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

Signature

def solution(nums: list[int], target: int) -> int: ...

Complexity

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

Hints

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

Python

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