What is the optimal time complexity of solving Search In Rotated Sorted Array?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Search In Rotated Sorted Array?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Search In Rotated Sorted Array?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Search In Rotated Sorted Array?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Search In Rotated Sorted Array

Learn how to solve the 'Search In Rotated Sorted Array' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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]].

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.

Write a function search(nums: List[int], target: int) -> int.

Constraints

•1 <= len(nums) <= 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

Examples

Example 1

Input

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

Output

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.

Example 3

Input

nums = [1], target = 0

Output

-1

Explanation

0 is not in the array.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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