Big O Notation Examples in JavaScript

This project demonstrates various Big O time complexities using practical JavaScript examples. It serves as a reference for understanding algorithm efficiency and performance scaling.

🚀 How to Use

1. Clone this repository.
2. Open index.html in your web browser.
3. View the interactive demos and code snippets directly on the page.

📚 Covered Time Complexities

Big O	Name	Description	Example
O(1)	Constant	Time matches input size? No. Always the same.	Array access, Stack push/pop
O(log n)	Logarithmic	Time grows logarithmically (search space halves).	Binary Search
O(n)	Linear	Time grows linearly with input size.	Linear Search
O(n log n)	Linearithmic	Standard for efficient sorting.	Merge Sort, Quick Sort
O(n²)	Quadratic	Time grows with square of input (nested loops).	Bubble Sort
O(2ⁿ)	Exponential	Time doubles with each addition to input.	Naive Fibonacci
O(n!)	Factorial	Grows extremely fast.	Permutations

📝 Code Examples

O(1) - Constant Time

Operations that take the same amount of time regardless of input size.

function getFirstElement(arr) {
    return arr[0];
}

O(log n) - Logarithmic Time

Common in algorithms that divide the problem in half each step.

function binarySearch(arr, target) {
    let left = 0, right = arr.length - 1;
    while (left <= right) {
        const mid = Math.floor((left + right) / 2);
        if (arr[mid] === target) return mid;
        // ... (see constant.js for full implementation)
    }
    return -1;
}

O(n) - Linear Time

Iterating through all elements once.

function linearSearch(arr, target) {
    for (let i = 0; i < arr.length; i++) {
        if (arr[i] === target) return i;
    }
    return -1;
}

O(n²) - Quadratic Time

Typically involves nested loops, like comparing every element with every other element.

function bubbleSort(arr) {
    for (let i = 0; i < arr.length; i++) {
        for (let j = 0; j < arr.length - i - 1; j++) {
            // Swap logic
        }
    }
}

📁 Files

• index.html: Main visual interface with demos.
• constant.js: Contains all the algorithm implementations and demo logic.

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Created for educational purposes to visualize algorithm efficiency.