#32 Medium Time O(log n) Space O(1) Animated

Search in Rotated Sorted Array

Search a target in a rotated sorted array.

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1 Predict
2 Trace
3 Explain
4 Implement

Pattern Binary search over a monotonic decision

Each comparison proves that half of the remaining search space cannot contain the answer.

Approach: Binary Search

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Core Insight

Each comparison proves that half of the remaining search space cannot contain the answer.

Common Pitfall

Choose inclusive or exclusive bounds once and update them consistently.

Description

Search a target in a rotated sorted array.

Constraints

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

Solution — Binary Search

TimeO(log n) SpaceO(1)

Implementation Plan

Translate the invariant into these small, testable moves.

Set the initial bounds.
Compute a midpoint.
Use the monotonic condition to discard one half.
Return when found or when the bounds cross.

def search(nums, target):
    l, r = 0, len(nums) - 1
    
    while l <= r:
        mid = (l + r) // 2
        if target == nums[mid]:
            return mid
            
        # Left sorted portion
        if nums[l] <= nums[mid]:
            if target > nums[mid] or target < nums[l]:
                l = mid + 1
            else:
                r = mid - 1
        # Right sorted portion
        else:
            if target < nums[mid] or target > nums[r]:
                r = mid - 1
            else:
                l = mid + 1
                
    return -1

Find Minimum in Rotated Sorted Array

Time Based Key-Value Store

Search in Rotated Sorted Array

Steps

Description

Constraints

Tags

Solution — Binary Search