O(log n) — Logarithmic Time
DSA · Big-O NotationEach step halves the remaining work. Classic sign: dividing the problem space in two.// JavaScript
function binarySearch(arr, target) {
let lo = 0, hi = arr.length - 1;
while (lo <= hi) {
const mid = lo + Math.floor((hi - lo) / 2);
if (arr[mid] === target) return mid;
else if (arr[mid] < target) lo = mid + 1;
else hi = mid - 1;
}
return -1;
}
# Python
def binary_search(arr, target):
lo, hi = 0, len(arr) - 1
while lo <= hi:
mid = lo + (hi - lo) // 2
if arr[mid] == target:
return mid
elif arr[mid] < target:
lo = mid + 1
else:
hi = mid - 1
return -1Time: O(log n) | Space: O(1)Note Balanced BST operations are O(log n). Use mid = lo + (hi - lo) // 2 instead of (lo + hi) // 2 to prevent integer overflow. If you see 'sorted array' in a problem, think binary search immediately.