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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Learn DSA - Code Arena</title>
<link rel="icon" type="image/svg+xml" href="favicon.svg">
<link rel="preconnect" href="https://fonts.googleapis.com">
<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
<link
href="https://fonts.googleapis.com/css2?family=Space+Grotesk:wght@400;500;600;700&family=JetBrains+Mono:wght@400;500&display=swap"
rel="stylesheet">
<script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/1.9.0/p5.min.js"></script>
<style>
* {
margin: 0;
padding: 0;
box-sizing: border-box;
}
body {
font-family: 'Space Grotesk', sans-serif;
background: linear-gradient(135deg, #0a0a12 0%, #12121c 100%);
color: #e8e8f0;
min-height: 100vh;
}
/* Header */
header {
display: flex;
justify-content: space-between;
align-items: center;
padding: 16px 30px;
background: linear-gradient(90deg, rgba(18, 18, 28, 0.95), rgba(26, 26, 40, 0.95));
border-bottom: 1px solid rgba(0, 255, 136, 0.1);
position: sticky;
top: 0;
z-index: 100;
backdrop-filter: blur(10px);
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.logo {
display: flex;
align-items: center;
gap: 12px;
font-weight: 700;
font-size: 1.3rem;
}
.logo-icon {
width: 40px;
height: 40px;
background: linear-gradient(135deg, #00ff88, #00aa66);
border-radius: 10px;
display: flex;
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justify-content: center;
font-size: 1.2rem;
}
.back-btn {
padding: 10px 20px;
background: linear-gradient(145deg, #2a2a3a, #1a1a28);
border: 1px solid #3a3a4a;
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text-decoration: none;
font-weight: 500;
transition: all 0.3s ease;
}
.back-btn:hover {
border-color: #00ff88;
box-shadow: 0 0 15px rgba(0, 255, 136, 0.2);
}
/* Main Layout */
.learn-container {
display: grid;
grid-template-columns: 280px 1fr;
height: calc(100vh - 73px);
}
/* Sidebar */
.sidebar {
background: linear-gradient(180deg, #0f0f18, #0a0a12);
border-right: 1px solid rgba(42, 42, 58, 0.5);
overflow-y: auto;
padding: 20px 0;
}
.sidebar-title {
padding: 0 20px 15px;
font-size: 0.75rem;
text-transform: uppercase;
letter-spacing: 2px;
color: #6a6a8a;
}
.topic-category {
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}
.category-header {
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align-items: center;
gap: 10px;
cursor: pointer;
font-weight: 600;
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.category-icon {
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}
.topic-item {
padding: 10px 20px 10px 50px;
cursor: pointer;
font-size: 0.9rem;
color: #8a8aa0;
transition: all 0.2s ease;
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.topic-item:hover {
color: #e8e8f0;
background: rgba(68, 136, 255, 0.05);
}
.topic-item.active {
color: #00ff88;
background: rgba(0, 255, 136, 0.08);
}
/* Content Area */
.content {
overflow-y: auto;
padding: 30px 40px;
}
.topic-header {
display: flex;
align-items: center;
gap: 15px;
margin-bottom: 25px;
}
.topic-header h1 {
font-size: 2rem;
background: linear-gradient(135deg, #00ff88, #4488ff);
background-clip: text;
-webkit-background-clip: text;
-webkit-text-fill-color: transparent;
}
.complexity-badges {
display: flex;
gap: 10px;
margin-left: auto;
}
.badge {
padding: 6px 12px;
border-radius: 20px;
font-size: 0.8rem;
font-weight: 600;
}
.badge-time {
background: rgba(68, 136, 255, 0.2);
color: #4488ff;
border: 1px solid rgba(68, 136, 255, 0.3);
}
.badge-space {
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color: #aa66ff;
border: 1px solid rgba(170, 102, 255, 0.3);
}
/* Visualization Box */
.viz-container {
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border: 1px solid rgba(42, 42, 58, 0.5);
border-radius: 16px;
overflow: hidden;
margin-bottom: 30px;
}
.viz-header {
padding: 15px 20px;
background: rgba(26, 26, 40, 0.8);
display: flex;
justify-content: space-between;
align-items: center;
border-bottom: 1px solid rgba(42, 42, 58, 0.5);
}
.viz-title {
font-weight: 600;
display: flex;
align-items: center;
gap: 8px;
}
.viz-controls {
display: flex;
gap: 8px;
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.viz-btn {
padding: 8px 16px;
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border-radius: 6px;
font-weight: 600;
cursor: pointer;
font-family: inherit;
transition: all 0.2s ease;
}
.viz-btn-primary {
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color: #0a0a12;
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.viz-btn-secondary {
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.speed-control {
display: flex;
align-items: center;
gap: 8px;
font-size: 0.85rem;
color: #8a8aa0;
}
.speed-control input {
width: 80px;
accent-color: #00ff88;
}
.viz-canvas {
display: flex;
justify-content: center;
padding: 20px;
min-height: 300px;
}
/* Theory Section */
.theory-section {
margin-bottom: 30px;
}
.section-title {
font-size: 1.3rem;
margin-bottom: 15px;
display: flex;
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gap: 10px;
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.theory-content {
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color: #c0c0d0;
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.theory-content p {
margin-bottom: 15px;
}
.theory-content ul,
.theory-content ol {
margin: 15px 0 15px 25px;
}
.theory-content li {
margin-bottom: 8px;
}
.highlight {
color: #00ff88;
font-weight: 600;
}
/* Steps Box */
.steps-box {
background: linear-gradient(145deg, rgba(26, 42, 26, 0.5), rgba(20, 35, 20, 0.5));
border: 1px solid rgba(0, 255, 136, 0.15);
border-radius: 12px;
padding: 20px 25px;
margin: 20px 0;
}
.steps-box h4 {
color: #00ff88;
margin-bottom: 12px;
}
.steps-box ol {
margin-left: 20px;
}
/* Code Block */
.code-section {
margin-bottom: 30px;
}
.code-block {
background: #0a0a12;
border: 1px solid rgba(42, 42, 58, 0.5);
border-radius: 12px;
overflow: hidden;
}
.code-header {
padding: 12px 18px;
background: #12121c;
display: flex;
justify-content: space-between;
align-items: center;
border-bottom: 1px solid rgba(42, 42, 58, 0.5);
}
.code-lang {
font-size: 0.8rem;
color: #6a6a8a;
display: flex;
align-items: center;
gap: 6px;
}
.code-lang::before {
content: '●';
color: #00ff88;
font-size: 0.6rem;
}
.code-content {
padding: 18px;
font-family: 'JetBrains Mono', monospace;
font-size: 0.85rem;
line-height: 1.7;
overflow-x: auto;
}
.code-content .keyword {
color: #ff79c6;
}
.code-content .function {
color: #50fa7b;
}
.code-content .string {
color: #f1fa8c;
}
.code-content .number {
color: #bd93f9;
}
.code-content .comment {
color: #6272a4;
}
/* Info Cards */
.info-grid {
display: grid;
grid-template-columns: repeat(auto-fit, minmax(250px, 1fr));
gap: 15px;
margin: 20px 0;
}
.info-card {
background: linear-gradient(145deg, #1a1a28, #12121c);
border: 1px solid rgba(42, 42, 58, 0.5);
border-radius: 12px;
padding: 18px;
}
.info-card h5 {
color: #4488ff;
margin-bottom: 8px;
font-size: 0.9rem;
}
.info-card p {
font-size: 0.85rem;
color: #a0a0b0;
line-height: 1.5;
}
</style>
</head>
<body>
<header>
<div class="logo">
<div class="logo-icon">📚</div>
<span>Learn DSA</span>
</div>
<a href="index.html" class="back-btn">← Back to Arena</a>
</header>
<div class="learn-container">
<nav class="sidebar">
<div class="sidebar-title">📖 Topics</div>
<div class="topic-category expanded" data-category="sorting">
<div class="category-header active">
<span class="category-icon">📊</span>
<span>Sorting Algorithms</span>
</div>
<div class="topic-list">
<div class="topic-item" data-topic="bubble-sort">Bubble Sort</div>
<div class="topic-item" data-topic="selection-sort">Selection Sort</div>
<div class="topic-item" data-topic="insertion-sort">Insertion Sort</div>
<div class="topic-item" data-topic="merge-sort">Merge Sort</div>
<div class="topic-item" data-topic="quick-sort">Quick Sort</div>
<div class="topic-item" data-topic="heap-sort">Heap Sort</div>
</div>
</div>
<div class="topic-category" data-category="searching">
<div class="category-header">
<span class="category-icon">🔍</span>
<span>Searching</span>
</div>
<div class="topic-list">
<div class="topic-item" data-topic="linear-search">Linear Search</div>
<div class="topic-item" data-topic="binary-search">Binary Search</div>
</div>
</div>
<div class="topic-category" data-category="data-structures">
<div class="category-header">
<span class="category-icon">🗃️</span>
<span>Data Structures</span>
</div>
<div class="topic-list">
<div class="topic-item" data-topic="arrays">Arrays</div>
<div class="topic-item" data-topic="linked-list">Linked Lists</div>
<div class="topic-item" data-topic="stack">Stacks</div>
<div class="topic-item" data-topic="queue">Queues</div>
<div class="topic-item" data-topic="hash-table">Hash Tables</div>
<div class="topic-item" data-topic="heap">Heaps</div>
</div>
</div>
<div class="topic-category" data-category="trees">
<div class="category-header">
<span class="category-icon">🌳</span>
<span>Trees</span>
</div>
<div class="topic-list">
<div class="topic-item" data-topic="binary-tree">Binary Trees</div>
<div class="topic-item" data-topic="bst">Binary Search Trees</div>
<div class="topic-item" data-topic="preorder">Pre-order Traversal</div>
<div class="topic-item" data-topic="inorder">In-order Traversal</div>
<div class="topic-item" data-topic="postorder">Post-order Traversal</div>
</div>
</div>
<div class="topic-category" data-category="graphs">
<div class="category-header">
<span class="category-icon">🌐</span>
<span>Graphs</span>
</div>
<div class="topic-list">
<div class="topic-item" data-topic="graph-basics">Graph Basics</div>
<div class="topic-item" data-topic="bfs">BFS Traversal</div>
<div class="topic-item" data-topic="dfs">DFS Traversal</div>
<div class="topic-item" data-topic="dijkstra">Dijkstra's Algorithm</div>
<div class="topic-item" data-topic="grid-pathfinding">Grid Pathfinding Visualizer</div>
</div>
</div>
<div class="topic-category" data-category="dp">
<div class="category-header">
<span class="category-icon">🔢</span>
<span>Dynamic Programming</span>
</div>
<div class="topic-list">
<div class="topic-item" data-topic="dp-fib">DP (Fibonacci)</div>
<div class="topic-item" data-topic="dp-knapsack">0/1 Knapsack</div>
<div class="topic-item" data-topic="dp-lcs">Longest Common Subsequence</div>
<div class="topic-item" data-topic="dp-coin">Coin Change</div>
</div>
</div>
<div class="topic-category" data-category="backtracking">
<div class="category-header">
<span class="category-icon">🔙</span>
<span>Backtracking</span>
</div>
<div class="topic-list">
<div class="topic-item" data-topic="n-queens">N-Queens Problem</div>
<div class="topic-item" data-topic="sudoku-solver">Sudoku Solver</div>
<div class="topic-item" data-topic="maze-solver">Maze Solver</div>
</div>
</div>
<div class="topic-category" data-category="array-techniques">
<div class="category-header">
<span class="category-icon">👆</span>
<span>Array Techniques</span>
</div>
<div class="topic-list">
<div class="topic-item" data-topic="two-pointer">Two Pointers</div>
<div class="topic-item" data-topic="sliding-window">Sliding Window</div>
<div class="topic-item" data-topic="intervals">Interval Problems</div>
</div>
</div>
</nav>
<main class="content" id="content">
<!-- Content will be loaded dynamically -->
</main>
</div>
<script>
// Topic content data
const TOPICS = {
'bubble-sort': {
title: 'Bubble Sort',
icon: '🫧',
timeComplexity: 'O(n²)',
spaceComplexity: 'O(1)',
description: `
<p><span class="highlight">Bubble Sort</span> is the simplest sorting algorithm.
It works by repeatedly stepping through the list, comparing adjacent elements,
and swapping them if they are in the wrong order.</p>
<p>The algorithm gets its name because smaller elements "bubble" to the top
of the list with each pass, like bubbles rising in water.</p>
`,
steps: [
'Start from the first element',
'Compare it with the next element',
'If the first is greater, swap them',
'Move to the next pair and repeat',
'After one pass, the largest element is at the end',
'Repeat for remaining elements'
],
code: `function bubbleSort(arr) {
const n = arr.length;
for (let i = 0; i < n - 1; i++) {
// Flag to optimize if no swaps occur
let swapped = false;
for (let j = 0; j < n - i - 1; j++) {
// Compare adjacent elements
if (arr[j] > arr[j + 1]) {
// Swap them
[arr[j], arr[j + 1]] = [arr[j + 1], arr[j]];
swapped = true;
}
}
// If no swaps, array is sorted
if (!swapped) break;
}
return arr;
}`,
infoCards: [
{ title: '✅ Pros', text: 'Simple to understand and implement. Works well for small datasets. Stable sort (maintains relative order).' },
{ title: '❌ Cons', text: 'Very slow for large datasets. O(n²) makes it impractical for production use.' },
{ title: '🎯 Best Use Cases', text: 'Educational purposes. Nearly sorted arrays. Small datasets (< 50 elements).' }
]
},
'selection-sort': {
title: 'Selection Sort',
icon: '👆',
timeComplexity: 'O(n²)',
spaceComplexity: 'O(1)',
description: `
<p><span class="highlight">Selection Sort</span> works by repeatedly finding the minimum element
from the unsorted portion and placing it at the beginning.</p>
<p>The algorithm divides the array into two parts: a sorted portion (left) and an unsorted
portion (right). In each iteration, it selects the smallest element from the unsorted part
and swaps it with the first unsorted element.</p>
<p>Unlike Bubble Sort which swaps adjacent elements, Selection Sort minimizes the number
of swaps to exactly <span class="highlight">n-1 swaps</span> in the worst case.</p>
`,
steps: [
'Start with the first position as sorted boundary',
'Find the minimum element in the unsorted portion',
'Swap it with the first unsorted element',
'Move the sorted boundary one position right',
'Repeat until the entire array is sorted'
],
code: `function selectionSort(arr) {
const n = arr.length;
for (let i = 0; i < n - 1; i++) {
// Find minimum element in unsorted portion
let minIndex = i;
for (let j = i + 1; j < n; j++) {
if (arr[j] < arr[minIndex]) {
minIndex = j;
}
}
// Swap minimum with first unsorted element
if (minIndex !== i) {
[arr[i], arr[minIndex]] = [arr[minIndex], arr[i]];
}
}
return arr;
}`,
infoCards: [
{ title: '✅ Pros', text: 'Simple implementation. Minimal swaps (O(n)). Works well when memory writes are expensive.' },
{ title: '❌ Cons', text: 'O(n²) comparisons regardless of input. Not stable. No benefit from partially sorted data.' },
{ title: '🎯 Best Use Cases', text: 'When swap operations are costly. Small datasets. When simplicity is preferred over efficiency.' }
]
},
'insertion-sort': {
title: 'Insertion Sort',
icon: '📥',
timeComplexity: 'O(n²)',
spaceComplexity: 'O(1)',
description: `
<p><span class="highlight">Insertion Sort</span> builds the final sorted array one element at a time.
It works similarly to how you might sort playing cards in your hand.</p>
<p>The algorithm picks one element at a time and inserts it into its correct position
among the previously sorted elements. Elements are shifted right to make room for the
inserted element.</p>
<p>This algorithm is <span class="highlight">adaptive</span> - it performs well on
nearly sorted data, achieving O(n) time complexity in the best case.</p>
`,
steps: [
'Start from the second element (first is considered sorted)',
'Pick the current element as the "key"',
'Compare the key with sorted elements (left side)',
'Shift larger elements one position right',
'Insert the key in its correct position',
'Move to the next unsorted element and repeat'
],
code: `function insertionSort(arr) {
const n = arr.length;
for (let i = 1; i < n; i++) {
// Element to be inserted
let key = arr[i];
let j = i - 1;
// Shift elements greater than key to the right
while (j >= 0 && arr[j] > key) {
arr[j + 1] = arr[j];
j--;
}
// Insert key at correct position
arr[j + 1] = key;
}
return arr;
}`,
infoCards: [
{ title: '✅ Pros', text: 'Efficient for small datasets. Adaptive (fast on nearly sorted data). Stable sort. Online (can sort as data arrives).' },
{ title: '❌ Cons', text: 'O(n²) worst case. Many shifts required for reverse-sorted data.' },
{ title: '🎯 Best Use Cases', text: 'Nearly sorted arrays. Small datasets. Online sorting. When stability matters.' }
]
},
'merge-sort': {
title: 'Merge Sort',
icon: '🔀',
timeComplexity: 'O(n log n)',
spaceComplexity: 'O(n)',
description: `
<p><span class="highlight">Merge Sort</span> is a divide-and-conquer algorithm that divides
the array into halves, recursively sorts them, and then merges the sorted halves.</p>
<p>It's one of the most efficient sorting algorithms with a guaranteed
<span class="highlight">O(n log n)</span> time complexity in all cases - best, average, and worst.</p>
<p>The key insight is that merging two sorted arrays is O(n), and we only need log(n)
levels of division, giving us O(n log n) total.</p>
`,
steps: [
'Divide the array into two halves',
'Recursively sort the left half',
'Recursively sort the right half',
'Merge the two sorted halves',
'Compare elements from both halves and place smaller one first',
'Continue until all elements are merged'
],
code: `function mergeSort(arr) {
if (arr.length <= 1) return arr;
// Divide
const mid = Math.floor(arr.length / 2);
const left = arr.slice(0, mid);
const right = arr.slice(mid);
// Conquer (recursive sort)
const sortedLeft = mergeSort(left);
const sortedRight = mergeSort(right);
// Merge
return merge(sortedLeft, sortedRight);
}
function merge(left, right) {
let result = [];
let i = 0, j = 0;
while (i < left.length && j < right.length) {
if (left[i] <= right[j]) {
result.push(left[i]);
i++;
} else {
result.push(right[j]);
j++;
}
}
// Add remaining elements
return result.concat(left.slice(i)).concat(right.slice(j));
}`,
infoCards: [
{ title: '✅ Pros', text: 'Guaranteed O(n log n). Stable sort. Predictable performance. Great for linked lists.' },
{ title: '❌ Cons', text: 'O(n) extra space required. Not in-place. Slower for small arrays due to recursion overhead.' },
{ title: '🎯 Best Use Cases', text: 'Large datasets. External sorting. When stability is required. Linked list sorting.' }
]
},
'quick-sort': {
title: 'Quick Sort',
icon: '⚡',
timeComplexity: 'O(n log n) avg',
spaceComplexity: 'O(log n)',
description: `
<p><span class="highlight">Quick Sort</span> is a highly efficient divide-and-conquer algorithm.
It picks a "pivot" element and partitions the array around it.</p>
<p>Elements smaller than the pivot go to the left, larger ones go to the right.
This process is repeated recursively on the sub-arrays.</p>
<p>Despite O(n²) worst case, Quick Sort is often <span class="highlight">faster in practice</span>
than Merge Sort due to better cache performance and smaller constant factors.</p>
`,
steps: [
'Choose a pivot element (often the last element)',
'Partition: move smaller elements left, larger right',
'Place pivot in its correct sorted position',
'Recursively apply to left sub-array',
'Recursively apply to right sub-array',
'Base case: arrays of size 0 or 1 are already sorted'
],
code: `function quickSort(arr, low = 0, high = arr.length - 1) {
if (low < high) {
// Partition and get pivot index
const pivotIdx = partition(arr, low, high);
// Recursively sort sub-arrays
quickSort(arr, low, pivotIdx - 1);
quickSort(arr, pivotIdx + 1, high);
}
return arr;
}
function partition(arr, low, high) {
const pivot = arr[high];
let i = low - 1;
for (let j = low; j < high; j++) {
if (arr[j] < pivot) {
i++;
[arr[i], arr[j]] = [arr[j], arr[i]];
}
}
// Place pivot in correct position
[arr[i + 1], arr[high]] = [arr[high], arr[i + 1]];
return i + 1;
}`,
infoCards: [
{ title: '✅ Pros', text: 'Fast in practice. In-place (O(log n) stack space). Cache efficient. Good for arrays.' },
{ title: '❌ Cons', text: 'O(n²) worst case (sorted input). Not stable. Recursion overhead.' },
{ title: '🎯 Best Use Cases', text: 'General purpose sorting. When average case matters more. Arrays (not linked lists).' }
]
},
'heap-sort': {
title: 'Heap Sort',
icon: '🏔️',
timeComplexity: 'O(n log n)',
spaceComplexity: 'O(1)',
description: `
<p><span class="highlight">Heap Sort</span> uses a <span class="highlight">Binary Heap</span> data structure
to sort elements. It treats the array as a complete binary tree.</p>
<p>Phase 1: Build a Max Heap (largest element at root).<br>
Phase 2: Swap root with last element, reduce heap size, and "heapify" down.</p>
<p>Guarantees <span class="highlight">O(n log n)</span> time complexity like Merge Sort, but sorts
<span class="highlight">in-place</span> like Quick Sort!</p>
`,
steps: [
'Build Max Heap from unordered array',
'Swap root (max value) with last element',
'Reduce heap size by 1',
'Heapify the new root to restore max heap property',
'Repeat until heap size is 1',
'Result: Array is sorted in ascending order'
],
code: `function heapSort(arr) {
const n = arr.length;
// Build max heap
for (let i = Math.floor(n / 2) - 1; i >= 0; i--) {
heapify(arr, n, i);
}
// Extract elements from heap one by one
for (let i = n - 1; i > 0; i--) {
// Move current root to end
[arr[0], arr[i]] = [arr[i], arr[0]];
// Call max heapify on the reduced heap
heapify(arr, i, 0);
}
return arr;
}
function heapify(arr, n, i) {
let largest = i;
const left = 2 * i + 1;
const right = 2 * i + 2;
if (left < n && arr[left] > arr[largest]) largest = left;
if (right < n && arr[right] > arr[largest]) largest = right;
if (largest !== i) {
[arr[i], arr[largest]] = [arr[largest], arr[i]];
heapify(arr, n, largest);
}
}`,
infoCards: [
{ title: '✅ Pros', text: 'O(n log n) worst case. In-place (O(1) extra space). No recursion stack overhead.' },
{ title: '❌ Cons', text: 'Unstable. Slower typical performace than Quick Sort due to poor locality of reference.' },
{ title: '🎯 Best Use Cases', text: 'Embedded systems (low memory). Real-time systems (guaranteed time limits).' }
]
},
'linear-search': {
title: 'Linear Search',
icon: '👁️',
timeComplexity: 'O(n)',
spaceComplexity: 'O(1)',
description: `
<p><span class="highlight">Linear Search</span> is the simplest searching algorithm.
It sequentially checks each element until a match is found or the entire list has been searched.</p>
<p>It works on both <span class="highlight">sorted and unsorted</span> arrays, making it
versatile but not optimal for large datasets.</p>
<p>While simple, it's often the only option when data is unsorted or when dealing with
linked lists where random access isn't available.</p>
`,
steps: [
'Start from the first element',
'Compare current element with target',
'If match found, return the index',
'If not, move to the next element',
'Repeat until element found or end reached',
'Return -1 if element not found'
],
code: `function linearSearch(arr, target) {
for (let i = 0; i < arr.length; i++) {
if (arr[i] === target) {
return i; // Element found at index i
}
}
return -1; // Element not found
}
// Example usage:
const numbers = [4, 2, 7, 1, 9, 3];
const result = linearSearch(numbers, 7);
// result = 2 (index of 7)`,
infoCards: [
{ title: '✅ Pros', text: 'Simple implementation. Works on unsorted data. No preprocessing needed. O(1) space.' },
{ title: '❌ Cons', text: 'O(n) time - slow for large datasets. Checks every element in worst case.' },
{ title: '🎯 Best Use Cases', text: 'Small datasets. Unsorted arrays. Linked lists. When data changes frequently.' }
]
},
'binary-search': {
title: 'Binary Search',
icon: '🎯',
timeComplexity: 'O(log n)',
spaceComplexity: 'O(1)',
description: `
<p><span class="highlight">Binary Search</span> is a highly efficient algorithm that works
on <span class="highlight">sorted arrays</span> by repeatedly dividing the search interval in half.</p>
<p>It compares the target with the middle element. If they're equal, we're done.
If target is smaller, search the left half. If larger, search the right half.</p>
<p>With each comparison, we eliminate half the remaining elements, giving us
<span class="highlight">O(log n)</span> time complexity - exponentially faster than linear search!</p>
`,
steps: [
'Find the middle element of the array',
'If middle equals target, return its index',
'If target is smaller, search left half',
'If target is larger, search right half',
'Repeat until found or range is empty',
'Return -1 if not found'
],
code: `function binarySearch(arr, target) {
let left = 0;
let right = arr.length - 1;
while (left <= right) {
const mid = Math.floor((left + right) / 2);
if (arr[mid] === target) {
return mid; // Found!
} else if (arr[mid] < target) {
left = mid + 1; // Search right half
} else {
right = mid - 1; // Search left half
}
}
return -1; // Not found
}
// Example: searching in sorted array
const sorted = [1, 3, 5, 7, 9, 11, 13];
binarySearch(sorted, 7); // returns 3`,
infoCards: [
{ title: '✅ Pros', text: 'O(log n) time - very fast! Efficient for large sorted datasets.' },
{ title: '❌ Cons', text: 'Requires sorted array. Random access needed (arrays only).' },
{ title: '🎯 Best Use Cases', text: 'Large sorted arrays. Dictionaries. Database indexing. Finding boundaries.' }
]
},
'arrays': {
title: 'Arrays',
icon: '📦',
timeComplexity: 'O(1) access',
spaceComplexity: 'O(n)',
description: `
<p><span class="highlight">Arrays</span> are the most fundamental data structure. They store
elements in contiguous memory locations, allowing direct access via index.</p>
<p>Key property: <span class="highlight">Random Access in O(1)</span> - you can access any
element instantly using its index, like arr[5].</p>
<p>Trade-off: Insertion and deletion are O(n) because elements need to be shifted.</p>
`,
steps: [
'Elements stored in contiguous memory',
'Access any element by index in O(1)',
'Insertion at end: O(1) amortized',
'Insertion at beginning/middle: O(n)',
'Deletion requires shifting elements',
'Fixed size (static) or dynamic (resizable)'
],
code: `// Array Operations in JavaScript
// Create array
const arr = [10, 20, 30, 40, 50];
// Access - O(1)
arr[2]; // 30