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MediumBinary Search

Search in Rotated Sorted Array

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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
Explanation: 0 is found at index 4.

Example 2:

Input: nums = [4,5,6,7,0,1,2], target = 3
Output: -1
Explanation: 3 is not in the array, so return -1.

Example 3:

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

Examples

Example 1

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

Output: 4

Explanation: 0 is found at index 4.

Example 2

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

Output: -1

Explanation: 3 is not in the array, so return -1.

Example 3

Input: nums = [1], target = 0

Output: -1

Explanation: 0 is not in the array.

Constraints

  • -1 <= nums.length <= 5000
  • --10^4 <= nums[i] <= 10^4
  • -All values of nums are unique.
  • -nums is an ascending array that is possibly rotated.
  • --10^4 <= target <= 10^4

Optimal Complexity

Time

O(log n)

Space

O(1)

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