Algorithmic Thinking & Big-O Complexity

Analyzing algorithm efficiency is essential for building scalable applications. We use asymptotic notations to describe computational complexity.

Big-O Notation

Big-O describes the upper bound of the running time or space complexity of an algorithm in the worst-case scenario.

Complexity Comparison Table

Complexity	Name	Example Algorithm
$O(1)$	Constant	Array Index Access
$O(\log n)$	Logarithmic	Binary Search
$O(n)$	Linear	Single Loop
$O(n \log n)$	Linearithmic	Merge Sort / QuickSort
$O(n^2)$	Quadratic	Bubble Sort / Selection Sort

Code Example: Binary Search

Here is a sample implementation of Binary Search in TypeScript:

function binarySearch(arr: number[], target: number): number {
  let left = 0;
  let right = arr.length - 1;
 
  while (left <= right) {
    const mid = Math.floor((left + right) / 2);
    if (arr[mid] === target) return mid;
    if (arr[mid] < target) left = mid + 1;
    else right = mid - 1;
  }
  return -1; // Not found
}