DSA interview question

Find the Minimum in a Rotated Sorted Array

Medium · Algorithms · Topics: binary search, rotated array

The problem

A weather station's circular buffer holds hourly temperatures in increasing order since midnight, but it wraps around, so the stored array looks like [3, 4, 5, 1, 2]. The smallest value, which is where the sequence restarted, marks the rotation point. Scanning is O(n); binary search finds it in O(log n) by comparing the middle element with the rightmost one. If the middle is bigger than the right end, the drop (and the minimum) must be to the right of mid; otherwise the minimum is at mid or to its left.

Example: [4, 5, 6, 7, 0, 1, 2] → 0.

Function signature

int findMin(const vector<int>& nums);  // distinct values, rotated increasing array, non-empty

Test cases

Input `nums`	Output	Explanation
`[3, 4, 5, 1, 2]`	1
`[4, 5, 6, 7, 0, 1, 2]`	0
`[11, 13, 15, 17]`	11	Not rotated
`[2, 1]`	1
`[1]`	1

(Confirm: values are distinct; the array is a rotation of an increasing array.)

How interviewers phrase it

"Find the minimum element in a rotated sorted array" (LeetCode 153).
With duplicates allowed (LeetCode 154), which needs the "shrink hi by one" trick.
"How many times has the array been rotated?" (S.No 112): the index of the minimum.

Clarifying questions to ask

Are the values distinct?
Could the array be unrotated?
Return the value or its index?

Follow-ups to expect

"Why compare with the right end, not the left?"
"Why hi = mid and not hi = mid − 1?"
"What changes with duplicates?"
"Complexity?"

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