Binary Search

Key idea

Each time, compare the target with the middle element:

1. If the middle element equals the target → found.

2. If the target is smaller → search the left half.

3. If the target is larger → search the right half.

This halves the search range every step → O(log n) time complexity.

Important condition

The array must be sorted (ascending or descending).

Implementation in C

int binary_search(int arr[], int n, int target) {
    int left = 0;
    int right = n - 1;

    while (left <= right) {
        int mid = left + (right - left) / 2; // avoid overflow

        if (arr[mid] == target) {
            return mid;  // found, return index
        } else if (arr[mid] < target) {
            left = mid + 1;  // search right half
        } else {
            right = mid - 1; // search left half
        }
    }

    return -1; // not found
}