FAANG · LeetCode #704

Binary Search — three-stage drill

1The ProblemEasy

Binary Search

Find a target's index in a sorted array (or −1).

Examples

[-1,0,3,5,9,12], t=9→ 4t=2→ -1

constraintArray is sorted ascending; distinct values.

2The PatternTIME O(log n) · SPACE O(1)

Binary Search

Halve the search space each step — check the middle, keep the half that can hold the answer.

Problems using this pattern

3The SolutionRESULT → 4

Step through it

left = 0, right = 5. target = 9 — search the whole sorted array

Step 1 / 3

Python▎check mid · discard a half

1def search(nums, target):
2    left, right = 0, len(nums) - 1
3    while left <= right:
4        mid = (left + right) // 2
5        if nums[mid] == target:
6            return mid
7        elif nums[mid] < target:
8            left = mid + 1
9        else:
10            right = mid - 1
11    return -1

why it worksBecause the array is sorted, comparing the middle element to the target rules out HALF the array every step: if nums[mid] is too small the answer must be to the right, otherwise to the left. log₂(n) steps instead of n.

Arrow keys to navigate · escape to reset

All problems by pattern

Two Pointers

Sliding Window

Prefix Sum

Monotonic Deque

Shortest Subarray with Sum at Least K

Binary Search

Arrays & Hashing

Monotonic Stack

Intervals

Binary Search — three-stage drill

Binary Search

Binary Search

Step through it

All problems by pattern

Two Pointers

Sliding Window

Prefix Sum

Monotonic Deque

Binary Search

Arrays & Hashing

Monotonic Stack

Intervals

Heap / Top-K

Backtracking

Recursive Descent