ask for permission, learn about preferences through observation, defer to human control.
|
||||
We want agents that are provably beneficial to humans.
|
||||
If we cannot transfer our objectives perfectly to the machine, we need the machine to know that is does not know the complete objective and have the incentive to act cautiously, ask for permission, learn about preferences through observation, defer to human control.
|
||||
We want agents that are provably beneficial to humans.
|
||||
|
||||
BIN
AI & Data Mining/Week 18/test.pdf
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@@ -27,16 +27,16 @@ Formula: p => q
|
||||
|
||||
(b) Increased spending overheats the economy.
|
||||
Atomic Propositions:
|
||||
Increased spending
|
||||
Increased spending
|
||||
Overheats the economy
|
||||
Connectives:
|
||||
Connectives:
|
||||
None, implied non-linguistic
|
||||
Formula: p => q
|
||||
|
||||
(c) Increased spending coupled with tax cuts overheats the economy.
|
||||
Atomic Propositions:
|
||||
Increased spending
|
||||
There are tax cuts
|
||||
There are tax cuts
|
||||
Overheated economy
|
||||
Connectives:
|
||||
Coupled with
|
||||
@@ -56,7 +56,7 @@ Atomic Propositions:
|
||||
Inflation does not rise
|
||||
Connectives:
|
||||
either / or
|
||||
Formula: p
|
||||
Formula: p
|
||||
|
||||
1. Remove as many brackets as possible from the following propositions without altering their meaning (i.e. the truth table).
|
||||
|
||||
|
||||
@@ -19,7 +19,9 @@
|
||||
- Disjunction (∨): p ∨ q is true if and only if at least one of p or q is true
|
||||
- Implication (⇒): p ⇒ q is false if and only if p is true and q is false
|
||||
- Equivalence (⇔): p ⇔ q is true if and only if p and q have the same truth value
|
||||
|
||||
## Precedence Order of Connectives
|
||||
|
||||
1. Negation (¬)
|
||||
2. Conjunction (∧)
|
||||
3. Disjunction (∨)
|
||||
@@ -27,6 +29,7 @@
|
||||
5. Equivalence (⇔)
|
||||
|
||||
This means that in a formula without parentheses, ¬ takes precedence over ∧ and ∨, ∧ and ∨ have the same precedence but associativity to the left, and ⇒ and ⇔ also have the same precedence but associativity to the right. For example, p ∧ q ⇒ r is equivalent to (p ∧ q) ⇒ r, not p ∧ (q ⇒ r).
|
||||
|
||||
### Propositions and Connectives (Examples)
|
||||
|
||||
#### Atomic Propositions:
|
||||
@@ -119,6 +122,7 @@ This means that in a formula without parentheses, ¬ takes precedence over ∧ a
|
||||
- Formalized as: p ∧ q ⇒ ¬r
|
||||
- Argument: If Bob eats carrots, then he will be able to see in the dark. Therefore, if Bob can’t see in the dark, then he hasn’t eaten carrots.
|
||||
- Formalized as: p ⇒ q ≡ ¬q ⇒ ¬p
|
||||
|
||||
# Summary
|
||||
|
||||
- Logicians focus on argument form
|
||||
|
||||
@@ -0,0 +1,44 @@
|
||||
1. George Boole
|
||||
2. Truth Tables for a) Negation b) Contraposition
|
||||
|
||||
a)
|
||||
Negation Law
|
||||
¬¬p ≡ p
|
||||
|
||||
| p | ¬p | ¬(¬p) | ¬(¬p) ⇔ p |
|
||||
| --- | --- | ----- | --------- |
|
||||
| T | F | T | T |
|
||||
| F | T | F | T |
|
||||
|
||||
b)
|
||||
|
||||
Contraposition Law
|
||||
p ⇒ q ≡ ¬q ⇒ ¬p
|
||||
|
||||
| p | ¬p | q | ¬q | p ⇒ q | ¬q ⇒ ¬p | p ⇒ q ⇔ ¬q ⇒ ¬p |
|
||||
| --- | --- | --- | --- | ----- | ------- | --------------- |
|
||||
| T | F | T | F | T | T | T |
|
||||
| T | F | F | T | F | F | T |
|
||||
| F | T | T | F | T | T | T |
|
||||
| F | T | F | T | T | T | T |
|
||||
|
||||
p ⇒ q ⇔ ¬q ⇒ ¬p MUST be true, since p ⇒ q and ¬q ⇒ ¬p are shown in the truth table to be the same logical equivalence
|
||||
|
||||
1. Provide names of laws
|
||||
1. Negation Law
|
||||
2. De Morgan's Law
|
||||
3. Negation Law
|
||||
4. De Morgan's Law
|
||||
5. Negation Law Twice
|
||||
6. Associative Law
|
||||
7. De Morgan's Law
|
||||
8. De Morgan's Law
|
||||
9. Negation Law Twice
|
||||
2. Show logical equivalence
|
||||
p ⇒ q
|
||||
¬q ⇒ ¬p
|
||||
p ⇒ q
|
||||
≡ (¬p) v q
|
||||
≡ q v (¬p)
|
||||
≡ ¬ (¬q) v (¬p)
|
||||
≡ (¬q) ⇒ (¬p)
|
||||
@@ -0,0 +1,154 @@
|
||||
**Notes on Slides and Exercises**
|
||||
|
||||
**Slide 0: Learning Objectives**
|
||||
- Prove equivalence of formulae using truth tables.
|
||||
- Remember and use laws of equivalence.
|
||||
- Carry out a transformational proof.
|
||||
|
||||
**Slide 1: Contents**
|
||||
- Why is propositional logic called Boolean logic/algebra?
|
||||
- Using truth tables to prove two formulae are identical in meaning.
|
||||
- A problem with truth tables.
|
||||
- Laws of logic.
|
||||
- Famous applications.
|
||||
- Summary, reading and references.
|
||||
|
||||
**Slide 2: George Boole (1815-1864)**
|
||||
- Son of a shoemaker, self-taught mathematician.
|
||||
- Professed mathematics at Queens College, Cork, Ireland.
|
||||
- Seminal work: attempted to apply algebraic and arithmetic principles to logic.
|
||||
|
||||
**Slide 3: Logical Equivalence (≡)**
|
||||
- Two formulae are equivalent if they have identical truth values under all possible assignments.
|
||||
- Example: p ≡ p ∨ p (Idempotence)
|
||||
|
||||
**Slide 4: Two Approaches to Logical Equivalence**
|
||||
1. Truth tables
|
||||
- Example: p ≡ ¬p (Negation)
|
||||
2. Transformational proofs
|
||||
- Uses laws of logic to prove equivalence.
|
||||
|
||||
**Slide 5: Logical Equivalence with One Variable**
|
||||
- Truth table for p ≡ p ∨ p (Idempotence)
|
||||
- T | T | T
|
||||
F | F | F
|
||||
|
||||
**Slide 6: Logical Equivalence with Two Variables**
|
||||
- Truth table for p ∨ q ≡ q ∨ p (Commutativity)
|
||||
- T | T | T | T
|
||||
F | T | T | T
|
||||
T | F | T | F
|
||||
F | F | F | F
|
||||
|
||||
**Slide 7: Exercise - De Morgan's First Law**
|
||||
- Prove ¬(p ∧ q) ≡ ¬p ∨ ¬q using a truth table.
|
||||
|
||||
**Slide 8: Solution to Exercise**
|
||||
- Truth table for ¬(p ∧ q) ≡ ¬p ∨ ¬q
|
||||
- T | F | F | T | F | F | T | F | F | F
|
||||
F | F | F | F | F | F | F | F | F | T
|
||||
|
||||
**Slide 9: Logical Equivalence with Three Variables**
|
||||
- Truth table for (p ∨ q) ∨ r ≡ p ∨ (q ∨ r) (Associativity)
|
||||
- Example: (2 × 3) × 4 = 2 × (3 × 4)
|
||||
|
||||
**Slide 10: A Problem with Truth Tables**
|
||||
- Truth tables become increasingly tedious as the number of variables increases.
|
||||
- n | Number of rows in truth table (2^n)
|
||||
1 | 2
|
||||
2 | 4
|
||||
3 | 8
|
||||
|
||||
**Slide 11: Laws of Logic**
|
||||
- Idempotence: p ≡ p ∨ p, p ≡ p ∧ p
|
||||
- Commutativity: p ∨ q ≡ q ∨ p, p ∧ q ≡ q ∧ p
|
||||
- Associativity: (p ∨ q) ∨ r ≡ p ∨ (q ∨ r), etc.
|
||||
- Negation law: ¬¬p ≡ p
|
||||
- Law of equivalence: p ⇔ q ≡ (p ⇒ q) ∧ (q ⇒ p)
|
||||
- Law of implication: p ⇒ q ≡ ¬p ∨ q
|
||||
- Contraposition Law: p ⇒ q ≡ ¬q ⇒ ¬p
|
||||
- De Morgan's first law: ¬(p ∧ q) ≡ ¬p ∨ ¬q
|
||||
- De Morgan's second law: ¬(p ∨ q) ≡ ¬p ∧ ¬q
|
||||
|
||||
**Slide 12: Proof of De Morgan's Second Law**
|
||||
- Using laws of logic to prove ¬(p ∨ q) ≡ ¬p ∧ ¬q.
|
||||
|
||||
**Slide 13: Idempotence**
|
||||
- Proof of p ∧ p ≡ p using laws of logic.
|
||||
- p ∧ p ≡ ¬¬p ∧ ¬¬p (Negation law twice)
|
||||
- ≡ ¬(¬p ∨ ¬p) (De Morgan's second law)
|
||||
- ≡ ¬false (Law of contradiction)
|
||||
- ≡ p (Simplification)
|
||||
|
||||
**Slide 14: Commutative Laws of Logic**
|
||||
- Proof of p ∧ q ≡ q ∧ p using laws of logic.
|
||||
- p ∧ q ≡ ¬¬p ∧ ¬¬q (Negation law twice)
|
||||
- ≡ ¬(¬p ∨ ¬q) (De Morgan's second law)
|
||||
- ≡ ¬(¬q ∨ ¬p) (Commutativity of ∨)
|
||||
- ≡ q ∧ p (Negation law twice)
|
||||
|
||||
**Slide 15: Associative Laws of Logic**
|
||||
- Example: (a × b) × c ≡ a × (b × c)
|
||||
|
||||
**Slide 16: Distributive Laws of Logic**
|
||||
- Example: a × (b + c) ≡ (a × b) + (a × c)
|
||||
|
||||
**Slide 17: T versus true and F versus false**
|
||||
- T represents a formula is true, F represents it is false.
|
||||
- Example: p ∧ true ≡ p (Law of simplification)
|
||||
|
||||
**Slide 18: Laws involving true and false**
|
||||
- Law of excluded middle: p ∨ ¬p ≡ true
|
||||
- Law of contradiction: p ∧ ¬p ≡ false
|
||||
- Laws of simplification: p ∧ true ≡ p, p ∨ true ≡ true, p ∧ false ≡ false, p ∨ false ≡ p
|
||||
|
||||
**Slide 19: Two More Laws of Simplification**
|
||||
- Proofs for:
|
||||
- p ∨ (p ∧ q) ≡ p
|
||||
- p ∧ (p ∨ q) ≡ p
|
||||
|
||||
**Slide 20: Transformational Proofs**
|
||||
- Two implicit rules:
|
||||
- Substitution Rule: Replace a sub-formula with an equivalent one without changing the meaning.
|
||||
- Transitivity Rule: If p ≡ q and q ≡ r, then p ≡ r.
|
||||
- Example: Modus Tollens (¬q ∧ (p ⇒ q) ⇒ ¬p)
|
||||
- Proof using laws of logic.
|
||||
|
||||
**Slide 21: Exercise**
|
||||
- Fill in the missing steps to prove (p ∨ q) ∧ (¬p ∨ q) ≡ q using transformational proofs.
|
||||
- Solution:
|
||||
- (p ∨ q) ∧ (¬p ∨ q)
|
||||
- ≡ (q ∨ p) ∧ (¬p ∨ q) (Commutativity)
|
||||
- ≡ q ∨ (p ∧ ¬p) (Distributive law)
|
||||
- ≡ q ∨ false (Law of contradiction)
|
||||
- ≡ q (Simplification)
|
||||
|
||||
**Slide 22: Example - Accommodation**
|
||||
- Prove ¬p ⇒ (q ∨ r) ≡ (¬p ∧ ¬q) ⇒ r using transformational proofs.
|
||||
- Solution:
|
||||
- Proof using laws of logic.
|
||||
|
||||
**Slide 23: Famous Applications**
|
||||
- Analysis of complex conditional commands in programming.
|
||||
- Design of digital circuits.
|
||||
- Algebraic approach to formal specifications in software engineering.
|
||||
|
||||
**Slide 24: Summary**
|
||||
- Boole's system was the foundation for propositional logic.
|
||||
- Two approaches to establishing equivalence:
|
||||
- Truth tables (tedious with many variables)
|
||||
- Transformational proofs (uses laws of logic)
|
||||
- Summary slides on Boole's system, truth tables, and transformational proofs.
|
||||
|
||||
**Slide 25: Reading and References**
|
||||
- Recommended textbook: Russell, S., & Norvig, P. (2022). Artificial Intelligence: A Modern Approach (4th ed.). Pearson.
|
||||
- Additional references:
|
||||
- Nissanke, M. (1999). Introductory Logic and Sets for Computer Scientists. Addison-Wesley.
|
||||
- Gray, P. (1984). Logic, Algebra and Databases. John Wiley & Sons.
|
||||
|
||||
**Exercises:**
|
||||
1. Prove the laws of idempotence, commutative, associative, and distributive using truth tables.
|
||||
2. Prove De Morgan's laws using truth tables or transformational proofs.
|
||||
3. Prove the laws involving true and false using truth tables or transformational proofs.
|
||||
4. Prove the laws of simplification using truth tables or transformational proofs.
|
||||
5. Prove the equivalence of two given formulae using transformational proofs (as demonstrated in slides 21 and 22).
|
||||
@@ -0,0 +1,53 @@
|
||||
1. A syllogism is an instance of a form of reasoning in which a conclusion is drawn from two given or assumed propositions; a common or middle term is present in the two premises but not in the conclusion, which may be invalid.
|
||||
2. Aristotle
|
||||
|
||||
**Double Negation ¬ Elim ¬ ¬ p p**
|
||||
|
||||
| Propositions | Premises | Conclusion |
|
||||
| ------------ | ------------ | ---------- |
|
||||
| p | $\neg\neg p$ | p |
|
||||
| T | T | T |
|
||||
| F | F | F |
|
||||
|
||||
**Hypothetical syllogism; this says that if p implies q and q implies r, then it can be logically concluded that p implies r. p ⇒ q q ⇒ r p ⇒ r**
|
||||
|
||||
| Propositions | | | Premises | | Conclusion |
|
||||
| ------------ | --- | --- | -------------- | -------------- | -------------- |
|
||||
| p | q | r | $p \implies q$ | $q \implies r$ | $p \implies r$ |
|
||||
| T | T | T | T | T | T |
|
||||
| T | T | F | T | F | |
|
||||
| T | F | T | F | T | |
|
||||
| T | F | F | F | T | |
|
||||
| F | T | T | T | T | T |
|
||||
| F | T | F | T | F | |
|
||||
| F | F | T | T | T | T |
|
||||
| F | F | F | T | T | T |
|
||||
|
||||
1. Involves linking implications together in a sequential manner, much like the links in a chain.
|
||||
|
||||
**p ∨ q q Therefore, p**
|
||||
|
||||
| Propositions | | Premises | | Conclusion |
|
||||
| ------------ | --- | ---------- | --- | ---------- |
|
||||
| $p$ | $q$ | $p \lor q$ | $q$ | p |
|
||||
| T | T | T | T | T |
|
||||
| T | F | T | F | T |
|
||||
| F | T | T | T | F |
|
||||
| F | F | F | F | F |
|
||||
|
||||
**p ⇒ q q ⇒ p Therefore, p ∧ q**
|
||||
|
||||
| Propositions | | Premises | | Conclusion |
|
||||
| ------------ | --- | -------------- | -------------- | ----------- |
|
||||
| p | q | $p \implies q$ | $q \implies p$ | $p \land q$ |
|
||||
| T | T | T | T | T |
|
||||
| T | F | F | T | F |
|
||||
| F | T | T | F | F |
|
||||
| F | F | T | T | F |
|
||||
|
||||
$p \implies q$
|
||||
$r \implies s$
|
||||
$p \lor r$ (p disjunction (or) r)
|
||||
Conclusion: $q \lor s$
|
||||
|
||||
The "Constructive Dilemma": If the disjunction of the antecedent of two implications holds then the disjunction of the conclusions also must hold
|
||||
163
AI & Data Mining/Week 22/Week 22 Validity and Inference Rules.md
Normal file
163
AI & Data Mining/Week 22/Week 22 Validity and Inference Rules.md
Normal file
@@ -0,0 +1,163 @@
|
||||
|
||||
|
||||
**Detailed Notes on Lectures 9 & 10: Validity and Inference Rules**
|
||||
|
||||
**Slide 1: Learning Objectives**
|
||||
- Define the notion of validity in an argument.
|
||||
- Establish validity using truth tables.
|
||||
- Demonstrate invalidity using truth tables.
|
||||
- Understand inference rules.
|
||||
|
||||
**Slide 2: Contents**
|
||||
- Objectives
|
||||
- Transformational proofs are not sufficient.
|
||||
- Comparison of deduction with induction.
|
||||
- Validity.
|
||||
- Demonstrating validity/invalidity using truth tables.
|
||||
- Problem with truth tables.
|
||||
- Inference rules.
|
||||
- Summary, reading, and references.
|
||||
|
||||
**Slide 3: Transformational Proofs do not Suffice**
|
||||
- Understanding transformations of formulas is useful but insufficient.
|
||||
- Logic uses rules of inference to deduce true propositions from other true propositions.
|
||||
- Invalid premises cannot lead to valid conclusions, preventing proofs of contradictions or useless systems.
|
||||
|
||||
**Slide 4: Premises and Conclusions**
|
||||
- An argument consists of premises (basis for accepting) and a conclusion.
|
||||
- Example:
|
||||
- Premises: Every adult is eligible to vote; John is an adult.
|
||||
- Conclusion: Therefore, John is eligible to vote.
|
||||
|
||||
**Slide 5: Deduction vs. Induction**
|
||||
- Deductive arguments: Conclusion is wholly justified by premises.
|
||||
- Inductive arguments: More general new knowledge inferred from facts or observations.
|
||||
|
||||
**Slide 6: Valid vs. Invalid Arguments**
|
||||
- Valid arguments: Conclusion always true when premises are true.
|
||||
- Invalid arguments: At least one assignment where premises are true, but conclusion is false.
|
||||
|
||||
**Slide 7: Example of Valid Argument**
|
||||
- If John is an adult, then he is eligible to vote (premise).
|
||||
- John is an adult (premise).
|
||||
- Therefore, John is eligible to vote (conclusion).
|
||||
|
||||
**Slide 8: Example of Valid Argument with False Conclusion**
|
||||
- If I catch the 19:32 train, I'll arrive in Glasgow at 19:53 (premise).
|
||||
- I catch the 19:32 train (premise).
|
||||
- Therefore, I arrive in Glasgow at 19:53 (conclusion) – Factually false but valid argument.
|
||||
|
||||
**Slide 9: Example of Invalid Argument**
|
||||
- If I win the lottery, then I am lucky (premise).
|
||||
- I do not win the lottery (premise).
|
||||
- Therefore, I am unlucky (conclusion) – Invalid argument with factually true premises and conclusion.
|
||||
|
||||
**Slide 10: Demonstrating Validity Using Truth Tables**
|
||||
- View argument as implication (p ⇒ q).
|
||||
- If premises entail conclusion, then argument is valid.
|
||||
|
||||
**Slide 12: Demonstrating Validity Using Truth Table (Example)**
|
||||
- Argument: If John is an adult, then he is eligible to vote; John is an adult; Therefore, John is eligible to vote.
|
||||
- Atomic Propositions: p (John is an adult), q (John is eligible to vote).
|
||||
|
||||
| p | q | p ⇒ q | p ∧ q |
|
||||
|---|---|------|-------|
|
||||
| T | T | T | T |
|
||||
| F | T | F | F |
|
||||
|
||||
- Argument is valid because conclusion (q) is always true when premises are true.
|
||||
|
||||
**Slide 13: Viewing Argument as Implication**
|
||||
- If premises logically imply conclusion, argument is valid.
|
||||
- Example: ((p ⇒ q) ∧ p) ⇒ q
|
||||
|
||||
**Slide 15: Demonstrating Invalidity Using Truth Tables**
|
||||
- Argument is invalid if there's at least one assignment where premises are true, but conclusion is false.
|
||||
|
||||
**Slide 16: Demonstrating Invalidity Using Truth Table (Example)**
|
||||
- Argument: p ⇔ q; p ⇒ r; Therefore, p – Invalid argument.
|
||||
|
||||
| p | q | r | p ⇔ q | p ⇒ r |
|
||||
|---|---|------|-------|--------|
|
||||
| T | T | T | T | T |
|
||||
| F | T | F | F | F |
|
||||
|
||||
- Argument is invalid because there's a row where premises are true, but conclusion (p) is false.
|
||||
|
||||
**Slide 17: Exercise**
|
||||
- Demonstrate the invalidity of the argument: p ∨ q; ¬p; Therefore, ¬q.
|
||||
|
||||
**Slide 18: Solution to Exercise**
|
||||
- Atomic Propositions: p, q.
|
||||
|
||||
| p | q | p ∨ q | ¬p |
|
||||
|---|---|------|-----|
|
||||
| F | T | T | T |
|
||||
|
||||
- Argument is invalid because there's a row where premises are true, but conclusion (¬q) is false.
|
||||
|
||||
**Slide 19: A Problem with Truth Tables**
|
||||
- Using truth tables to establish validity becomes tedious as the number of variables increases.
|
||||
|
||||
**Slide 20: Deductive Proofs**
|
||||
- Approach to establishing validity using a series of simpler arguments known to be valid.
|
||||
- Uses laws of logic (logical equivalences) and inference rules.
|
||||
|
||||
**Slide 21: Inference Rules**
|
||||
- Primitive valid argument forms eliminating or introducing logical connectives.
|
||||
- Categories: Intro (introduces connective), Elim (eliminates connective).
|
||||
|
||||
**Slide 22: The Layout of an Inference Rule**
|
||||
- Premises (above the line): List of formulas already in proof.
|
||||
- Conclusion (below the line): What may be deduced by applying the inference rule.
|
||||
|
||||
**Slide 23: Conjunction (∧Intro)**
|
||||
- Introduces the connective ∧.
|
||||
- Example: p, q; Therefore, p ∧ q.
|
||||
|
||||
**Slide 24: Simplification (∧Elim)**
|
||||
- Eliminates the connective ∧.
|
||||
- Example: p ∧ q; Therefore, p.
|
||||
|
||||
**Slide 25: Addition (∨Intro)**
|
||||
- Introduces the connective ∨.
|
||||
- Example: p; Therefore, p ∨ q.
|
||||
|
||||
**Slide 26: Exercise on Disjunctive Syllogism**
|
||||
- Demonstrate the validity of the inference rule using a truth table.
|
||||
|
||||
**Slide 27: Solution to Exercise**
|
||||
- Atomic Propositions: p, q.
|
||||
|
||||
| p | q | ¬p |
|
||||
|---|---|-----|
|
||||
| F | T | T |
|
||||
|
||||
- Argument is valid because conclusion (q) is always true when premises are true.
|
||||
|
||||
**Slide 28: Modus Ponens (⇒Elim)**
|
||||
- Eliminates the connective ⇒.
|
||||
- Example: p ⇒ q; p; Therefore, q.
|
||||
|
||||
**Slide 29: Modus Tollens (⇒Elim)**
|
||||
- Eliminates the connective ⇒.
|
||||
- Example: p ⇒ q; ¬q; Therefore, ¬p.
|
||||
|
||||
**Slide 30: Other Inference Rules**
|
||||
- Double Negation (¬Elim): ¬¬p; Therefore, p.
|
||||
- Laws of Equivalence (⇔Elim): p ⇔ q; Therefore, p ⇒ q and q ⇒ p.
|
||||
|
||||
**Slide 31: Transitive Inference Rules**
|
||||
- Transitivity of Equivalence: If p ≡ q and q ≡ r, then p ≡ r.
|
||||
- Hypothetical Syllogism: If p ⇒ q and q ⇒ r, then p ⇒ r.
|
||||
|
||||
**Slide 32: Summary**
|
||||
- Valid arguments: Conclusion always true when premises are true.
|
||||
- Invalid arguments: At least one assignment where premises are true, but conclusion is false.
|
||||
- Truth tables demonstrate invalidity.
|
||||
- Inference rules deduce true propositions from other true propositions.
|
||||
|
||||
**Slide 33: Reading and References**
|
||||
- Russell, Norvig (2022). Artificial Intelligence. 4th Edition.
|
||||
- Nissanke (1999). Introductory Logic and Sets for Computer Scientists.
|
||||
- Gray (1984). Logic, Algebra and Databases.
|
||||
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AI & Data Mining/Week 22/Week 22 Validity and Inference Rules.pdf
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AI & Data Mining/Week 22/Week 22 Validity and Inference Rules.pdf
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AI & Data Mining/Week 22/test.pdf
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16
AI & Data Mining/Week 23/Chapter 23 - Deductive Proofs.md
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16
AI & Data Mining/Week 23/Chapter 23 - Deductive Proofs.md
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@@ -0,0 +1,16 @@
|
||||
|
||||
|
||||
|
||||
| Line | | | |
|
||||
| ---- | --------------------------- | ---------- | --------------------------------- |
|
||||
| 1 | $A \implies \lnot B$ | Premise | |
|
||||
| 2 | $(B \lor C) \lor D$ | Premise | |
|
||||
| 3 | $\lnot C \lor D \implies A$ | Premise | |
|
||||
| 4 | $\lnot C$ | Premise | |
|
||||
| 5 | $\lnot C \lor D$ | From 4 | $\lor Intro$ |
|
||||
| 6 | $A$ | From 3 & 5 | $\implies Elim$ Modus Ponens |
|
||||
| 7 | $\lnot B$ | From 1 & 6 | $\implies Elim$ Modus Ponens |
|
||||
| 8 | $\lnot B \land \lnot C$ | From 2 & 7 | $\land Intro$ |
|
||||
| 9 | $\lnot (B \lor C)$ | From 8 | De Morgans Law |
|
||||
| 10 | $D$ | From 9 | $\lor Elim$ Disjunctive Syllogism |
|
||||
B or C is not true, therefore D must be true from step 2.
|
||||
204
AI & Data Mining/Week 23/Week 23 - Deductive Proofs.md
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204
AI & Data Mining/Week 23/Week 23 - Deductive Proofs.md
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|
||||
|
||||
**Slide 3: Recap on Logical Implication (Entailment) |-|=-**
|
||||
|
||||
- Entailment notation: p |=q if and only if the implication p$\implies$q is a tautology.
|
||||
- Example:
|
||||
- p $\land$ q |=q
|
||||
- Truth table for p $\implies$ q:
|
||||
|
||||
| p | q | p $\land$ q | p $\implies$ q |
|
||||
|---|---|------|--------|
|
||||
| T | T | T | T |
|
||||
| T | F | F | F |
|
||||
| F | T | F | T |
|
||||
| F | F | F | T |
|
||||
|
||||
**Slide 4: (r $\implies$ s) $\land$ (r $\implies$ $\lnot$s) |-|=-**
|
||||
|
||||
- Intuitively, if r implies both s and $\lnot$s, then r must be false.
|
||||
- Truth table for (r $\implies$ s) $\land$ (r $\implies$ $\lnot$s):
|
||||
|
||||
| r | s | $\lnot$s | (r $\implies$ s) $\land$ (r $\implies$ $\lnot$s) |
|
||||
|---|---|---|------------------------|
|
||||
| T | T | F | F |
|
||||
| T | F | F | F |
|
||||
| F | T | T | T |
|
||||
| F | F | T | T |
|
||||
|
||||
**Slide 5: p $\vdash$ q**
|
||||
|
||||
- Notation: p $\vdash$ q means q is provable from p using inference rules.
|
||||
- Example:
|
||||
- A $\implies$ B, $\lnot$A, therefore $\lnot$B
|
||||
|
||||
**Slide 6: Differences Between |-|=- and $\vdash$**
|
||||
|
||||
- |= indicates semantic entailment (truth conditions).
|
||||
- $\vdash$ represents syntactic derivation (inference rules).
|
||||
|
||||
**Slide 7: Recap on Inference Rules**
|
||||
|
||||
- Example inference rules:
|
||||
- Modus Ponens ($\implies$Elim):
|
||||
|
||||
p $\implies$ q, p $\vdash$ q
|
||||
|
||||
- Conjunction Introduction ($\land$Intro):
|
||||
|
||||
p $\vdash$ q, p $\vdash$ r $\vdash$ p $\land$ q
|
||||
|
||||
- Conditional Proof ($\implies$Intro):
|
||||
|
||||
p $\vdash$ r, p $\vdash$ s $\vdash$ p $\implies$ (r $\land$ s)
|
||||
|
||||
**Slide 8: Layout of an Inference Rule**
|
||||
|
||||
- Premises above the line, conclusion below the line.
|
||||
- Example inference rule ($\implies$Intro):
|
||||
|
||||
p $\vdash$ r, p $\vdash$ s
|
||||
p $\implies$ (r $\land$ s)
|
||||
|
||||
**Slide 9: Presentation of Proofs**
|
||||
|
||||
- Steps:
|
||||
- Number each step.
|
||||
- Justify each step with previous line(s) and inference rule used.
|
||||
|
||||
**Slide 10: Deriving $\lnot$p $\implies$ r From (p $\land$ q) $\lor$ r**
|
||||
|
||||
- Example proof:
|
||||
|
||||
(p $\land$ q) $\lor$ r, $\lnot$E
|
||||
…
|
||||
$\lnot$p $\implies$ r
|
||||
|
||||
**Slide 11: Two Special Inference Rules**
|
||||
|
||||
- Deductive Theorem ($\implies$Intro):
|
||||
|
||||
p $\vdash$ r, p $\vdash$ s
|
||||
p $\implies$ (r $\land$ s)
|
||||
|
||||
- Reductio ad absurdum ($\lnot$Intro):
|
||||
|
||||
p $\vdash$ r, p $\vdash$ $\lnot$s
|
||||
p $\vdash$ $\lnot$r
|
||||
|
||||
**Slide 12: Conditional Proofs**
|
||||
|
||||
- Strategy: Assume p, deduce q if possible, discharge assumption.
|
||||
- Example:
|
||||
|
||||
(p $\land$ q) $\lor$ r
|
||||
…
|
||||
$\lnot$p $\implies$ r
|
||||
|
||||
**Slide 13: Indirect Proofs**
|
||||
|
||||
- Strategy: Assume negation of goal, deduce contradiction.
|
||||
- Example:
|
||||
|
||||
(p $\land$ q) $\lor$ r
|
||||
…
|
||||
$\lnot$p $\implies$ r
|
||||
|
||||
**Slide 14: Solution to Exercise**
|
||||
|
||||
Given argument:
|
||||
A (You eat carefully) ⇒ B (You have a healthy digestive system)
|
||||
C (You exercise regularly) ⇒ D (You are very fit)
|
||||
B ∨ D ⇒ E (You live to a ripe old age)
|
||||
¬E
|
||||
Therefore, ¬A ∧ ¬C
|
||||
|
||||
**Proof:**
|
||||
|
||||
| Line | Formula | Justification |
|
||||
| ---- | --------- | -------------------- |
|
||||
| 1 | A ⇒ B | Premise |
|
||||
| 2 | C ⇒ D | Premise |
|
||||
| 3 | B ∨ D ⇒ E | Premise |
|
||||
| 4 | ¬E | Premise |
|
||||
| 5 | ¬(B ∨ D) | Modus Tollens (3, 4) |
|
||||
| 6 | ¬B ∧ ¬D | De Morgan's Law (5) |
|
||||
| 7 | ¬B | ∧Elim (6) |
|
||||
| 8 | ¬A | Modus Tollens (1, 7) |
|
||||
| 9 | ¬D | ∧Elim (6) |
|
||||
| 10 | ¬C | Modus Tollens (2, 9) |
|
||||
| 11 | ¬A ∧ ¬C | ∧Intro (8, 10) |
|
||||
|
||||
**Conclusion:**
|
||||
We have proven that ¬A ∧ ¬C, i.e., you did not eat carefully and you did not exercise regularly.
|
||||
|
||||
**Slide 15: Two Special Inference Rules (continued)**
|
||||
|
||||
- Deductive Theorem:
|
||||
|
||||
p $\vdash$ r, p $\vdash$ s
|
||||
p $\implies$ (r $\land$ s)
|
||||
|
||||
- Reductio ad absurdum:
|
||||
|
||||
p $\vdash$ r, p $\vdash$ $\lnot$s
|
||||
p $\vdash$ $\lnot$r
|
||||
|
||||
**Slide 16: Soundness and Completeness**
|
||||
|
||||
- Sound: Valid argument with true premises.
|
||||
- Complete: Derives any sentence entailed by premises.
|
||||
|
||||
**Slide 17: Formal Proofs of Natural Language Arguments**
|
||||
|
||||
- Steps:
|
||||
- Identify atomic propositions.
|
||||
- Formalize argument in logic.
|
||||
- Check for invalidity.
|
||||
- Attempt proof.
|
||||
|
||||
**Slide 18: Example - Travel**
|
||||
|
||||
- Argument:
|
||||
|
||||
…
|
||||
Therefore, if my neighbours claim to be impressed then they are just pretending.
|
||||
|
||||
**Slide 19: Example - Travel (continued)**
|
||||
|
||||
- Formalize argument:
|
||||
|
||||
p $\implies$ q, $\lnot$p $\implies$ $\lnot$r, $\lnot$q
|
||||
…
|
||||
$\lnot$r
|
||||
|
||||
- Proof:
|
||||
|
||||
…
|
||||
$\lnot$p $\implies$ r
|
||||
|
||||
**Slide 20: Example - Nutrition**
|
||||
|
||||
- Argument:
|
||||
|
||||
…
|
||||
Therefore, you did not eat carefully and you did not exercise regularly.
|
||||
|
||||
**Slide 21: Example - Nutrition (continued)**
|
||||
|
||||
- Formalize argument:
|
||||
A $\implies$ B, C $\implies$ D, B $\lor$ D $\implies$ E, $\lnot$E
|
||||
…
|
||||
$\lnot$A $\land$ $\lnot$C
|
||||
- Proof:
|
||||
…
|
||||
$\lnot$A $\land$ $\lnot$C
|
||||
|
||||
**Slide 22: Application to Software Engineering**
|
||||
|
||||
- Questions about software specifications and claims are arguments.
|
||||
|
||||
**Slide 23: Reading and References**
|
||||
|
||||
- Russell and Norvig, Artificial Intelligence (4th Edition)
|
||||
- Nissanke, Introductory Logic and Sets for Computer Scientists
|
||||
- Gray, Logic, Algebra and Databases
|
||||
BIN
AI & Data Mining/Week 23/test.pdf
Executable file
BIN
AI & Data Mining/Week 23/test.pdf
Executable file
Binary file not shown.
@@ -0,0 +1,18 @@
|
||||
1. Just the following propositions hold true:
|
||||
1. male(Ahmed) male(Patel) male(Scott) tall(Ahmed) tall(Patel) short(Khan) short(Scott)
|
||||
Evaluate the truth of the following formula
|
||||
|
||||
| x | tall(x) | male(x) | short(x) | $\lnot$short(x) | male(x) $\land \lnot$short(x) | tall(x) $\iff$ male(x) $\land \lnot$short(x) | $\forall x \bullet$tall(x) $\iff$ male(x) $\land \lnot$short(x) |
|
||||
| --- | ------- | ------- | -------- | --------------- | ----------------------------- | -------------------------------------------- | --------------------------------------------------------------- |
|
||||
| Ah | T | T | F | T | T | T | |
|
||||
| Kh | F | F | T | F | F | T | |
|
||||
| Pa | T | T | F | T | T | T | |
|
||||
| Sc | F | T | T | F | F | T | |
|
||||
| | | | | | | | T |
|
||||
2. Using appropriate binary predicates, express each of the following sentences in predicate logic
|
||||
a) Salford stores only supply stores outside of Salford.
|
||||
- $\forall x \bullet \forall y \bullet \textsf{in(x, Salford)} \land \textsf{supples}$
|
||||
b) No store supplies itself
|
||||
c) There are no stores in Eccles but there are some in Trafford.
|
||||
d) Stores do not supply stores that are supplied by stores which they supply
|
||||
e) Stores which supply each other are always in the same place
|
||||
@@ -0,0 +1,171 @@
|
||||
**Slide 1: Learning Objectives**
|
||||
|
||||
- Understand when the order of quantifiers is important.
|
||||
- Understand how ∀ and ∃ are connected.
|
||||
- Use and remember scoping rules.
|
||||
- Identify bound and free variables in formulae.
|
||||
- Establish the truth of formulae in predicate logic.
|
||||
- Understand why predicate logic is described as undecidable.
|
||||
- Understand the difference between zero-order, first-order, and higher-order predicate logics.
|
||||
|
||||
**Slide 2: Objectives & Recap**
|
||||
|
||||
- Quantifiers and their alternative view.
|
||||
- Distributive laws of quantifiers.
|
||||
- De Morgan's laws with quantifiers.
|
||||
- Scope of quantifiers.
|
||||
- Bound and free variables.
|
||||
|
||||
**Slide 3: The Universal Quantifier (∀)**
|
||||
|
||||
- Pronounced as "for all".
|
||||
- Example: ∀x (human(x) ⇒ mortal(x)) = All humans are mortal.
|
||||
- In terms of conjunction: ∀x p(x) ≡ p(x₁) ∧ p(x₂) ∧... ∧ p(xₙ)
|
||||
|
||||
**Slide 4: The Existential Quantifier (∃)**
|
||||
|
||||
- Pronounced as "there exists" or "for some".
|
||||
- Example: ∃x (human(x) ∧ happy(x)) = Some humans are happy.
|
||||
- In terms of disjunction: ∃x p(x) ≡ p(x₁) ∨ p(x₂) ∨... ∨ p(xₙ)
|
||||
|
||||
**Slide 5: Distributive Laws of Quantifiers**
|
||||
|
||||
- ∀x (p(x) ∧ q(x)) ≡ (∀x p(x)) ∧ (∀x q(x))
|
||||
- ∃x (p(x) ∨ q(x)) ≡ (∃x p(x)) ∨ (∃x q(x))
|
||||
|
||||
**Slide 6: The Order of Quantification**
|
||||
|
||||
- Example 1 (Everyone loves someone): ∀x ∃y loves(x, y)
|
||||
- Example 2 (There is someone loved by everyone): ∃y ∀x loves(x, y)
|
||||
|
||||
**Slide 7: De Morgan's Laws and Quantifiers**
|
||||
|
||||
- ¬∃x p(x) ≡ ∀x ¬p(x)
|
||||
- ¬∀x p(x) ≡ ∃x ¬p(x)
|
||||
|
||||
**Slide 8: Scope of Quantifiers**
|
||||
|
||||
- In absence of brackets, scope extends to the end of the formula.
|
||||
- Brackets can enforce different scoping patterns.
|
||||
|
||||
**Slide 9: Bound and Free Variables**
|
||||
|
||||
- Bound variable: occurrence introduced by a quantifier within its scope.
|
||||
- Example:
|
||||
```
|
||||
Formula Variable status
|
||||
child(x) Only one occurrence of x, free.
|
||||
∀x child(x) ∧ clever(x) Both occurrences of x are bound by the same quantifier.
|
||||
((∀x child(x)) ∧ clever(x)) The first occurrence of x is bound, the second is free.
|
||||
```
|
||||
- Free variable: occurrence not within any quantifier's scope.
|
||||
|
||||
**Slide 10: Meaning of Bound Variables**
|
||||
|
||||
- The meaning of a bound variable does not depend on its name.
|
||||
- Example:
|
||||
```
|
||||
∀x (child(x) ∧ clever(x)) ⇒ ∃y loves(y, x)
|
||||
∀B (child(B) ∧ clever(B)) ⇒ ∃C loves(C, B)
|
||||
```
|
||||
|
||||
**Slide 11: Meaning of Free Variables**
|
||||
|
||||
- Free variables denote unknowns or unspecified objects.
|
||||
- Example:
|
||||
```
|
||||
∀x (child(x) ∧ clever(x)) ⇒ x is loved.
|
||||
∀x (child(x) ∧ clever(x)) ⇒ z is loved.
|
||||
```
|
||||
|
||||
**Slide 12: Exercise**
|
||||
|
||||
- Identify bound and free variables in the formula:
|
||||
```
|
||||
∃x taller(y, x) ∃x ∃y taller(x, y) ∧ taller(x, z)
|
||||
```
|
||||
- Solution:
|
||||
- In the first formula: x is bound, y is free.
|
||||
- In the second formula: y is bound by ∃y, z is free. Both occurrences of x are bound and refer to the same variable.
|
||||
|
||||
**Slide 13: The Equality Symbol (=)**
|
||||
|
||||
- ⊢ Richard has at least two brothers:
|
||||
```
|
||||
∃x ∃y (brother(x, richard) ∧ brother(y, richard) ∧ ¬(x = y))
|
||||
```
|
||||
- Definition of sibling using parent:
|
||||
```
|
||||
∀x ∀y sibling(x, y) ≡ (¬(x = y) ∧ ∃m ∃f ¬(m = f) ∧ parent(m, x) ∧ parent(f, x) ∧ parent(m, y) ∧ parent(f, y))
|
||||
```
|
||||
|
||||
**Slide 14: Establishing the Truth Values of Formulae**
|
||||
|
||||
- Example (slide 21 and 22):
|
||||
- Individuals: Ahmed, Khan, Patel, Scott.
|
||||
- Properties: male, tall, short.
|
||||
- Formula: ∀x (male(x) ⇒ tall(x) ∨ short(x))
|
||||
- Truth table shows the formula is false (Patel is male but not tall or short).
|
||||
|
||||
**Slide 15: Exercise**
|
||||
|
||||
- Given individuals, properties, and true propositions as in slide 23.
|
||||
- Evaluate the truth of: ∀x ¬male(x) ⇒ short(x)
|
||||
- Solution (slide 24):
|
||||
```
|
||||
x male(x) ¬male(x) short(x) ¬male(x) ⇒ short(x)
|
||||
Ahmed T F F F T
|
||||
Khan F T T T T
|
||||
Patel T F F F T
|
||||
Scott T F T F F
|
||||
```
|
||||
- The formula is false (Patel is male but not short).
|
||||
|
||||
**Slide 16: Example Involving ∃**
|
||||
|
||||
- Given individuals, properties, and true propositions as in slide 25.
|
||||
- Formula: ∃x (male(x) ∧ ¬tall(x) ⇒ short(x))
|
||||
- Truth table (slide 26):
|
||||
```
|
||||
x male(x) ¬tall(x) short(x) ¬tall(x) ⇒ short(x) male(x) ∧ ¬tall(x) ⇒ short(x)
|
||||
Ahmed T F F F T T
|
||||
Khan F F T F F F
|
||||
Patel T F F F F F
|
||||
Scott T T T F T F
|
||||
```
|
||||
- The formula is true (Scott is male, not tall but short).
|
||||
|
||||
**Slide 17: Exercise**
|
||||
|
||||
- Given individuals, properties, and true propositions as in slide 27.
|
||||
- Evaluate the truth of: ∃x (male(x) ∧ (tall(x) ∨ ¬short(x)))
|
||||
- Solution (slide 28):
|
||||
```
|
||||
x male(x) tall(x) short(x) ¬short(x) tall(x) ∨ ¬short(x) male(x) ∧ (tall(x) ∨ ¬short(x))
|
||||
Ahmed T T F T T T T
|
||||
Khan F F T F F F F
|
||||
Patel T T F F T T F
|
||||
Scott T F T F F F F
|
||||
```
|
||||
- The formula is true (Ahmed and Patel are males, tall or not short).
|
||||
|
||||
**Slide 29: Predicate Logic is Undecidable**
|
||||
|
||||
- Universal quantification introduces computational impossibility when testing truth values with an infinite number of possible values.
|
||||
|
||||
**Slide 30: First-order Predicate Logic**
|
||||
|
||||
- Quantifiers refer only to objects (constants), not predicate or function names.
|
||||
- Propositional logic is zero-order logic.
|
||||
|
||||
**Slide 31: Summary**
|
||||
|
||||
- Order of quantifiers matters when both ∀ and ∃ are present.
|
||||
- Quantifiers are connected through negation, obey De Morgan's laws.
|
||||
- Scope of quantifiers extends to the end of the formula without brackets.
|
||||
- Bound variables are introduced by a quantifier within its scope; free variables are not within any quantifier's scope.
|
||||
|
||||
**Slide 32: Reading, References and Acknowledgements**
|
||||
|
||||
- Reading from Artificial Intelligence textbook by Russell and Norvig.
|
||||
- References: Introductory Logic and Sets for Computer Scientists by Nissanke.
|
||||
159
AI & Data Mining/Week 26 - Deductive Proofs.md
Normal file
159
AI & Data Mining/Week 26 - Deductive Proofs.md
Normal file
@@ -0,0 +1,159 @@
|
||||
### **Slide Notes:**
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 0: Learning Objectives**
|
||||
- Identify genuine variables and variables standing for unknowns.
|
||||
- Describe the role of inference rules for eliminating and introducing quantifiers.
|
||||
- Justify constraints on handling variables when eliminating and introducing quantifiers.
|
||||
- Conduct proofs in predicate logic.
|
||||
- Prove the validity of an argument presented in English.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 1: Contents**
|
||||
- Recap on inference rules
|
||||
- Deductive proof in predicate logic
|
||||
- Genuine variables versus unknown variables
|
||||
- Extra inference rules for predicate logic
|
||||
- Constraints on variables
|
||||
- Summary, reading and references
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 2: Recap on Inference Rules**
|
||||
| **Connective** | **Introduction Rule** | **Elimination Rule** |
|
||||
| ------------------ | --------------------------------------------------------------------- | ------------------------------------------------------------ |
|
||||
| ∧ (and) | ∧ Intro:$p, q \vdash p \land q$ | ∧ Elim:$p \land q, p \vdash q$ |
|
||||
| ∨ (or) | ∨ Intro:$p \vdash p \lor q$,$q \vdash p \lor q$ | ∨ Elim:$p \vdash \varnothing$,$p \lor q \vdash \varnothing$x |
|
||||
| ¬ (not) | N/A | ¬ Elim:$\neg p, q \vdash p$ |
|
||||
| ⇒ (implies) | ⇒ Intro:$p, p \Rightarrow q \vdash q$ | ⇒ Elim (Modus Ponens):$p \Rightarrow q, p \vdash q$ |
|
||||
| ⇔ (if and only if) | ⇔ Intro:$p \Rightarrow q, q \Rightarrow p \vdash p \leftrightarrow q$ | ⇔ Elim:$p \leftrightarrow q, p, q \vdash \varnothing$ |
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 3: Deductive Proof in Predicate Logic**
|
||||
1. Reduce formulae to propositional form by removing quantifiers.
|
||||
2. Manipulate formulae using inference rules and logical laws of propositional logic.
|
||||
3. Reintroduce quantifiers at the end, depending on the goal.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 4: Genuine Variables vs. Unknown Variables**
|
||||
- **Genuine variable**:
|
||||
- A free variable whose universal quantification yields a true formula.
|
||||
- **Unknown variable**:
|
||||
- A free variable whose existential quantification yields a true formula.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 5: Exercise**
|
||||
**Example**:
|
||||
-$\frac{9}{z} = 3$
|
||||
-$\text{even}(n) \lor \text{odd}(n)$
|
||||
|
||||
| **Variable** | **Status** | **Justification** |
|
||||
|--------------|-------------------------|-----------------------------------|
|
||||
|$z$ | Unknown variable |$\exists z \cdot \frac{9}{z} = 3$|
|
||||
|$n$ | Genuine variable |$\forall n \cdot (\text{even}(n) \lor \text{odd}(n))$|
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 6: Extra Inference Rules for Predicate Logic**
|
||||
| **Quantifier** | **Introduction Rule** | **Elimination Rule** |
|
||||
|-----------------|----------------------------------------|---------------------------------------------------|
|
||||
|$\forall$(for all) |$\forall \text{Intro}: \varphi(x), x \neq y \vdash \varphi(x)$|$\forall \text{Elim}: \forall x \cdot \varphi(x), \varphi(x) \vdash \varnothing$|
|
||||
|$\exists$(there exists) |$\exists \text{Intro}: \varphi(x), x \neq y \vdash \exists x \cdot \varphi(x)$|$\exists \text{Elim}: \exists x \cdot \varphi(x), \varphi(x) \vdash \varnothing$|
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 7: Freeing Variables from$\forall$**
|
||||
- Example:
|
||||
-$\forall x \cdot \text{lecturer}(x), \text{lecturer}(bryant)$
|
||||
-$\forall x \cdot \text{lecturer}(x), \text{lecturer}(y)$
|
||||
-$y$is a genuine variable.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 8: Freeing Variables from$\exists$**
|
||||
- Example:
|
||||
-$\exists x \cdot \text{student}(x), \text{student}(y)$
|
||||
-$y$is an unknown variable.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 9: Introduction of$\forall$**
|
||||
- Constraint:
|
||||
- Do not introduce$\forall$on the basis of an individual (a constant).
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 10: Constraint 1**
|
||||
- When eliminating$\exists$, do not instantiate its variable with a constant.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 11: Constraint 2**
|
||||
- When eliminating$\exists$, do not instantiate its variable with an existing free variable.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 12: Constraint 3**
|
||||
- Do not introduce$\forall$on the basis of an individual (a constant).
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 13: Constraint 4**
|
||||
- Do not introduce$\forall$on the basis of an unknown.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 14: Constraint 5**
|
||||
- Do not quantify a variable by introducing$\forall$in a formula if the formula contains another var obtained by eliminating$\exists$.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 15: Constraint 6**
|
||||
- Within the scope of an assumption, do not introduce$\forall$on the basis of a variable appearing in the assumption.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 16: Constraint 7**
|
||||
- Every instantiation, whether following the elimination of a$\forall$or$\exists$, must always be done with a free var, rather than a bound var.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 17: Constraint 8**
|
||||
- Beware of binding any newly quantified var by an unintended quantifier.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 18: Summary**
|
||||
- Use inference rules to eliminate and introduce logical connectives.
|
||||
- Handle quantifiers carefully, following constraints when eliminating and introducing them.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 19: Summary of Constraints**
|
||||
1. Do not assume a property holds for a particular individual based on it holding for at least one individual.
|
||||
2. When eliminating$\exists$, do not instantiate its var with a constant or existing free var.
|
||||
3. Do not introduce$\forall$on the basis of a constant or unknown.
|
||||
4. Do not quantify a variable by introducing$\forall$if the formula contains another var from$\exists$elimination.
|
||||
5. Within an assumption, do not introduce$\forall$based on a var in the assumption.
|
||||
6. Instantiate variables only with free vars, not bound vars.
|
||||
7. Avoid binding newly quantified vars by unintended quantifiers.
|
||||
|
||||
---
|
||||
|
||||
#### **Slide 20: Deducing a Conclusion**
|
||||
Example:
|
||||
1.$\forall x \cdot (\text{master}(x) \lor \text{slave}(x)) \Rightarrow \text{adult}(x) \land \text{man}(x)$
|
||||
2.$\neg \forall x \cdot (\text{adult}(x) \land \text{man}(x))$
|
||||
3.$\exists x \cdot (\neg (\text{adult}(x) \land \text{man}(x)))$
|
||||
4.$\neg (\text{master}(x) \lor \text{slave}(x))$
|
||||
5.$\neg \text{master}(x) \land \neg \text{slave}(x)$
|
||||
6.$\neg \text{master}(x)$
|
||||
7.$\exists y \cdot (\neg \text{master}(y))$
|
||||
|
||||
---
|
||||
|
||||
@@ -55,13 +55,17 @@
|
||||
# Modified Probability Estimates
|
||||
|
||||
- Consider attribute *outlook* for class *yes*
|
||||
|
||||
# $\frac{2+\frac{1}{3}\mu}{9+\mu}$
|
||||
|
||||
Sunny
|
||||
|
||||
# $\frac{4+\frac{1}{3}\mu}{9+\mu}$
|
||||
|
||||
Overcast
|
||||
|
||||
# $\frac{3+\frac{1}{3}\mu}{9+\mu}$
|
||||
|
||||
Rainy
|
||||
|
||||
- Each value treated the same way
|
||||
@@ -73,13 +77,16 @@ Rainy
|
||||
## Fully Bayesian Formulation
|
||||
|
||||
# $\frac{2+\frac{1}{3}\mu p_1}{9+\mu}$
|
||||
|
||||
Sunny
|
||||
|
||||
# $\frac{4+\frac{1}{3}\mu p_2}{9+\mu}$
|
||||
|
||||
Overcast
|
||||
|
||||
# $\frac{3+\frac{1}{3}\mu p_3}{9+\mu}$
|
||||
|
||||
Rainy
|
||||
|
||||
- Where $p_1 + p_2 + p_3 = 1$
|
||||
- $p_1, p_2, p_3$ are prior probabilities of outlook being sunny, overcast or rainy before seeing the training set. However, in practice it is not clear how these prior probabilities should be assigned.
|
||||
- Where $p_1 + p_2 + p_3 = 1$
|
||||
- $p_1, p_2, p_3$ are prior probabilities of outlook being sunny, overcast or rainy before seeing the training set. However, in practice it is not clear how these prior probabilities should be assigned.
|
||||
|
||||
@@ -27,20 +27,25 @@
|
||||
| High | 2/5 | 1/9 | Red | 3/5 | 2/9 | | | | | | | | |
|
||||
|
||||
# Problem 1
|
||||
|
||||
# $Pr[Diagnosis=N|E] = \frac{2}{5} \times \frac{2}{5} \times \frac{4}{5} \times \frac{3}{5} \times \frac{5}{14} = 0.027428571$
|
||||
|
||||
# $Pr[Diagnosis = B|E] = \frac{3}{9} \times \frac{4}{9} \times \frac{3}{9} \times \frac{3}{9} \times \frac{9}{14} = 0.010582011$
|
||||
|
||||
# $p(B) = \frac{0.0106}{0.0106+0.0274} = 0.2789$
|
||||
|
||||
# $p(N) = \frac{0.0274}{0.0106+0.0274} = 0.7211$
|
||||
# $p(N) = \frac{0.0274}{0.0106+0.0274} = 0.7211$
|
||||
|
||||
Diagnosis N is much more likely than Diagnosis B
|
||||
|
||||
# Problem 2
|
||||
|
||||
# $Pr[Diagnosis = N|E] = \frac{2}{5} \times \frac{1}{5} \times \frac{3}{5} \times \frac{5}{14} = 0.0171$
|
||||
|
||||
# $Pr[Diagnosis = B|E] = \frac{3}{9} \times \frac{6}{9} \times \frac{3}{9} \times \frac{9}{14} = 0.0476$
|
||||
|
||||
# $p(N) = \frac{0.0171}{0.0171+0.0476} = 0.2643$
|
||||
|
||||
# $p(B) = \frac{0.0474}{0.0476+0.0171} = 0.7357$
|
||||
|
||||
Diagnosis B is much more likely than Diagnosis N
|
||||
@@ -48,4 +53,5 @@ Diagnosis B is much more likely than Diagnosis N
|
||||
# Problem 3
|
||||
|
||||
# $Pr[Diagnosis = N|E] = \frac{0}{5} \times \frac{2}{5} \times \frac{4}{5} \times \frac{3}{5} \times \frac{5}{14} = 0$
|
||||
|
||||
# $Pr[Diagnosis = B|E] = \frac{5}{9} \times \frac{4}{9} \times \frac{3}{9} \times \frac{3}{9} \times \frac{9}{14} = 0.018$
|
||||
|
||||
@@ -274,4 +274,4 @@ Root mean squared error 0.3223
|
||||
Relative absolute error 70.1487 %
|
||||
Root relative squared error 68.0965 %
|
||||
Total Number of Instances 3
|
||||
```
|
||||
```
|
||||
|
||||
@@ -12,6 +12,7 @@
|
||||
# $a_i = \frac{v_i - minv_i}{maxv_i - minv_i}$
|
||||
|
||||
Where:
|
||||
|
||||
- $a_i$ is normalised value for attribute $i$
|
||||
- $v_i$ is the current value for attribute $i$
|
||||
- $maxv_i$ is largest value of attribute $i$
|
||||
@@ -19,8 +20,10 @@ Where:
|
||||
|
||||
## Example
|
||||
|
||||
# $maxv_{humidity} = 96$
|
||||
# $maxv_{humidity} = 96$
|
||||
|
||||
# $minv_{humidity} = 65$
|
||||
|
||||
# $v_{humidity} = 80.5$
|
||||
|
||||
# $a_i = \frac{80.5-65}{96-55} = \frac{15.5}{31} = 0.5$
|
||||
@@ -28,8 +31,11 @@ Where:
|
||||
## Example (Transport Dataset)
|
||||
|
||||
# $maxv_{doors} = 5$
|
||||
|
||||
# $minv_{doors} = 2$
|
||||
|
||||
# $v_{doors} = 3$
|
||||
|
||||
# $a_i = \frac{3-2}{5-2} = \frac{1}{3}$
|
||||
|
||||
# Nearest Neighbor Applied (Transport Dataset)
|
||||
@@ -39,14 +45,18 @@ Where:
|
||||
- Right most column shows euclidean distances between each vehicle and new vehicle
|
||||
- New vehicle is closest to the 1st example, a taxi, NN predicts taxi
|
||||
|
||||
|
||||
# $vmin_{doors} = 2$
|
||||
|
||||
# $vmax_{doors} = 5$
|
||||
|
||||
# $vmin_{seats} = 7$
|
||||
|
||||
# $vmax_{seats} = 65$
|
||||
|
||||
# Missing Values
|
||||
|
||||
## Missing Nominal Values
|
||||
## Missing Nominal Values
|
||||
|
||||
- Assume missing feature is maximally different from any other value
|
||||
- Distance is:
|
||||
@@ -72,7 +82,7 @@ Where:
|
||||
- Number of seats of one example = 16
|
||||
- Normalised = 9/58
|
||||
- One missing
|
||||
- 1 - 9/58 = 49/58
|
||||
- 1 - 9/58 = 49/58
|
||||
|
||||
## Normalised Transport Data with Missing Values
|
||||
|
||||
@@ -85,13 +95,13 @@ Where:
|
||||
|
||||
## Euclidean Distance
|
||||
|
||||
# $\sqrt{(a_1-a_1')^2) + (a_2-a_2')^2 + ... + (a_n-a_n')^2}$
|
||||
# $\sqrt{(a_1-a_1')^2) + (a_2-a_2')^2 + … + (a_n-a_n')^2}$
|
||||
|
||||
Where $a$ and $a'$ are two examples with $n$ attributes and $a'$ is the value of attribute $i$ for $a$
|
||||
|
||||
## Manhattan Distance
|
||||
|
||||
# $|a_1-a_1'|+|a_2-a_2'|+...+|a_n-a_n'|$
|
||||
# $|a_1-a_1'|+|a_2-a_2'|+…+|a_n-a_n'|$
|
||||
|
||||
Vertical bar means absolute value
|
||||
Negative becomes positive
|
||||
@@ -109,4 +119,3 @@ Euclidean distance is generally a good compromise
|
||||
- Does not detect noise
|
||||
- Use k-NN, get k closest examples and take majority vote on solutions
|
||||
|
||||
|
||||
|
||||
@@ -1,18 +1,21 @@
|
||||
|
||||
|
||||
|
||||
## Normalisation Equation
|
||||
# $a_i = \frac{v_i - minv_i}{maxv_i - minv_i}$
|
||||
## Euclidean Distance Equation
|
||||
# $\sqrt{(a_1-a_1')^2) + (a_2-a_2')^2 + ... + (a_n-a_n')^2}$
|
||||
|
||||
# $a_i = \frac{v_i - minv_i}{maxv_i - minv_i}$
|
||||
|
||||
## Euclidean Distance Equation
|
||||
|
||||
# $\sqrt{(a_1-a_1')^2) + (a_2-a_2')^2 + … + (a_n-a_n')^2}$
|
||||
|
||||
# $vmax_{temp} = 85$
|
||||
|
||||
# $vmin_{temp} = 64$
|
||||
|
||||
# $a_{temp} = \frac{v_{temp} - 64}{21}$
|
||||
|
||||
# $vmax_{humidity} = 96$
|
||||
|
||||
# $vmin_{humidity} = 65$
|
||||
|
||||
# $a_{humidity} = \frac{v_{humidity} - 65}{31}$
|
||||
|
||||
@@ -39,4 +39,4 @@ Root mean squared error 0.3409
|
||||
Relative absolute error 90.9091 %
|
||||
Root relative squared error 90.9091 %
|
||||
Total Number of Instances 2
|
||||
```
|
||||
```
|
||||
|
||||
@@ -18,6 +18,7 @@
|
||||
## Selecting a Test
|
||||
|
||||
Goal: Maximise probability of desired class
|
||||
|
||||
- $t$ = total number of examples covered by rule
|
||||
- $p$ = number of positive examples of the class covered by rule
|
||||
- $t - p$ = number of errors made by rule
|
||||
@@ -44,7 +45,7 @@ Stop Condition: $t-p=0$
|
||||
|
||||
|
||||
|
||||
#### Modified Rule and its Coverage
|
||||
#### Modified Rule and Its Coverage
|
||||
|
||||
- Rule with best test added: If astigmatism = Yes and tear rate = Normal { then recommendation = Hard }
|
||||
|
||||
@@ -92,4 +93,4 @@ For each class C
|
||||
- Default Rule
|
||||
- If no rules cover example, prediction is the majority class (most frequent in training data)
|
||||
- Conflict Resolution Strategy
|
||||
- If more than one rule covers an example, select predicted class with highest recurrance in training data
|
||||
- If more than one rule covers an example, select predicted class with highest recurrence in training data
|
||||
|
||||
@@ -41,6 +41,7 @@ IF Income = 0-15k THEN risk = high
|
||||
| debt = high | 4/6 |
|
||||
| debt = low | 2/4 |
|
||||
| **collateral = none** | **6/6** |
|
||||
|
||||
IF Income = 0-15k AND collateral = none THEN risk = high
|
||||
|
||||
| Credit History | Debt | Collateral | Income | Risk |
|
||||
@@ -59,5 +60,3 @@ IF Income = 0-15k AND collateral = none THEN risk = high
|
||||
| credit history = unknown | 1/4 |
|
||||
| debt = high | 2/4 |
|
||||
| debt = low | 2/4 |
|
||||
|
||||
|
||||
|
||||
@@ -1,6 +1,7 @@
|
||||
# Logarithms
|
||||
|
||||
$log_2X$ used for generating decision trees
|
||||
|
||||
- Power to which we have to raise 2 to get X
|
||||
- When using, X will be probability between 0 and 1
|
||||
- log of probability is always negative
|
||||
@@ -48,19 +49,23 @@ $log_2X$ used for generating decision trees
|
||||
- Given probability distribution, info required to predict an event is the distributions entropy
|
||||
- Entropy gives the information required in bits
|
||||
|
||||
# $I(p_1,p_2,...,p_n)=-p_{1}\log_{2}p_1 -p_{2}\log_{2}p_2 ... -p_{n}\log_{2}p_n$
|
||||
Where n = number of classes, and $p_1 + p_2 + ... p_{n} = 1$
|
||||
# $I(p_1,p_2,…,p_n)=-p_{1}\log_{2}p_1 -p_{2}\log_{2}p_2 … -p_{n}\log_{2}p_n$
|
||||
|
||||
Where n = number of classes, and $p_1 + p_2 + … p_{n} = 1$
|
||||
Minus signs included since output must be positive
|
||||
|
||||
### Expected Information for Outlook
|
||||
|
||||
- Outlook = Sunny
|
||||
|
||||
# $info([2,3]) = I(\frac{2}{5},\frac{3}{5}) = -\frac{2}{5}\log_2(\frac{2}{5}) - \frac{3}{5}\log_2(\frac{3}{5}) = 0.971 bits$
|
||||
|
||||
- Outlook = Overcast
|
||||
|
||||
# $info([4,0]) = I(\frac{4}{4},\frac{0}{4}) = -1\log_2(1) -0\log_2(0) = 0 bits$
|
||||
|
||||
- Outlook = Rainy
|
||||
|
||||
# $info([3,2]) = I(\frac{3}{5},\frac{2}{5}) = -\frac{3}{5}\log_2(\frac{3}{5}) - \frac{2}{5}\log_2(\frac{2}{5}) = 0.693 bits$
|
||||
|
||||
### Computing Information Gain
|
||||
|
||||
@@ -1,2 +1 @@
|
||||
|
||||
|
||||
|
||||
@@ -0,0 +1 @@
|
||||
|
||||
|
||||
@@ -1,21 +1,21 @@
|
||||
1)
|
||||
a) Binomial Distribution
|
||||
b) Measures dispersion of probabilities with respect to a mean average value. Each possible value of S from 0 to N, the probability of observing S correct predictions given a sample of N independent examples of true accuracy P
|
||||
|
||||
2)
|
||||
a) (150 + 180 + 420) / (150 + 180 + 420 + 30 + 50 + 50 + 40 + 50 + 30) = 0.75
|
||||
|
||||
# Variance of S $\sigma^2_S = N_p(1-p)$
|
||||
# Variance of S $\sigma^2_S = N_p(1-p)$
|
||||
|
||||
# Std Dev of S $\sigma_S = \sqrt{N_p(1-p)}$
|
||||
|
||||
# Variance in F $\sigma_f = \frac{\sigma_S}{N} = \sqrt{\frac{N_p(1-p)}{N^2}} = \sqrt{\frac{p(1-p)}{N}}$
|
||||
|
||||
# Estimate of Predictive Accuracy $\mu_f = \frac{S}{N}$
|
||||
|
||||
# Successful Trials $S$
|
||||
|
||||
# Number of Trials $N$
|
||||
|
||||
|
||||
750 Successes 1000 Trials
|
||||
S = 750
|
||||
S = 750
|
||||
N = 1000
|
||||
$\mu_f$ = 0.75
|
||||
$\sqrt{(0.75 \times 0.25)/1000} = 0.0137$
|
||||
@@ -25,9 +25,7 @@ $\mu_f \pm z \times \sigma_f = 0.75 \pm (1.28 \times 0.0137)$
|
||||
$= 0.75 \pm 0.0175$
|
||||
|
||||
p lies between 73.25% and 76.75%, with 80% confidence.
|
||||
|
||||
3)
|
||||
a)
|
||||
Stratified Holdout, data split to guarantee same distribution of class values in training and test set
|
||||
b)
|
||||
Repeated Holdout, training and testing done several times with different splits. Overall estimate of predictive accuracy is average of predicted accuracy in different iteration
|
||||
Repeated Holdout, training and testing done several times with different splits. Overall estimate of predictive accuracy is average of predicted accuracy in different iteration
|
||||
|
||||
@@ -1,20 +1,23 @@
|
||||
# Questions
|
||||
A bit of confusion in our store which we haven't been able to find out is the Code S in the training, we are unsure where that would go or if it is even still used.
|
||||
|
||||
A bit of confusion in our store which we haven't been able to find out is the Code S in the training, we are unsure where that would go or if it is even still used.
|
||||
|
||||
- Purposefully write information wrong, call agent "Code S referral"
|
||||
Churn option, loyalty bonus not clear, should say for leaving customers only.
|
||||
Churn option, loyalty bonus not clear, should say for leaving customers only.
|
||||
- Discretion, case by case.
|
||||
Should have in-store device guides
|
||||
Where can we feed-back suggestions
|
||||
Where can we feed-back suggestions
|
||||
- (Area Manager, or Manager)
|
||||
If existing customer, can we use banking app for card information
|
||||
|
||||
|
||||
Human Connection
|
||||
|
||||
- Treat how wanted to be treated
|
||||
- Try hard for customers
|
||||
- Be yourself (already do)
|
||||
|
||||
Why Tesco Mobile?
|
||||
|
||||
- People come to Tesco Mobile for our reliability, competitive deals and information we can give, but they stay for our consistent customer service and lack of hassle
|
||||
- 1 in 100k official ofcom complaints
|
||||
- EU roaming
|
||||
@@ -24,6 +27,7 @@ Why Tesco Mobile?
|
||||
- Convenience, people come with their shopping
|
||||
|
||||
Why
|
||||
|
||||
- Long standing MVMO (2003)
|
||||
- 5m customers
|
||||
- Clubcard prices
|
||||
@@ -39,10 +43,12 @@ Love
|
||||
- anytime upgrade
|
||||
|
||||
*********
|
||||
|
||||
Every upgrade, TM app.
|
||||
Start pushing for 4G upgrades
|
||||
Home insurance, show the excess compared to protect. Claim = higher insurance
|
||||
Log notes as much as possible on carehub, open cases and close for everything less than inquiry
|
||||
|
||||
****
|
||||
|
||||
Excellent; Trustpilot
|
||||
@@ -52,8 +58,11 @@ Network of the year, best customer service; Uswitch (3rd year)
|
||||
# Consistency
|
||||
|
||||
Everyday, dedication, simple stuff.
|
||||
|
||||
## Pillars
|
||||
|
||||
### Customer Ready <<<<
|
||||
|
||||
- Not distracted, someone available in our shops all the time, unless impossible
|
||||
- Not on phones all the time, browsing on computers, etc
|
||||
- If cleaning for example, be ready to drop it quickly to serve a customer
|
||||
@@ -64,7 +73,9 @@ Everyday, dedication, simple stuff.
|
||||
- Stand up
|
||||
- Understand the Customer's needs
|
||||
- Engagement
|
||||
|
||||
### Safe and Legal
|
||||
|
||||
- Ensuring protection of PII
|
||||
- CLEANING MODE? Quantum Stores!
|
||||
- Must Informs
|
||||
@@ -72,13 +83,17 @@ Everyday, dedication, simple stuff.
|
||||
- mpro
|
||||
- Fraud
|
||||
- Panic Alarms
|
||||
|
||||
### Fit for Trade
|
||||
|
||||
- Professional
|
||||
- POS > WGLL
|
||||
- Standards
|
||||
- Clean, Tidy
|
||||
- Accessories and SIMs
|
||||
|
||||
### Walk out Happy
|
||||
|
||||
- Teaching rather than doing
|
||||
- SmartSwitch > Public WiFi unsafe, banking.
|
||||
- TM App
|
||||
@@ -86,4 +101,3 @@ Everyday, dedication, simple stuff.
|
||||
- App Activations
|
||||
- More time with all customers
|
||||
- Reduce unnecessary contact and visits
|
||||
|
||||
|
||||
@@ -1,10 +1,13 @@
|
||||
# Questions to ask people
|
||||
# Questions to Ask People
|
||||
|
||||
- Trade / Business Account?
|
||||
- Colleague?
|
||||
- Prioritise person over phone, dont ask "what phone do you have" as first question.
|
||||
|
||||
# Tesco Families
|
||||
|
||||
Roshni - Single, Cohabitance, Work, Middle (Class)
|
||||
|
||||
- Social schedule 10 activities per week, social
|
||||
- Health wellness
|
||||
- Phone 24/7
|
||||
@@ -37,6 +40,7 @@ Dawn - Rich retired, working adults
|
||||
- Pleasure in top quality, pays the best for gadgets.
|
||||
|
||||
# Understanding Customers
|
||||
|
||||
- Who are our customers
|
||||
- Family composition
|
||||
- Buying on behalf of someone else?
|
||||
@@ -53,6 +57,7 @@ Dawn - Rich retired, working adults
|
||||
- Researcher
|
||||
|
||||
# Consistent Conversations
|
||||
|
||||
1. Genuine and Transparent
|
||||
2. Listen Actively and Empathetic
|
||||
3. Focus on building relationships
|
||||
@@ -64,6 +69,7 @@ Dawn - Rich retired, working adults
|
||||
4. Provide Value and Solve Problems
|
||||
|
||||
# Pre-Welcome
|
||||
|
||||
Looking around, eye contact
|
||||
Looking at phones rather than colleagues
|
||||
On their phones outside the shop
|
||||
@@ -79,7 +85,7 @@ Engagement
|
||||
Warm Welcome
|
||||
Understand Needs
|
||||
|
||||
# What you See
|
||||
# What You See
|
||||
|
||||
Clothing
|
||||
Uniform
|
||||
@@ -88,7 +94,7 @@ Sports Watch
|
||||
Shopping Basket
|
||||
Family
|
||||
|
||||
# What you hear
|
||||
# What You Hear
|
||||
|
||||
Most needed apps
|
||||
Hobbies
|
||||
@@ -99,4 +105,4 @@ Pets
|
||||
|
||||
# Network Switch-Off
|
||||
|
||||
Get people on new 4G handsets, 2G unreliable to recommend.
|
||||
Get people on new 4G handsets, 2G unreliable to recommend.
|
||||
|
||||
@@ -93,6 +93,7 @@ Want to think about it - Urgency, deal only on for x days.
|
||||
- Device Helps
|
||||
- WebChat & Customer Care
|
||||
- SMS Support
|
||||
|
||||
## Set up Customers
|
||||
|
||||
Turn on WiFi calling & VoLTE
|
||||
@@ -126,10 +127,11 @@ Factory reset customer's phone.
|
||||
|
||||
# Returning Customers
|
||||
|
||||
Sales IS more important than service. Service will bring people through the door, but 50 served with 0 sales < 5 served with 5 sales.
|
||||
Sales IS more important than service. Service will bring people through the door, but 50 served with 0 sales < 5 served with 5 sales.
|
||||
Mediocre / Good NPS in exchange for more sales is unfortunately a good thing.
|
||||
|
||||
Why do customers return to your store?
|
||||
|
||||
- CCP, satisfied with pricing.
|
||||
- Communications sent to them.
|
||||
- Happy with customer service.
|
||||
@@ -137,5 +139,6 @@ Why do customers return to your store?
|
||||
- Physical stores, can see phones and reps.
|
||||
- Consistent colleagues, customer knows what they're going to get.
|
||||
|
||||
# Growth vs Fixed Mindset
|
||||
|
||||
# Growth Vs Fixed Mindset
|
||||
|
||||
|
||||
|
||||
93
Career Development/Assessment 2 Diary.md
Normal file
93
Career Development/Assessment 2 Diary.md
Normal file
@@ -0,0 +1,93 @@
|
||||
### Lecture 1 - Overview and Basic Skills
|
||||
|
||||
The lecture focused on the importance of soft skills in career development, exploring communication, problem-solving, and time management with the goal of equipping us with knowledge to enhance our employability and prepare for professional environments.
|
||||
|
||||
The most relevant aspect of the lecture to me was the emphasis on soft skills like interpersonal communication and adaptability, along with my ability to reflect on performance. For example, I struggle with time management and self-organisation during note taking and assignments. While I feel I excel in problem solving, I need to work on my communication, priorities, and self-reflection. I plan to implement notetaking and organisation tools, such as Obsidian and a calendar, to improve my time management. Additionally, I will inherently be practicing reflective writing to gain better understanding of my progress as I learn.
|
||||
|
||||
### Lecture 2 - CVs and Placements
|
||||
|
||||
The lecture focused on creating effective CVs, writing covering letters, and preparing for interviews with the goal of helping us present ourselves professionally, increasing our chances of placements. The CV section stood out to me the most; how CVs are not lists of qualifications, but a tool to give good impressions, helping employers see how my skills meet their needs. One area I need to work on is emphasising achievements, not just duties. For example, knowing certain languages and having relevant experience - these are selling points, however by incorporating metrics alongside actions, will make my CV more impactful. Additionally, I liked the emphasis on proofreading and clarity; I regularly overlook key requirements in briefs and skip important points. Implementing checklists for proofreading and checking grammar with tools will help improve the professionalism of my CV.
|
||||
|
||||
### Lecture 3 - Skills Audit
|
||||
|
||||
The lecture focused on understanding the importance of both soft and hard skills for computer science students, with the goal of identifying current skills, recognising gaps, and outlining actions to enhance employability. From this, I recognise my communication and interpersonal skills lack development, requiring me to rely on my problem solving, given my computer science background. For this reason, I am actively seeking out employment that will fall outside of my comfort zone to bridge this skill gap. This will force me to be more adaptable and versatile, developing skills I lack. Additionally, I plan to utilise the STAR technique to convey my skills more effectively in both technical and non-technical situations by reflecting on past experiences, such as assignment feedback - Hack Camp will be perfect for this. I also understand my existing skills, such as problem-solving and technical analysis, can always improve, so I have just subscribed to TryHackMe to address skill gaps in my learning.
|
||||
|
||||
### Lecture 4 - Personal Branding
|
||||
The lecture focused on personal branding and its importance professionally, along with creating a personal brand with the goal of improving self-awareness, naming strengths and values, and learning how to effectively present myself.
|
||||
What I found most interesting is how this involves presenting myself how others see me, not how I see myself, to stand out and create a lasting impression. One area I need to work on is consistency of applying my personal values to my professional brand, I value integrity and authenticity, but values are useless if I am inconsistent. The idea of archetypes was also interesting, I identify with multiple but see myself as a reluctant leader, never enjoying it but being the person in the room to take charge due to not liking chaos. I plan to develop a personal brand that is authentic yet impactful using platforms like LinkedIn to connect with peers and employers.
|
||||
|
||||
### Lecture 5 - CV's, Placements & Applications
|
||||
|
||||
The lecture provided understanding of the recruitment process for placements, how to apply effectively and where to find opportunities, with the goal of finding proper roles, and developing a successful application.
|
||||
What stood out to me was the competitiveness of placements - to start early, using multiple platforms to secure a useful opportunity. I also realised that my current CV should be more targeted, specifying technical skills, metrics, and achievements dependent on roles, to ensure my CV aligns with job descriptions and specifications. I will register on platforms like Gradcracker and Handshake, to access relevant opportunities and reduce the time spent on less suitable roles. Additionally, psychometric tests and interview preparation tools are something I need to prioritise since I often neglect practice for self-assessment; working on this improves my self-awareness and shows initiative. I plan to start by finding roles that align with my interests and skills and tailor my CV accordingly.
|
||||
|
||||
### Lecture 6 - Peak Performance
|
||||
|
||||
The lecture focused on achieving 'peak performance' and setting goals, emphasising mindset and self-awareness in personal development, with the goal of identifying limiting beliefs, setting achievable targets, and overcoming challenges.
|
||||
The idea of possibility thinking interested me, since I realised that my mindset often limits my potential, believing that I am not good enough to achieve. By recognising that I can improve and assessing my ability, I can consider the opportunities that may present themselves. I aim to apply for soft skill focused jobs before the end of the month to develop my weaker skills to become more confident in myself. Additionally, acknowledging opportunities is essential, by applying the 4As (Acknowledge, Analyse, Assimilate, Apply), I can turn these opportunities into actionable steps. This lecture has shown me I should adopt a more positive and proactive mindset by using possibility thinking to stop negative beliefs, set clear goals, and stay consistent, this mindset shift will aid my professional development as I pursue both my education and career.
|
||||
|
||||
### Lecture 7 - Psychometric Testing
|
||||
|
||||
The lecture focused on psychometric tests, their types, purposes, and preparation, with the goal of understanding how they are used in recruitment and the common types.
|
||||
I found the different types of tests (numerical and verbal) to be quite relevant; since the tests are often used in placement applications, I should aim to improve my performance in them to prepare properly. By practicing with Graduates First, I will familiarise myself with test formats, reducing my anxiety and improving my performance under pressure. Additionally, the advice to guide practice to specific roles was valuable - numerical tests require critical thinking and accuracy, which are common skills for opportunities in computer science. Although psychometric tests can be high pressure, I have found I can be quite introspective, and by acknowledging my strengths and weaknesses well, I can address skill gaps and seek feedback. I plan to create a schedule, focus on weak points, and use available resources to build confidence and prepare for these assessments.
|
||||
|
||||
### Lecture 8 - Self Management Skills
|
||||
|
||||
The lecture focused on the importance of self-management skills in both education and professional situations. It covered skills such as planning, organisation, communication, flexibility, initiative, and resilience, to understand how these skills can contribute to growth.
|
||||
The part I found the most applicable was self-management not just being about achievement, but about how I approach my actions and learn from success and failures, due to my recent employment as a Sales Technician at a phone network provider and acting on improving my soft skills in a professional environment. I realised while I am actively working on communication and organisation, skills like adaptability and resilience be improved. For example, when I have been challenged while training at work, I struggle to adapt and lose motivation. Overall, this lecture has given me a better understanding of self-management and steps to seek growth. By focusing on these areas, I aim to become more confident, efficient, and effective in both my education and professional pursuits.
|
||||
|
||||
### Lecture 9 - Working in Industry
|
||||
|
||||
During this lecture, Warren focused on the importance of LinkedIn to network and improve professional presentation, and the use of social media. He displayed his journey in various jobs to starting a tech career later in life, stressing the value of connections and consistency on LinkedIn.
|
||||
The part about LinkedIn's role in networking stood out to me, since I’ve used it for connections, but not as effectively as suggested; active engagement (commenting on posts, sharing achievements, etc.) can attract recruiters. While I update my profile and make connections, I have never posted or interacted in this way. The focus on social media on my professional image had not occurred to me, since I use no public facing platforms; long-term, this could be harmful to my goal of presenting myself as a professional, lacking work-related posts. I will work on LinkedIn engagement, and ensure my posts add value to my image.
|
||||
|
||||
### Lecture 10 - Professional Presence - LinkedIn
|
||||
|
||||
The lecture highlighted the importance of leveraging LinkedIn for career development, networking, and building a professional brand. Most important was the need for a proactive approach to presence online, given the increasing reliance on social media for recruitment.
|
||||
The section on crafting an effective LinkedIn profile was useful, explaining the significance of a professional photo, compelling headline, and a summary that highlights skills and aspirations. Additionally, engaging consistently on LinkedIn to attract recruiters being mentioned again was relevant, considering the impact of my online presence on my professional image. The advice to avoid personal content on a professional platform reaffirming as it aligns with my want to preserve my online privacy while presenting as professional. I plan to join interesting communities on LinkedIn and engage with posts to increase my online presence.
|
||||
|
||||
### Lecture 11 - International Opportunities
|
||||
|
||||
The lecture covered international study exchanges, placements, and research opportunities at partner universities in Australia, USA, Vietnam, and others, along with funding options and application processes.
|
||||
The most interesting part was the thought of gaining new experiences from diverse cultures and new perspectives, enhancing my interpersonal skills, making me a more adaptable professional. The opportunity to learn from leading universities also aligns with my career goals, providing valuable professional networking. While I have strong problem-solving abilities, time management is an area that needs improvement. Staying organised during international placements, especially with differing time zones and cultural norms, could be challenging. I would plan to use strategies I have been working on - such as planning ahead and prioritising tasks - to manage my responsibilities more effectively. Overall, I feel this would be a valuable addition to my CV and could open doors for future career prospects in cybersecurity, where global connections are increasingly important.
|
||||
|
||||
### Lecture 12 - Emotional Intelligence
|
||||
|
||||
The lecture discussed Emotional Intelligence (EQ) and its 4 components: Self-Awareness, Self-Management, Social Awareness, and Relationship Management, highlighting the importance of understanding both my own emotions and others.
|
||||
The lecture explained how critical EQ is in every aspect of life, which I see particularly with customer interaction. The discussion of EQ's 4 components revealed weak points in my emotional intelligence, namely Self-Awareness, as I often act impulsively under pressure without considering my emotions' impact. I will aim to think and reflect before responding when stressed, working towards improving my interactions both in my current role and in my future career. I relate to the methods of managing emotions, since they are all taught in my current role, along with understanding others' emotions through body language and tone. While I am feeling more confident in my communication skills, I will aim to develop further by being more understanding and adaptive.
|
||||
|
||||
### Lecture 13 - Art of Freelancing
|
||||
|
||||
The lecture explored freelancing, covering topics such as identifying USP, understanding customer needs, marketing strategies, pricing models, and legal considerations, also addressed overcoming psychological barriers.
|
||||
Many points discussed are relevant to my current role, which has 3, 3-hour "Connecting with Customers" workshops to understand customers, set expectations, and build trusting, long-term customer relationships. The legal and financial aspects of freelancing were a bit overwhelming to me, such as tax obligations and contract management. These would be areas where I would need to improve given I consider solo freelance work; I would plan to implement time management techniques to manage tasks efficiently, which would be essential as I take on more responsibilities and see opportunities. Overall, this lecture has equipped me with tools that can be directly applied to enhance my sales performance and professional growth.
|
||||
|
||||
### Lecture 14 - Professionalism and Confidence
|
||||
|
||||
The lecture focused on professionalism and confidence in work environments, explaining how to overcome challenges during physical and remote work.
|
||||
The most valuable part to me was consistency, which has become a prominent value of mine with health, using apps like MacroFactor to build discipline in my personal life. The discussion on punctuality also stood out to me, highlighting reliability and consistency in order to build trust with employers. To elevate this, I have and will continue to use digital calendars and reminders to help me better manage my tasks and deadlines. I feel confident in my ability to handle criticism and objections, however I will improve this by using active listening and tailoring my responses. The session's focus on adaptability is particularly relevant, as sales often requires quick adjustments due to unexpected client needs.
|
||||
### Lecture 15 - Assessment Insights
|
||||
|
||||
The lecture on assessment insights showed the importance of interpersonal and communication skills our submissions, but also explaining that the same soft are important for success in the workplace.
|
||||
Emphasis was placed on these skills not being able to be solely assessed through right or wrong answers but require evaluating how well an individual can express their thoughts and ideas effectively. The information on the next assignment was relevant, stressing that it is not just about correctness but also about the quality of expression. The use of AI tools was mentioned; while AI tools can help identify grammatical errors and inconsistencies, it was made clear that AI should not generate content for students. Instead, it serves as a tool to enhance the overall quality of submissions. Common pitfalls were failing to follow the brief, and a lack of structured writing; self-reflection was encouraged, and careful review of submissions to meet brief requirements. I will focus on clear communication and self-reflection in preparation for the next assessment.
|
||||
|
||||
### Lecture 16 - Placement Insights and Career Journey
|
||||
|
||||
The presentation discussed Safaa's experience during her placement year at Dematic, a company specialising in supply-chain automation and software solutions, highlighting the software, project insights, and customer relations in the company. She also emphasised the benefits of a placement year, gaining real-world experience, learning agile skills, and developing time management under pressure.
|
||||
Safaa's experiences provided insight into the real-world application of software development, but more importantly, project management. Upon reflection, over HackCamp, I feel like project management could be a strong career choice due to to my tendency to take charge as a Scrum Master. The highlight for me was the mention of working with strict deadlines in a fast-paced environment, which is the biggest weakness of mine. Safaa's post-graduation journey, from securing a development job, to becoming a project manager, showed me the long-term benefits of gaining practical industry experience. Overall, Safaa's journey further reinforced me with the potential of a placement year for personal and professional growth.
|
||||
|
||||
### Lecture 17 - Fear and Loathing in the Tech Community
|
||||
|
||||
My personal favourite so far, I found Chris' presentation into his experience very authentic, offering insights into navigating the tech industry and discussing challenges like managing estimates and dealing with changing requirements, emphasising collaboration, continuous learning, and adaptability.
|
||||
Chris' journey through different companies highlighted the importance of flexibility and adaptability, and the balance between long-term work and taking new job offers. Standing out across every lecture so far, I enjoyed the discussion on AI tools and the concept of programming purely being problem solving, with a focus on proper use of AI tools to enhance productivity, rather than to replace programming. Chris' advice on work-life balance was particularly helpful - I am building my confidence in soft-skilled work, but my goal is to integrate my technical knowledge into my professional life, knowing that adaptability from my problem solving skills will come naturally. Overall, Chris' presentation was an engaging and reaffirming reminder the importance of continually improving myself.
|
||||
### Lecture 18 - Effective Networking
|
||||
|
||||
This lecture returned to the focus of networking and provided tips for professional and personal growth, aiming to make us reflect on the skills to build mutually beneficial relationships (whether in-person or through online platforms), understanding networking beyond formal interactions, the benefits of sharing resources, and the value of connections in career development.
|
||||
The most useful aspect was learning how to initiate conversations and build relationships, which I have gained a lot of experience with during my time in sales. These skills have and will help me establish trust and create opportunities for upselling or referrals. Additionally, the emphasis on online networking is relevant as more interactions are shifting to digital platforms.
|
||||
Reflecting on my current situation, I feel my problem-solving is refined, and my communication skills improving every day, but could work on expanding my network beyond friends and family. I plan to reinforce consistent weak-points like time management and self-reflection, and aim to improve on my networking efforts through LinkedIn.
|
||||
|
||||
### Lecture 19 - 11 P's to Success in Industry
|
||||
|
||||
The lecture focused on the concept of "The 11 P's to success in industry", aiming to help us understand how these factors contribute to professional growth and advancement in careers.
|
||||
The best takeaway for me, was how passion drives achievement; the importance of people in building relationships and teams; and the necessity of patience in relationships. These core concepts resonated particularly with my role in sales, where enthusiasm, interpersonal skills, and resilience are implied for consistency.
|
||||
I aim to improve my ability to be more patient with myself and others, since I find that my lack of patience can lead to stress. This will allow me to better my critical-thinking and relationship-building by fostering a better mindset and understanding towards others.
|
||||
Reflecting on my current work, I find that while can be adaptable, I could expand my collaboration skills; the discussion highlighted the need for passion to stay motivated, and I find the motivation of others drives me. I will aim to build a better level of trust with colleagues and peers, to improve my teamwork.
|
||||
51
Career Development/Assessment 2 Plan.md
Normal file
51
Career Development/Assessment 2 Plan.md
Normal file
@@ -0,0 +1,51 @@
|
||||
### **Plan for Final Self-Assessment Report and Weekly Reflective Diary**
|
||||
|
||||
#### **1. Final Self-Assessment Report**
|
||||
- **Step 1:** Review the soft skills mentioned in your module (e.g., communication, teamwork, adaptability, critical thinking, problem-solving).
|
||||
- **Step 2:** Identify which skills you feel comfortable claiming you possess and which ones you need to develop further.
|
||||
- **Step 3:** For each skill:
|
||||
- Assess your current level (high, medium, low).
|
||||
- Provide a personal example using the STAR method (Situation, Task, Action, Result).
|
||||
- Plan specific steps to improve (SMART goals).
|
||||
- **Step 4:** Organize your report using the structure provided:
|
||||
- Introduction
|
||||
- List of skills (5-8)
|
||||
- For each skill: assessment, reflection, example, and improvement plan.
|
||||
- Concluding remarks.
|
||||
|
||||
### **Final Self-Assessment Report Structure**
|
||||
|
||||
1. **Introduction (Approx. 100 words):**
|
||||
|
||||
- Briefly introduce the purpose of the report.
|
||||
- Mention the soft skills you will discuss (e.g., communication, teamwork, adaptability).
|
||||
- State your overall approach to self-assessment.
|
||||
2. **List of Skills (Approx. 200 words):**
|
||||
|
||||
- Choose 5-8 soft skills relevant to your context (e.g., communication, teamwork, adaptability, time management, emotional intelligence).
|
||||
- For each skill:
|
||||
- **Assessment:** Provide your current level (high, medium, low) with a brief explanation.
|
||||
- **Reflection:** Discuss your thoughts on this skill and how it applies to your life.
|
||||
- **Example:** Use the STAR method to describe a personal experience where this skill was demonstrated.
|
||||
- **Improvement Plan:** Outline specific, SMART goals to enhance this skill.
|
||||
3. **Concluding Remarks (Approx. 100 words):**
|
||||
|
||||
- Summarize your strengths and areas for development.
|
||||
- Optionally, mention any additional skills you developed beyond the initial list.
|
||||
|
||||
---
|
||||
|
||||
#### **2. Weekly Reflective Diary**
|
||||
- **Step 1:** Go through each week of your academic journey.
|
||||
- **Step 2:** For each week:
|
||||
- Describe the session or activity you attended.
|
||||
- Reflect on what it meant for you (e.g., how it impacted your soft skills).
|
||||
- Highlight the most useful part and what you learned.
|
||||
- **Step 3:** Use reflective phrases provided in your lectures to structure your thoughts.
|
||||
|
||||
---
|
||||
|
||||
### **Additional Tips**
|
||||
- **Revisit Resources:** Use the soft skills audit, personality test, and previous self-reflection reports to gather evidence.
|
||||
- **Be Honest:** Be truthful about your strengths and areas for improvement.
|
||||
- **Be Specific:** Use concrete examples and SMART goals to make your plans actionable.
|
||||
@@ -8,23 +8,23 @@
|
||||
### **2. Current Soft Skills**
|
||||
|
||||
- **2.1 Problem-Solving**
|
||||
|
||||
|
||||
- Define problem-solving as the ability to identify and resolve issues effectively.
|
||||
- **Evidence**: Discuss how building and deploying virtual machines and Docker applications often required troubleshooting issues such as configuration errors or failed deployments. Highlight specific examples of challenges you resolved.
|
||||
- **2.2 Communication**
|
||||
|
||||
|
||||
- Define communication as the ability to convey information clearly and effectively.
|
||||
- **Evidence**: Share examples from your phone shop role, such as explaining technical details to non-technical customers, resolving complaints, or ensuring customer understanding of credit and data protection policies.
|
||||
- **2.3 Time Management**
|
||||
|
||||
|
||||
- Define time management as the ability to prioritize tasks and use time effectively.
|
||||
- **Evidence**: Highlight instances where you balanced multiple responsibilities, such as meeting deployment deadlines for technical projects while managing your commitments at the phone shop.
|
||||
- **2.4 Adaptability**
|
||||
|
||||
|
||||
- Define adaptability as the ability to adjust to new challenges or environments.
|
||||
- **Evidence**: Provide examples of adapting to new tools or technologies in your technical work (e.g., learning Docker or new hosting systems) or adjusting to varied customer needs and situations in your shop role.
|
||||
- **2.5 Attention to Detail**
|
||||
|
||||
|
||||
- Define attention to detail as the ability to focus on accuracy and precision.
|
||||
- **Evidence**: Mention your success in configuring virtual machines and Docker containers without critical errors, as well as ensuring compliance with credit and data protection regulations in your phone shop role.
|
||||
|
||||
@@ -59,4 +59,4 @@
|
||||
|
||||
---
|
||||
|
||||
This structure seamlessly integrates your strengths while providing space to address growth areas and future plans.
|
||||
This structure seamlessly integrates your strengths while providing space to address growth areas and future plans.
|
||||
|
||||
BIN
Career Development/Wilkinson_George_FinalReport.docx
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Executable file
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BIN
Career Development/Wilkinson_George_WeeklyDiary.docx
Normal file
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Career Development/Wilkinson_George_WeeklyDiary.docx
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Career Development/Wilkinson_George_WeeklyDiary.pdf
Executable file
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Career Development/Wilkinson_George_WeeklyDiary.pdf
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Client Server Systems/.DS_Store
vendored
BIN
Client Server Systems/.DS_Store
vendored
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Submodule Client Server Systems/Ecobuddy updated: 8de2b7f29e...709596eea2
Submodule Client Server Systems/PHPStorm Repo updated: 2238305d65...f64a9eadbe
@@ -5,6 +5,7 @@ This study guide provides an in-depth overview of the Abstract Data Type (ADT) L
|
||||
## 1. Overview of Linear Lists
|
||||
|
||||
A linear list is a sequential collection of elements where each element can be accessed via an index. For instance, an instance of a linear list is represented as (e0, e1, e2, …, en-1), where:
|
||||
|
||||
- $e_i$ denotes the i-th element.
|
||||
- $n$ is the finite size of the list, with n >= 0.
|
||||
- $e_0$ is the first element and en-1 is the last.
|
||||
@@ -54,6 +55,7 @@ Element[0], Element[1], Element[2], ...
|
||||
### 5.1 Array-Based Implementation
|
||||
|
||||
The array-based implementation is straightforward:
|
||||
|
||||
- **Class Declaration**: Define a class for the ArrayLinearList.
|
||||
- **Data Members**: Utilize a protected array (Object[]) for storing elements and a variable to track size.
|
||||
- **Constructor Example**: Create constructors to initiate the list with a default or user-defined size.
|
||||
@@ -68,6 +70,7 @@ A linked list version of the linear list provides dynamic memory allocation, whe
|
||||
## 6. Method Implementations in ADT Linear List
|
||||
|
||||
Each method associated with the ADT Linear List is essential for its functionality:
|
||||
|
||||
- **isEmpty()**: Returns true if the size is 0.
|
||||
- **size()**: Simply returns the count of elements.
|
||||
- **get(int index)**: Requires validating the index with *checkIndex()* before accessing the array.
|
||||
|
||||
@@ -11,13 +11,12 @@ A **data structure** is defined as an arrangement or organization of data in a c
|
||||
An **abstract data type (ADT)** is a model that defines the high-level operations and characteristics of a data structure without delving into its implementation details. Before actually implementing a data structure, it is imperative to establish what operations the ADT should support. For instance, when creating a linked list ADT, one might specify operations such as:
|
||||
|
||||
- Inserting an item into the linked list.
|
||||
|
||||
|
||||
- Deleting an item from the linked list.
|
||||
|
||||
|
||||
- Searching for an item in the linked list.
|
||||
|
||||
|
||||
- Checking if the linked list is empty.
|
||||
|
||||
|
||||
This abstraction helps programmers focus on what functionalities the data structure must provide, rather than how those functionalities will be executed.
|
||||
|
||||
@@ -26,9 +25,8 @@ This abstraction helps programmers focus on what functionalities the data struct
|
||||
Two significant programming principles are reviewed: **abstraction** and **modularization**. Abstraction allows programmers to handle complex systems by focusing on high-level functionalities rather than implementation specifics, while modularization aids in breaking down a problem into manageable components.
|
||||
|
||||
1. **Abstraction:** This concept helps in reducing complexity by allowing programmers to concentrate on essential aspects and ignore unnecessary details.
|
||||
|
||||
|
||||
2. **Modularization:** By dividing problems into smaller sub-problems, programmers can tackle complex issues more efficiently.
|
||||
|
||||
|
||||
**Encapsulation** works closely with these concepts by bundling data and methods that operate on that data into a single entity, such as a class in Java, thus hiding the internal state and requiring interaction only through specified methods.
|
||||
|
||||
@@ -37,21 +35,20 @@ Two significant programming principles are reviewed: **abstraction** and **modul
|
||||
Several fundamental data structures form the backbone of programming:
|
||||
|
||||
- **Primitive Data Types:** These include Integers, Floats, Characters, and Booleans, which represent basic data values.
|
||||
|
||||
|
||||
- **Composite Data Types:** These include essential data structures such as:
|
||||
|
||||
|
||||
- **Arrays:** Collections of elements identified by indices, commonly used in mathematical contexts.
|
||||
|
||||
|
||||
- **Linked Lists:** Data elements structured as nodes, each containing information and a link to the next node.
|
||||
|
||||
|
||||
- **Stacks:** Last-in-First-out (LIFO) structures that allow insertion and deletion at one end, termed the top.
|
||||
|
||||
|
||||
- **Queues:** First-in-First-out (FIFO) structures where insertion occurs at the rear and deletion at the front.
|
||||
|
||||
|
||||
- **Trees:** Non-linear structures representing hierarchical relationships, ideal for organizing data hierarchically.
|
||||
|
||||
|
||||
- **Graphs:** These consist of nodes and edges, representing pairwise relationships among elements.
|
||||
|
||||
|
||||
## Concrete Implementations of ADTs
|
||||
|
||||
@@ -61,4 +58,4 @@ Within programming languages, data structures can act as concrete implementation
|
||||
|
||||
In software development, the foundation of a solution begins with the specification of a problem, followed by the formulation of an **algorithm**. An algorithm is a defined sequence of operations that transforms inputs into outputs, effectively addressing the problem. As programmers develop algorithms, they gain insights into which data structures may best suit their needs, leading to efficient solutions.
|
||||
|
||||
Ultimately, the understanding and application of data structures and ADTs are paramount in achieving effective software design and development, making them a cornerstone of efficient programming practices.
|
||||
Ultimately, the understanding and application of data structures and ADTs are paramount in achieving effective software design and development, making them a cornerstone of efficient programming practices.
|
||||
|
||||
@@ -1,27 +1,23 @@
|
||||
## Advantages
|
||||
|
||||
- This has the advantage of making certain actions easier to perform but at the cost of increased maintenance of the code overall.
|
||||
|
||||
- Allows traversal of nodes in both direction which is not possible in singly linked list.
|
||||
|
||||
- Can allocate or de-allocate memory easily when required during its execution.
|
||||
|
||||
- It is one of most efficient data structure to implement when traversing in both direction is required.
|
||||
## Disadvantages
|
||||
|
||||
## Disadvantages
|
||||
|
||||
- Using extra memory when compared to array and singly linked list.
|
||||
|
||||
- Slow in search as its elements are stored randomly in memory, hence elements are accessed sequentially (no direct access is allowed).
|
||||
|
||||
## ADT Liner list could be implemented by two ways:
|
||||
## ADT Liner List Could Be Implemented by Two Ways:
|
||||
|
||||
- Array
|
||||
- Used when you search is the highest priority
|
||||
|
||||
- Linked list
|
||||
- Singly linked list
|
||||
- Used when you addition/deletion is the highest priority
|
||||
|
||||
|
||||
- Doubly linked list
|
||||
- Used when you addition/deletion is the highest priority
|
||||
- Navigate next and pervious
|
||||
- Navigate next and previous
|
||||
|
||||
@@ -28,37 +28,34 @@ For example, a constructor header like `public PrintWriter(String fileName) thro
|
||||
At the core of Java's exception handling is the **Throwable** class, which serves as the superclass for all exceptions and errors. It has two key subclasses:
|
||||
|
||||
- **Error**: Indicates serious problems that a user application should not catch.
|
||||
|
||||
|
||||
- **Exception**: Represents conditions that a user application might want to catch.
|
||||
|
||||
|
||||
Within the Exception hierarchy, we find numerous subclasses such as **IOException** and **RuntimeException**, which themselves have numerous subclasses. For example:
|
||||
|
||||
- **IOException** can lead to specific exceptions like:
|
||||
|
||||
|
||||
- **FileNotFoundException**
|
||||
|
||||
|
||||
- **EOFException**
|
||||
|
||||
|
||||
- **RuntimeException** encompasses:
|
||||
|
||||
|
||||
- **ArithmeticException**
|
||||
|
||||
|
||||
- **IndexOutOfBoundsException**
|
||||
|
||||
|
||||
- **NullPointerException**
|
||||
|
||||
|
||||
- **IllegalArgumentException**
|
||||
|
||||
|
||||
## Dealing with Exceptions
|
||||
|
||||
Handling exceptions can be approached in two primary ways:
|
||||
|
||||
- **Catching the Exception**: This involves writing code to handle the exception immediately where it occurs. To achieve this, any potentially exception-generating code must reside within a **try** block, followed by one or more **catch** blocks that process the exception.
|
||||
|
||||
|
||||
- **Propagating the Exception**: Alternatively, the method can propagate the exception, allowing higher levels of the program to handle it. This is done by throwing the exception again after catching it or not catching it at all.
|
||||
|
||||
|
||||
### Catch Blocks Example
|
||||
|
||||
@@ -73,7 +70,7 @@ A fundamental aspect of handling exceptions is the use of a **try** and **catch*
|
||||
> }
|
||||
> ```
|
||||
|
||||
Here, _XXXException_ can be various types of exceptions, such as **IOException** or **RuntimeException**. When multiple types of exceptions can be thrown, several catch blocks can be utilized, ordered from the most specific to the most general. For instance:
|
||||
Here, *XXXException* can be various types of exceptions, such as **IOException** or **RuntimeException**. When multiple types of exceptions can be thrown, several catch blocks can be utilized, ordered from the most specific to the most general. For instance:
|
||||
|
||||
> ```
|
||||
> try {
|
||||
@@ -127,4 +124,4 @@ In a sample application, if the main() method adds **throws IOException**, the m
|
||||
|
||||
## Final Thoughts on Exception Handling
|
||||
|
||||
Java's exception handling framework is robust and designed to enable developers to write code that can gracefully manage unexpected problems. This system incorporates custom exceptions using the **throw** keyword, enjoyable error messages, and fine-tuned control over program flow. The use of exception handling not only aids in maintaining the reliability of applications but also provides clearer diagnostic messages for debugging. Overall, proper understanding and implementation of Java exceptions are essential for writing resilient Java applications.
|
||||
Java's exception handling framework is robust and designed to enable developers to write code that can gracefully manage unexpected problems. This system incorporates custom exceptions using the **throw** keyword, enjoyable error messages, and fine-tuned control over program flow. The use of exception handling not only aids in maintaining the reliability of applications but also provides clearer diagnostic messages for debugging. Overall, proper understanding and implementation of Java exceptions are essential for writing resilient Java applications.
|
||||
|
||||
@@ -7,9 +7,8 @@ This study material provides a concise overview of the Abstract Data Type (ADT)
|
||||
The Linear List can be implemented using different structures, including linked lists. The main focus here is on:
|
||||
|
||||
- Linear List based on LinkedList
|
||||
|
||||
|
||||
- Doubly-linked list
|
||||
|
||||
|
||||
Each of these implementations has its unique characteristics, advantages, and considerations.
|
||||
|
||||
@@ -18,13 +17,12 @@ Each of these implementations has its unique characteristics, advantages, and co
|
||||
Understanding the size of primitive types is fundamental in memory allocation:
|
||||
|
||||
- **boolean & byte** - 1 byte
|
||||
|
||||
|
||||
- **char & short** - 2 bytes
|
||||
|
||||
|
||||
- **int & float** - 4 bytes
|
||||
|
||||
|
||||
- **long & double** - 8 bytes
|
||||
|
||||
|
||||
It's important to note that, in modern 64-bit Java Virtual Machines (JVM), the minimum size of an object is 16 bytes due to the header size and padding requirements.
|
||||
|
||||
@@ -33,9 +31,8 @@ It's important to note that, in modern 64-bit Java Virtual Machines (JVM), the m
|
||||
When comparing Array Lists and Linked Lists:
|
||||
|
||||
- **Addition and Removal**: Linked Lists excel in scenarios where frequent addition and removal of elements are required due to their dynamic size and absence of resizing overhead.
|
||||
|
||||
|
||||
- **Memory Overhead**: Linked Lists consume more memory because each node contains a reference to both the next and, in doubly-linked lists, the previous node, which increases complexity and size.
|
||||
|
||||
|
||||
## Memory Allocation Concepts
|
||||
|
||||
@@ -52,48 +49,43 @@ A linked list is a collection of nodes where each node contains data and a refer
|
||||
Some common operations performed on linked lists include:
|
||||
|
||||
- **Insertion**: Nodes may be inserted at the beginning, middle, or end of the list, requiring adjustments of pointers accordingly.
|
||||
|
||||
|
||||
- **Removal**: Similar to insertion, removal requires accessing the right node and adjusting pointers to maintain list integrity.
|
||||
|
||||
|
||||
### Algorithm Visualizations
|
||||
|
||||
Visual representations can help understand operations such as inserting or deleting nodes. For example, to insert a node in a linked list, one must:
|
||||
|
||||
1. Create the new node.
|
||||
|
||||
|
||||
2. Adjust the pointers of the surrounding nodes to include the new node.
|
||||
|
||||
|
||||
## Doubly-Linked Lists
|
||||
|
||||
Doubly-linked lists add an extra pointer, allowing traversal in both forward and backward directions, enhancing flexibility:
|
||||
|
||||
- **Advantages**: They can traverse in both directions and manage dynamic memory more efficiently.
|
||||
|
||||
|
||||
- **Disadvantages**: They require more memory for pointers and tend to have slower access times due to their random memory allocation.
|
||||
|
||||
|
||||
### Inserting and Deleting in Doubly-Linked Lists
|
||||
|
||||
The process of inserting or deleting nodes involves managing the **prev** and **next** pointers to maintain the structure of the list. As illustrated:
|
||||
|
||||
1. For insertion, properly link the new node with its neighbors.
|
||||
|
||||
|
||||
2. For deletion, ensure that surrounding nodes bypass the removed node, effectively maintaining list integrity.
|
||||
|
||||
|
||||
## Key Takeaways
|
||||
|
||||
In conclusion, choosing between an array and a linked list largely depends on the intended operations:
|
||||
|
||||
- **Arrays** are optimal for scenarios where quick search operations are prioritized.
|
||||
|
||||
- **Linked Lists** are preferred for scenarios where insertion and deletion operations are frequent, with variations including:
|
||||
|
||||
- **Singly Linked List**: Best suited for simple sequential access and minimal memory overhead.
|
||||
|
||||
- **Doubly Linked List**: Ideal when navigating both forwards and backwards is necessary.
|
||||
|
||||
|
||||
Understanding these structures and their operations is essential for effective programming and data management.
|
||||
- **Linked Lists** are preferred for scenarios where insertion and deletion operations are frequent, with variations including:
|
||||
|
||||
- **Singly Linked List**: Best suited for simple sequential access and minimal memory overhead.
|
||||
|
||||
- **Doubly Linked List**: Ideal when navigating both forwards and backwards is necessary.
|
||||
|
||||
Understanding these structures and their operations is essential for effective programming and data management.
|
||||
|
||||
@@ -1,4 +1,5 @@
|
||||
## What is an interface?
|
||||
## What is an Interface?
|
||||
|
||||
- An interface is a device or a system that unrelated entities use to interact.
|
||||
- A remote control is an interface between you and a television set.
|
||||
|
||||
@@ -6,10 +7,7 @@ basically the interface has and abstract method which classes have to implement
|
||||
|
||||
Concert realisation of the otherwise abstract method.
|
||||
|
||||
|
||||
|
||||
|
||||
## What is a linked list?
|
||||
## What is a Linked List?
|
||||
|
||||
- On the linked list every node is an object.
|
||||
- Has more memory overhead than an ArrayList.
|
||||
@@ -17,6 +15,6 @@ Concert realisation of the otherwise abstract method.
|
||||
- It mainly allows efficient *insertion* and *deletion* operations compared to arrays
|
||||
- Its dynamic, the size of it changes with every change.
|
||||
|
||||
# Protected
|
||||
prevents the method to be used by anyone but its sub classes.
|
||||
# Protected
|
||||
|
||||
prevents the method to be used by anyone but its sub classes.
|
||||
|
||||
@@ -7,41 +7,38 @@ A queue is an important abstract data type (ADT) characterised by its FIFO (Firs
|
||||
## Key Concepts of Queues
|
||||
|
||||
- **Structure:** A queue consists of two primary ends:
|
||||
|
||||
- _Front:_ The position from which elements are removed.
|
||||
|
||||
- _Rear:_ The position where elements are added.
|
||||
|
||||
|
||||
- *Front:* The position from which elements are removed.
|
||||
|
||||
- *Rear:* The position where elements are added.
|
||||
|
||||
- **Core Operations:** The basic operations associated with a queue are:
|
||||
|
||||
|
||||
- **isEmpty():** Checks if the queue is empty.
|
||||
|
||||
|
||||
- **peek():** Returns the front element without removing it.
|
||||
|
||||
|
||||
- **put(x):** Adds an element x at the rear of the queue.
|
||||
|
||||
|
||||
- **remove():** Removes and returns the front element.
|
||||
|
||||
|
||||
## Queue Applications
|
||||
|
||||
Queues have various applications due to their structure, such as:
|
||||
|
||||
- CPU and disk scheduling, where resources are shared among multiple consumers.
|
||||
|
||||
|
||||
- Buffering in asynchronous data transfers like I/O operations, where data may not be received at the same rate as it is sent.
|
||||
|
||||
|
||||
- Handling jobs in a network printer which generally follows a FIFO order.
|
||||
|
||||
|
||||
## Queue Representation
|
||||
|
||||
Queues can be implemented in two ways:
|
||||
|
||||
- **Linear Array Queue:** Uses a one-dimensional array along with pointers for front and rear.
|
||||
|
||||
|
||||
- **Circular Array Queue:** Employs a circular structure to efficiently utilize array space, preventing the needs of shifting elements when the array is full.
|
||||
|
||||
|
||||
## Linear Queue Representation
|
||||
|
||||
@@ -56,20 +53,18 @@ Queue: A B C D (front = 1, rear = 4)
|
||||
A circular queue, uses the following logic:
|
||||
|
||||
- Front points 'anti-clockwise' from the first element while rear points to the last inserted element.
|
||||
|
||||
|
||||
- Utilizes the modulo operator to wrap around the indices as elements are added or removed.
|
||||
|
||||
|
||||
## Implementation of a Circular Queue
|
||||
|
||||
The implementation comprises several stages:
|
||||
|
||||
1. **Initialization:** Set front and rear to 0.
|
||||
|
||||
|
||||
2. **Insertion:** Update the rear index with a modulo operation. For example, rear=(rear+1)\%queue.length.
|
||||
|
||||
|
||||
3. **Removal:** Increment the front index to remove an element.
|
||||
|
||||
|
||||
## Challenges with Circular Queues
|
||||
|
||||
@@ -77,26 +72,25 @@ One of the critical issues with circular queues is distinguishing between a full
|
||||
|
||||
## Queue Implementation Using Array
|
||||
|
||||
The _ArrayQueue_ class illustrates array-based implementation:
|
||||
The *ArrayQueue* class illustrates array-based implementation:
|
||||
|
||||
``` java
|
||||
public class ArrayQueue implements Queue { ... }
|
||||
```
|
||||
|
||||
This class defines data members like _front_ and _rear_, along with methods for manipulating the queue.
|
||||
This class defines data members like *front* and *rear*, along with methods for manipulating the queue.
|
||||
|
||||
## Queue Methods Overview
|
||||
|
||||
Here are key methods defined in the Queue interface:
|
||||
|
||||
1. **isEmpty():** Returns true if the queue is empty.
|
||||
|
||||
|
||||
2. **peek():** Returns the front element or null if the queue is empty.
|
||||
|
||||
|
||||
3. **put(Object theObject):** Adds an element to the queue and may increase array length if the queue is full.
|
||||
|
||||
|
||||
4. **remove():** Removes the front element and updates the front pointer to the next element.
|
||||
|
||||
|
||||
## Queue Implementation Using Linked List
|
||||
|
||||
@@ -111,10 +105,9 @@ This structure provides constant time complexity for insertions and deletions, o
|
||||
## Summarizing Queue Operations
|
||||
|
||||
- **Adding Elements:** In a linked implementation, a new node is created and linked appropriately.
|
||||
|
||||
|
||||
- **Removing Elements:** The front element is removed and the front pointer is updated.
|
||||
|
||||
|
||||
## Conclusion
|
||||
|
||||
Queues are fundamental data structures in computer science with a range of applications spanning from scheduling tasks to implementing buffers. Their efficient management of elements through well-defined operations supports numerous algorithms and data handling strategies in programming.
|
||||
Queues are fundamental data structures in computer science with a range of applications spanning from scheduling tasks to implementing buffers. Their efficient management of elements through well-defined operations supports numerous algorithms and data handling strategies in programming.
|
||||
|
||||
@@ -7,4 +7,4 @@
|
||||
| The SLL occupies less memory than DLL as it has only 2 fields. | The DLL occupies more memory than SLL as it has 3 fields. |
|
||||
| Complexity of deletion with a given node is O(n), because the previous node needs to be known, and traversal takes O(n) | Complexity of deletion with a given node is O(1) because the previous node can be accessed easily |
|
||||
| A singly linked list consumes less memory as compared to the doubly linked list. | The doubly linked list consumes more memory as compared to the singly linked list. |
|
||||
| Singly linked list is relatively less used in practice due to limited number of operations | Doubly linked list is implemented more in libraries due to wider number of operations. For example [Java LinkedList](https://www.geeksforgeeks.org/linked-list-in-java/) implements Doubly Linked List. |
|
||||
| Singly linked list is relatively less used in practice due to limited number of operations | Doubly linked list is implemented more in libraries due to wider number of operations. For example [Java LinkedList](https://www.geeksforgeeks.org/linked-list-in-java/) implements Doubly Linked List. |
|
||||
|
||||
@@ -1,35 +1,30 @@
|
||||
# Overview
|
||||
|
||||
|
||||
- A stack is ta LIFO list. Meaning "last in first out"
|
||||
- Access is allowed only from one end of the stack
|
||||
- adding an item is called pulsing the stack
|
||||
- retrieving an item is called popping the stack
|
||||
- Access is allowed only from one end of the stack
|
||||
- adding an item is called pulsing the stack
|
||||
- retrieving an item is called popping the stack
|
||||
|
||||
# Typical uses
|
||||
# Typical Uses
|
||||
|
||||
- Parentheses matching; ()), or (())
|
||||
- Parentheses matching; ()), or (())
|
||||
- compiler's syntax check for matching braces is implemented by using stack
|
||||
- The simplest application of a stack is to reverse a word.
|
||||
- You push a given word to stack - letter by letter - and then pop letters from the stack.
|
||||
- Another application is an "undo" mechanism in text editors;
|
||||
-this operation is accomplished by keeping all text changes in a stack
|
||||
|
||||
- The simplest application of a stack is to reverse a word.
|
||||
• You push a given word to stack - letter by letter - and then pop letters from the stack.
|
||||
# Parenthesis Count
|
||||
|
||||
- Another application is an "undo" mechanism in text editors;
|
||||
•this operation is accomplished by keeping all text changes in a stack
|
||||
- Methodology (logical steps to solve the problem):
|
||||
- scan expression from left to right;
|
||||
- when a left parenthesis is encountered, add its position to the stack;
|
||||
- when a right parenthesis is encountered, remove matching position from stack (more example in a moment).
|
||||
|
||||
# Parenthesis count
|
||||
# Try-catch-throw
|
||||
|
||||
- Methodology (logical steps to solve the problem):
|
||||
- scan expression from left to right;
|
||||
- when a left parenthesis is encountered, add its position to the stack;
|
||||
- when a right parenthesis is encountered, remove matching position from stack (more example in a moment).
|
||||
|
||||
# try-catch-throw
|
||||
|
||||
- When you enter a try block, push the address of this block onto a stack.
|
||||
- When you enter a try block, push the address of this block onto a stack.
|
||||
\
|
||||
- When an exception is thrown, pop the try block that is at the top of the stack; if the stack is empty, terminate the program.
|
||||
|
||||
- If the popped try block has no matching catch block, go back to the previous step.
|
||||
|
||||
- When an exception is thrown, pop the try block that is at the top of the stack; if the stack is empty, terminate the program.
|
||||
- If the popped try block has no matching catch block, go back to the previous step.
|
||||
- If the popped try block has a matching catch block, execute the matching catch block.
|
||||
|
||||
@@ -9,29 +9,17 @@ Linear lists, which include arrays and linked lists, are ideal for serially orde
|
||||
### Examples of Hierarchical Data in Trees
|
||||
|
||||
- Corporate Structure:
|
||||
|
||||
|
||||
- In a company, positions such as president, vice presidents, managers, etc., can be represented in a tree format.
|
||||
|
||||
|
||||
- Object-Oriented Programming:
|
||||
|
||||
|
||||
- In Java, classes form a hierarchy where the Object class is at the top, followed by subclasses.
|
||||
|
||||
|
||||
## Tree Terminologies
|
||||
|
||||
Understanding tree terminologies is crucial for grasping more complex operations and implementations.
|
||||
|
||||
- **Depth:** The number of edges from the root node to a specific node. For example, if node G is three levels down from the root, its depth is 3.
|
||||
|
||||
|
||||
- **Height:** The height of a tree is defined as the number of levels it possesses. A tree's maximum depth helps determine its overall height.
|
||||
|
||||
|
||||
- **Degree of a Node:** This refers to the number of child nodes a specific node has. A tree where each node has a maximum of two children is termed a **binary tree**.
|
||||
|
||||
|
||||
### Binary Trees
|
||||
|
||||
@@ -42,13 +30,8 @@ A binary tree is defined such that each node has at most two children, known tra
|
||||
When analyzing binary trees, certain properties can be established:
|
||||
|
||||
- A binary tree of height h must have at least h nodes.
|
||||
|
||||
|
||||
- In a full binary tree, each node has either two children or none. It contains the maximum number of nodes defined as 2^h - 1.
|
||||
|
||||
|
||||
- The number of nodes and tree height relationship is succinctly expressed with the inequalities: h \leq n \leq 2^h -1.
|
||||
|
||||
|
||||
## Binary Operations and Traversals
|
||||
|
||||
@@ -59,47 +42,31 @@ Performing operations on binary trees is essential to manage and manipulate data
|
||||
Traversal techniques allow for processing each node in a specified order:
|
||||
|
||||
- **Pre-order Traversal:** Process the root, then traverse the left subtree, followed by the right subtree.
|
||||
|
||||
|
||||
- **In-order Traversal:** Visit the left subtree first, then process the root, followed by the right subtree.
|
||||
|
||||
|
||||
- **Post-order Traversal:** Traverse the left subtree, right subtree, and then process the root.
|
||||
|
||||
|
||||
- **Level-order Traversal:** Process nodes level by level from the root down to the leaves.
|
||||
|
||||
|
||||
### Arithmetic Expressions as Trees
|
||||
|
||||
Binary trees are particularly useful for representing arithmetic expressions. An _expression tree_ is structured such that:
|
||||
Binary trees are particularly useful for representing arithmetic expressions. An *expression tree* is structured such that:
|
||||
|
||||
- Leaves represent operands.
|
||||
|
||||
|
||||
- Non-leaf nodes denote operators.
|
||||
|
||||
|
||||
- Subtrees represent sub-expressions.
|
||||
|
||||
|
||||
## Conversion Between Expression Formats
|
||||
|
||||
Moving between infix, prefix, and postfix expressions requires constructing expression trees first.
|
||||
|
||||
1. Infix expression (a + b) can be converted to a postfix expression (a b +) by building the corresponding expression tree and performing a post-order traversal.
|
||||
|
||||
|
||||
## Constructing Binary Trees from Traversals
|
||||
|
||||
Creating a binary tree from given traversals (like in-order and pre-order) involves recognizing patterns in the data:
|
||||
|
||||
- From in-order and pre-order traversals, one identifies the root and splits left and right subtrees accordingly.
|
||||
|
||||
|
||||
- The process can illustrate various scenarios and result in multiple valid trees for the same traversal combinations.
|
||||
|
||||
|
||||
## Conclusion
|
||||
|
||||
Tree data structures are indispensable in computer science, providing efficient methods for data organization, retrieval, and management. Understanding their properties and operations enables clearer problem-solving strategies and effective programming techniques.
|
||||
Tree data structures are indispensable in computer science, providing efficient methods for data organization, retrieval, and management. Understanding their properties and operations enables clearer problem-solving strategies and effective programming techniques.
|
||||
|
||||
@@ -1,50 +1,78 @@
|
||||
# Interfaces, Linked Lists, Array Lists
|
||||
|
||||
## Definitions
|
||||
|
||||
### Interface
|
||||
|
||||
A contract that defines methods, field variables, return types, a class must implement. An example of this is the `List` interface in Java.
|
||||
|
||||
### Linked List
|
||||
|
||||
A data structure where nodes are linked using pointers. Each node contains data - storing a value, and pointer - referencing the next node (and previous in doubly linked).
|
||||
|
||||
#### Types
|
||||
|
||||
- Singly Linked (Unidirectional)
|
||||
- Doubly Linked (Bidirectional)
|
||||
- Circular Linked (Last node points to first node)
|
||||
|
||||
### Array List
|
||||
|
||||
A resizable array-based data structure where elements are stored in contiguous memory locations. Arrays allow for random access through an index corresponding to a location in the array. When capacity is exceeded, the list can resize dynamically.
|
||||
|
||||
## Difference between Linked and Array Lists
|
||||
|
||||
- Memory Allocation
|
||||
- LL -> Dynamic; Array -> Contiguous
|
||||
- Performance
|
||||
- LL -> Good for Insert/Delete; Array -> Good for searching
|
||||
|
||||
## Use Case
|
||||
|
||||
### Linked List
|
||||
|
||||
#### Stacks / Queues
|
||||
|
||||
Linked lists can efficiently add or remove from either end.
|
||||
|
||||
- Stack: Singly Linked List, insert/remove at head. O(1)
|
||||
- Queue: Doubly Linked List, efficient tail and head operations (enqueue dequeue)
|
||||
|
||||
#### Task Scheduling
|
||||
|
||||
- Dynamic data, removing / adding tasks easier with linked list
|
||||
|
||||
#### Undo Function
|
||||
|
||||
- Doubly Linked List, track user actions. move back or forward allows for easy undo / redo
|
||||
|
||||
### Array List
|
||||
|
||||
#### Database Caching
|
||||
|
||||
- Frequent random access, ideal for storing cached records.
|
||||
|
||||
#### Dropdown Menus
|
||||
|
||||
- Store and dynamically resize when elements need to be added to UI drop-downs that change based on input.
|
||||
|
||||
#### Inventory Systems
|
||||
|
||||
- Elements added or accessed without many deletions, Array List would allow for predictable resizing.
|
||||
|
||||
## Implementation
|
||||
|
||||
### Interface
|
||||
|
||||
```java
|
||||
interface Interface {
|
||||
void method();
|
||||
int method2(int param)
|
||||
}
|
||||
```
|
||||
|
||||
### Linked List
|
||||
|
||||
```java
|
||||
class Node {
|
||||
int data;
|
||||
@@ -80,7 +108,9 @@ class LinkedList {
|
||||
}
|
||||
}
|
||||
```
|
||||
|
||||
### Array List
|
||||
|
||||
```java
|
||||
import java.util.ArrayList;
|
||||
class ArrayList {
|
||||
@@ -168,11 +198,13 @@ class Stack {
|
||||
```
|
||||
|
||||
## Parenthesis Matching
|
||||
|
||||
- Push opening brackets, closing brackets pop correspondingly, if no match, false.
|
||||
|
||||
## Dijkstra's Two-Stack Algorithm
|
||||
|
||||
- Eval parenthesized arithmetic expressions
|
||||
- One stack operands
|
||||
- One stack operators
|
||||
- Processes expression by push/pop elements on stacks, eval subexpression when closing parenthesis encountered.
|
||||
- Assumed expression is fully parenthesised
|
||||
- Assumed expression is fully parenthesised
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
# Write a Java method pop() for a stack implemented using an array.
|
||||
# Write a Java Method pop() for a Stack Implemented Using an Array.
|
||||
|
||||
```java
|
||||
public class Stack {
|
||||
|
||||
@@ -4,6 +4,7 @@ To insert a node into a **binary search tree (BST)** while keeping the tree **ba
|
||||
2. After insertion, **rebalance the tree** (if necessary) to ensure that it remains balanced. A tree is considered balanced if the height difference between the left and right subtrees of any node is at most 1 (this is the **balanced binary tree** or **AVL tree** property).
|
||||
|
||||
### **Given Binary Search Tree**:
|
||||
|
||||
```
|
||||
10
|
||||
/ \
|
||||
@@ -21,6 +22,7 @@ We start by inserting **4** into the BST:
|
||||
- 4 is greater than 2, so 4 will be placed as the **right child** of 2.
|
||||
|
||||
After insertion, the tree looks like this:
|
||||
|
||||
```
|
||||
10
|
||||
/ \
|
||||
@@ -44,6 +46,7 @@ Since the tree is balanced at all levels, **no further rebalancing is necessary*
|
||||
### **Final Balanced Tree**:
|
||||
|
||||
The final tree after inserting 4 is:
|
||||
|
||||
```
|
||||
10
|
||||
/ \
|
||||
@@ -56,4 +59,4 @@ The final tree after inserting 4 is:
|
||||
|
||||
### **Conclusion**:
|
||||
|
||||
After inserting 4, the tree remains balanced and no rotations are needed.
|
||||
After inserting 4, the tree remains balanced and no rotations are needed.
|
||||
|
||||
@@ -1,6 +1,7 @@
|
||||
# Describe a scenario where a stack data structure would be more suitable than a Queue
|
||||
# Describe a Scenario where a Stack Data Structure Would Be More Suitable than a Queue
|
||||
|
||||
A **stack data structure** is more suitable than a queue in scenarios where you need to process items in a **Last-In, First-Out (LIFO)** order
|
||||
|
||||
### Scenario: **Undo Operation in Text Editors**
|
||||
|
||||
- **Description**: In text editors, when a user types, deletes, or performs other actions, these operations are stored so they can be undone in reverse order of execution.
|
||||
@@ -36,5 +37,5 @@ A **stack data structure** is more suitable than a queue in scenarios where you
|
||||
- A **queue** is more suitable when processing items in a **First-In, First-Out (FIFO)** order, such as serving customer requests or scheduling tasks.
|
||||
- A stack is better when you need **reversal** or to **process the most recent element first**, such as undo operations, recursion, or browser backtracking.
|
||||
|
||||
Describe a scenario where a stack data structure would be more suitable than a
|
||||
Queue
|
||||
Describe a scenario where a stack data structure would be more suitable than a
|
||||
Queue
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
# What is a binary search tree, and how does it differ from a regular binary tree?
|
||||
# What is a Binary search Tree, and how Does it Differ from a Regular Binary Tree?
|
||||
|
||||
### **Binary Search Tree (BST):**
|
||||
|
||||
@@ -38,6 +38,7 @@ A **Binary Tree** is a tree data structure where each node has at most two child
|
||||
#### Binary Tree:
|
||||
|
||||
A binary tree with no ordering constraints:
|
||||
|
||||
```
|
||||
10
|
||||
/ \
|
||||
@@ -45,11 +46,13 @@ A binary tree with no ordering constraints:
|
||||
/
|
||||
40
|
||||
```
|
||||
|
||||
- Node values are not in any specific order.
|
||||
|
||||
#### Binary Search Tree:
|
||||
|
||||
A binary search tree:
|
||||
|
||||
```
|
||||
10
|
||||
/ \
|
||||
@@ -64,13 +67,13 @@ A binary search tree:
|
||||
|
||||
---
|
||||
|
||||
### **Advantages of BST Over a General Binary Tree:**
|
||||
### **Advantages Of BST Over a General Binary Tree:**
|
||||
|
||||
1. **Efficient Searching**: Searching in a BST takes $O(h)$, where $h$ is the height of the tree. In a balanced BST, $h=O(logn)$.
|
||||
2. **Ordered Traversal**: In-order traversal of a BST produces the nodes in sorted order.
|
||||
3. **Efficient Range Queries**: BSTs can efficiently find all elements within a specific range.
|
||||
|
||||
### **Disadvantages of BST:**
|
||||
### **Disadvantages Of BST:**
|
||||
|
||||
1. If unbalanced (e.g., when nodes are inserted in sorted order), the BST can degrade to a linked list, resulting in $O(n)$ time for operations.
|
||||
2. Maintaining balance (e.g., in AVL or Red-Black Trees) adds complexity.
|
||||
2. Maintaining balance (e.g., in AVL or Red-Black Trees) adds complexity.
|
||||
|
||||
@@ -1,8 +1,8 @@
|
||||
# What is an interface in object-oriented programming and how does it differ from a class?
|
||||
# What is an Interface in Object-oriented Programming and how Does it Differ from a Class?
|
||||
|
||||
### **What is an Interface in Object-Oriented Programming?**
|
||||
### **What Is an Interface in Object-Oriented Programming?**
|
||||
|
||||
An **interface** is a contract in object-oriented programming (OOP) that defines a set of methods (and sometimes properties) that a class must implement. It specifies _what_ a class should do, but not _how_ it should do it.
|
||||
An **interface** is a contract in object-oriented programming (OOP) that defines a set of methods (and sometimes properties) that a class must implement. It specifies *what* a class should do, but not *how* it should do it.
|
||||
|
||||
Key characteristics of an interface:
|
||||
|
||||
@@ -12,6 +12,7 @@ Key characteristics of an interface:
|
||||
4. **No State**: Interfaces do not contain instance variables or state but may include constants.
|
||||
|
||||
#### Example in Java:
|
||||
|
||||
```java
|
||||
// Define an interface
|
||||
public interface Animal {
|
||||
@@ -33,7 +34,7 @@ public class Dog implements Animal {
|
||||
}
|
||||
```
|
||||
|
||||
### **What is a Class?**
|
||||
### **What Is a Class?**
|
||||
|
||||
A **class** is a blueprint for creating objects in OOP. It defines the structure (fields or attributes) and behavior (methods) of objects. Unlike interfaces, classes can have implementations, state, and behavior.
|
||||
|
||||
@@ -45,6 +46,7 @@ Key characteristics of a class:
|
||||
4. **Constructors**: Classes can have constructors to initialize objects.
|
||||
|
||||
#### Example in Java:
|
||||
|
||||
```java
|
||||
// Define a class
|
||||
public class Dog {
|
||||
@@ -73,13 +75,14 @@ public class Dog {
|
||||
|**Constructors**|Cannot have constructors.|Can have constructors to initialize objects.|
|
||||
|**Abstract**|Interfaces are entirely abstract (unless extended in modern versions).|Can be abstract or concrete.|
|
||||
|**Default Methods**|Starting from Java 8, interfaces can have default methods (methods with a body).|Classes always support method implementation.|
|
||||
### **When to Use an Interface?**
|
||||
|
||||
### **When To Use an Interface?**
|
||||
|
||||
- **Polymorphism**: When you want different classes to provide their specific implementation of the same behavior.
|
||||
- **Decoupling**: To decouple code by relying on abstractions rather than concrete classes.
|
||||
- **Multiple Inheritance**: When you need a class to inherit behavior from multiple sources.
|
||||
|
||||
### **When to Use a Class?**
|
||||
### **When To Use a Class?**
|
||||
|
||||
- When you need to define an object with both state and behavior.
|
||||
- When you need concrete implementations of methods.
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
# Convert the infix expression A * (B + C) / D to a postfix expression
|
||||
# Convert the Infix Expression A * (B + C) / D to a Postfix Expression
|
||||
|
||||
To convert the infix expression `A * (B + C) / D` into postfix notation, we use the following rules:
|
||||
|
||||
@@ -16,19 +16,20 @@ To convert the infix expression `A * (B + C) / D` into postfix notation, we use
|
||||
#### Infix Expression: `A * (B + C) / D`
|
||||
|
||||
1. Start with the subexpression inside the parentheses `(B + C)`:
|
||||
|
||||
|
||||
- Convert `B + C` to postfix: `BC+`.
|
||||
2. Substitute the postfix for `(B + C)` back into the original expression:
|
||||
|
||||
|
||||
- The expression becomes `A * BC+ / D`.
|
||||
3. Process the multiplication (`*`) and division (`/`):
|
||||
|
||||
|
||||
- `A * BC+` becomes `ABC+*`.
|
||||
- `ABC+* / D` becomes `ABC+*D/`.
|
||||
|
||||
---
|
||||
|
||||
### **Final Postfix Expression**:
|
||||
|
||||
```
|
||||
ABC+*D/
|
||||
```
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
# Evaluate the postfix expression `6 2 3 + -.`
|
||||
# Evaluate the Postfix Expression `6 2 3 + -.`
|
||||
|
||||
### **Postfix Evaluation Rules**
|
||||
|
||||
@@ -13,25 +13,25 @@
|
||||
**Expression**: `6 2 3 + -`
|
||||
|
||||
1. **Read `6`**:
|
||||
|
||||
|
||||
- Push `6` onto the stack.
|
||||
- **Stack**: `[6]`
|
||||
2. **Read `2`**:
|
||||
|
||||
|
||||
- Push `2` onto the stack.
|
||||
- **Stack**: `[6, 2]`
|
||||
3. **Read `3`**:
|
||||
|
||||
|
||||
- Push `3` onto the stack.
|
||||
- **Stack**: `[6, 2, 3]`
|
||||
4. **Read `+`**:
|
||||
|
||||
|
||||
- Pop the top two operands (`3` and `2`).
|
||||
- Perform `2 + 3 = 5`.
|
||||
- Push the result (`5`) onto the stack.
|
||||
- **Stack**: `[6, 5]`
|
||||
5. **Read `-`**:
|
||||
|
||||
|
||||
- Pop the top two operands (`5` and `6`).
|
||||
- Perform `6 - 5 = 1`.
|
||||
- Push the result (`1`) onto the stack.
|
||||
@@ -42,4 +42,3 @@
|
||||
### **Final Result**:
|
||||
|
||||
The result of the postfix expression `6 2 3 + -` is **`1`**.
|
||||
|
||||
|
||||
@@ -1,6 +1,6 @@
|
||||
# Compare and contrast a queue with a stack.
|
||||
# Compare and Contrast a Queue with a Stack.
|
||||
|
||||
### **Comparison of Queue and Stack**
|
||||
### **Comparison Of Queue and Stack**
|
||||
|
||||
|**Aspect**|**Stack**|**Queue**|
|
||||
|---|---|---|
|
||||
@@ -47,4 +47,4 @@
|
||||
### **Summary**:
|
||||
|
||||
- A **stack** is suitable for tasks where the most recent action needs to be undone or processed first (**LIFO**).
|
||||
- A **queue** is ideal for tasks where the first action needs to be processed first (**FIFO**).
|
||||
- A **queue** is ideal for tasks where the first action needs to be processed first (**FIFO**).
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
# Consider a min heap with these elements: [4, 5, 6, 7, 8, 9, 10]. Insert 3 into this min heap.
|
||||
# Consider a Min Heap with These Elements: [4, 5, 6, 7, 8, 9, 10]. Insert 3 into This Min Heap.
|
||||
|
||||
In a **min heap**, the root node contains the smallest element, and every parent node is less than its children. When we insert a new element into a min heap, we follow these steps:
|
||||
|
||||
@@ -8,10 +8,13 @@ In a **min heap**, the root node contains the smallest element, and every parent
|
||||
### Given Min Heap:
|
||||
|
||||
The given min heap is represented as an array:
|
||||
|
||||
```csharp
|
||||
[4, 5, 6, 7, 8, 9, 10]
|
||||
```
|
||||
|
||||
This corresponds to the following binary tree:
|
||||
|
||||
```
|
||||
4
|
||||
/ \
|
||||
@@ -19,13 +22,17 @@ This corresponds to the following binary tree:
|
||||
/ \ / \
|
||||
7 8 9 10
|
||||
```
|
||||
|
||||
### **Step 1: Insert 3 into the Heap**
|
||||
|
||||
First, insert 3 at the end of the heap:
|
||||
|
||||
```csharp
|
||||
[4, 5, 6, 7, 8, 9, 10, 3]
|
||||
```
|
||||
|
||||
This corresponds to the following binary tree:
|
||||
|
||||
```
|
||||
4
|
||||
/ \
|
||||
@@ -35,6 +42,7 @@ This corresponds to the following binary tree:
|
||||
/
|
||||
3
|
||||
```
|
||||
|
||||
### **Step 2: Bubble Up**
|
||||
|
||||
Now, we need to **bubble up** the element `3` to restore the heap property. We compare `3` with its parent and swap if necessary:
|
||||
@@ -42,6 +50,7 @@ Now, we need to **bubble up** the element `3` to restore the heap property. We c
|
||||
- The parent of `3` is `7` (index 3). Since `3 < 7`, we swap them.
|
||||
|
||||
After the swap, the heap becomes:
|
||||
|
||||
```
|
||||
4
|
||||
/ \
|
||||
@@ -57,6 +66,7 @@ Now, we continue the bubbling up process:
|
||||
- The parent of `3` is `5` (index 1). Since `3 < 5`, we swap them.
|
||||
|
||||
After the swap, the heap becomes:
|
||||
|
||||
```
|
||||
4
|
||||
/ \
|
||||
@@ -86,6 +96,7 @@ After the swap, the heap becomes:
|
||||
### **Final Array Representation**:
|
||||
|
||||
The final min heap as an array is:
|
||||
|
||||
```csharp
|
||||
[3, 4, 6, 5, 8, 9, 10, 7]
|
||||
```
|
||||
|
||||
@@ -1,4 +1,5 @@
|
||||
# Create an adjacency matrix for the following weighted undirected graph.
|
||||
# Create an Adjacency Matrix for the following Weighted Undirected Graph.
|
||||
|
||||
```
|
||||
A-3-B
|
||||
| |
|
||||
@@ -17,10 +18,10 @@ To create an **adjacency matrix** for the given **weighted undirected graph**, w
|
||||
|
||||
### **Graph Details**:
|
||||
|
||||
- **A -3- B**: There is an edge between A and B with weight 3.
|
||||
- **A -2- C**: There is an edge between A and C with weight 2.
|
||||
- **B -1- D**: There is an edge between B and D with weight 1.
|
||||
- **C -4- D**: There is an edge between C and D with weight 4.
|
||||
- **A -3B**: There is an edge between A and B with weight 3.
|
||||
- **A -2C**: There is an edge between A and C with weight 2.
|
||||
- **B -1D**: There is an edge between B and D with weight 1.
|
||||
- **C -4D**: There is an edge between C and D with weight 4.
|
||||
|
||||
---
|
||||
|
||||
@@ -49,4 +50,4 @@ Let's map the nodes to indices:
|
||||
- `B-D` has a weight of 1, so `matrix[1][3] = 1` and `matrix[3][1] = 1`.
|
||||
- `C-D` has a weight of 4, so `matrix[2][3] = 4` and `matrix[3][2] = 4`.
|
||||
|
||||
This adjacency matrix accurately represents the weighted undirected graph.
|
||||
This adjacency matrix accurately represents the weighted undirected graph.
|
||||
|
||||
@@ -7,4 +7,3 @@ flowchart BT
|
||||
iae[IllegalArgumentException] --> re
|
||||
npe[NullPointerException] --> re
|
||||
```
|
||||
|
||||
|
||||
@@ -0,0 +1 @@
|
||||
|
||||
|
||||
@@ -4,4 +4,4 @@ Next job to be selected is one with highest prio
|
||||
|
||||
Add / Insert new item
|
||||
Remove / Delete highest or lowest prio
|
||||
Get / find highest or lowest prio
|
||||
Get / find highest or lowest prio
|
||||
|
||||
@@ -0,0 +1 @@
|
||||
|
||||
|
||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user