How do you approach Binary Search?

Use two pointers: left and right.

What is the time complexity of Binary Search?

Time complexity: O(log n). Space complexity: O(1).

What are common mistakes on Binary Search?

Computing the midpoint as (low + high) / 2. In a fixed-width integer language that overflows on large ranges; low + (high - low) / 2 does not. An update that fails to shrink the range, which spins forever on a two-element window. Answering "does it exist" when the question asked for the first or last occurrence - the boundary variants need a different post-loop return.

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Binary Search

EasyAlgorithms

Description

Given an array of integers nums which is sorted in ascending order, and an integer target, write a function to search target in nums. If target exists, then return its index. Otherwise, return -1.

You must write an algorithm with O(log n) runtime complexity.

Example 1

Input: nums = [-1,0,3,5,9,12], target = 9

Output: 4

Explanation: 9 exists in nums and its index is 4.

Example 2

Input: nums = [-1,0,3,5,9,12], target = 2

Output: -1

Explanation: 2 does not exist in nums so return -1.

Constraints

- 1 <= nums.length <= 10^4 - -10^4 < nums[i], target < 10^4 - All the integers in nums are unique. - nums is sorted in ascending order.

Binary Search: approach, complexity and pitfalls

An easy binary search problem, graded against 6 test cases (4 of them hidden).

The pattern: Binary Search

Halving a search space each step - on sorted arrays, and on answers themselves.

Reach for it when you see: A sorted input, or a monotonic "is this value feasible?" predicate you can binary search over.

If you are stuck

Show the 3-step hint ladder

Use two pointers: left and right.
Calculate the middle index and compare with target.
Adjust left or right pointer based on comparison.

The optimal approach

Show the approach: Binary Search

Repeatedly divide the search space in half by comparing the middle element with the target.

Time: O(log n)
Space: O(1)

The full reference solution in every supported language stays in the editor above - reveal it there once you have had a real attempt.

What the tests check

Read off this problem's own test suite, so these are the cases a submission actually has to survive.

Single element. A one-element case is included. Two-pointer and window solutions frequently return the wrong thing when the two indices start out equal.
Negative numbers. The suite includes negative values. Running-sum, min/max seeding and any "initialise to zero" step need to handle them.
Zero. Zero appears in the input, which is the value most likely to break a truthiness check used in place of an explicit comparison.

Common Binary Search mistakes

These apply to the pattern as a whole, not just this problem.

Computing the midpoint as `(low + high) / 2`. In a fixed-width integer language that overflows on large ranges; `low + (high - low) / 2` does not.
An update that fails to shrink the range, which spins forever on a two-element window.
Answering "does it exist" when the question asked for the first or last occurrence - the boundary variants need a different post-loop return.