DSA TrainerFind Minimum in Rotated Sorted Array
An originally sorted array was rotated at some unknown pivot. Find the minimum element in O(log n) time. All values are unique.
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Problem
Suppose an array of length n sorted in ascending order is rotated between 1 and n times. Given the sorted rotated array nums of unique elements, return the minimum element of this array.
Input
An integer array `nums` that was sorted then rotated at some pivot.
Output
The minimum element in the array.
Examples
Input: nums = [3,4,5,1,2]
Output: 1
Original sorted array [1,2,3,4,5] was rotated. Minimum is 1.
Input: nums = [4,5,6,7,0,1,2]
Output: 0
Rotated from [0,1,2,4,5,6,7]. Minimum is 0.
Input: nums = [11,13,15,17]
Output: 11
Not rotated (or rotated by 0). Minimum is the first element.
The brute-force approach
Scan the entire array once and track the minimum.
return min(nums)Linear scan is O(n). The array was originally sorted, it has structure you can exploit. Binary search can find the minimum in O(log n) by deciding which half contains the rotation point.
Spotting the pattern
This is a Binary Search problem. The key question to ask yourself:
The array was sorted and then rotated, how do I tell which half still holds the minimum?
Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.
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