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 < 10^4All the integers in nums are uniquenums is sorted in ascending order
Complexity
Show Complexity
- Time:
O(log n) - Space:
O(1)
Hints
Show 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
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