33-search-in-rotated-sorted-array.py

"""
33. Search in Rotated Sorted Array
Medium - 43.6%

There is an integer array nums sorted in ascending order (with distinct values).

Prior to being passed to your function, nums is possibly rotated at an unknown pivot index k (1 <= k < nums.length) such that the resulting array is [nums[k], nums[k+1], ..., nums[n-1], nums[0], nums[1], ..., nums[k-1]] (0-indexed). For example, [0,1,2,4,5,6,7] might be rotated at pivot index 3 and become [4,5,6,7,0,1,2].

Given the array nums after the possible rotation and an integer target, return the index of target if it is in nums, or -1 if it is not in nums.

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

Example 1:
Input: nums = [4,5,6,7,0,1,2], target = 0
Output: 4

Example 2:
Input: nums = [4,5,6,7,0,1,2], target = 3
Output: -1

Example 3:
Input: nums = [1], target = 0
Output: -1
"""

from typing import List

class Solution:
    def search(self, nums: List[int], target: int) -> int:
        left, right = 0, len(nums) - 1
        
        while left <= right:
            mid = left + (right - left) // 2
            
            if nums[mid] == target:
                return mid
            
            # Check which half is sorted
            if nums[left] <= nums[mid]:
                # Left half is sorted
                if nums[left] <= target < nums[mid]:
                    right = mid - 1  # Target is in left half
                else:
                    left = mid + 1   # Target is in right half
            else:
                # Right half is sorted
                if nums[mid] < target <= nums[right]:
                    left = mid + 1   # Target is in right half
                else:
                    right = mid - 1  # Target is in left half
        
        return -1  # Target not found