What is the optimal time complexity of solving Find Minimum 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 Find Minimum 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 Find Minimum 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 Find Minimum 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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Find Minimum In Rotated Sorted Array

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

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Problem Statement

Easy

Suppose an array of length n sorted in ascending order is rotated between 1 and n times. For example, the array [0,1,2,4,5,6,7] might become [4,5,6,7,0,1,2] if it was rotated 4 times.

Notice that rotating an array [a[0], a[1], ..., a[n-1]] 1 time results in [a[n-1], a[0], a[1], ..., a[n-2]].

Given the sorted rotated array nums of unique elements, return the minimum element of this array.

You must write an algorithm that runs in O(log n) time.

Write a function findMin(nums: List[int]) -> int.

Constraints

•n == len(nums)
•1 <= n <= 5000
•-5000 <= nums[i] <= 5000
•All integers in nums are unique
•nums is sorted and rotated between 1 and n times

Examples

Example 1

Input

nums = [3, 4, 5, 1, 2]

Output

Explanation

The original array was [1,2,3,4,5] rotated 3 times. The minimum is 1.

Example 2

Input

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

Output

Explanation

The original array was [0,1,2,4,5,6,7] rotated 4 times. The minimum is 0.

Example 3

Input

nums = [11, 13, 15, 17]

Output

Explanation

Array is not rotated (or rotated n times). The minimum is the first element.

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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