Introduction to Algorithms

What are algorithms and why they matter

What is an Algorithm?##

An algorithm is a step-by-step procedure for solving a problem or accomplishing a task.

Time Complexity###

The most common way to measure algorithm efficiency is Big O notation:

Notation	Name	Example
O(1)	Constant	Hash table lookup
O(log n)	Logarithmic	Binary search
O(n)	Linear	Linear search
O(n log n)	Linearithmic	Merge sort
O(n²)	Quadratic	Bubble sort

# Example: Binary Search
def binary_search(arr, target):
    left, right = 0, len(arr) - 1
    while left <= right:
        mid = (left + right) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            left = mid + 1
        else:
            right = mid - 1
    return -1