Binary Search

array binary-search

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

Complexity

Show Complexity
  • Time: O(log n)
  • Space: O(1)

Hints

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Pattern
Classic binary search
Approach
Maintain left and right pointers. Compare middle element with target. If equal, return index. If target is smaller, search left half. If target is larger, search right half.
Complexity
Divide search space in half each iteration

Solutions

Show PY Solution
def solution(nums: list[int], target: int) -> int:
    left = 0
    right = len(nums) - 1

    while left <= right:
        mid = left + (right - left) // 2

        if nums[mid] == target:
            return mid

        if nums[mid] < target:
            left = mid + 1
        else:
            right = mid - 1

    return -1