DSA interview question

Find How Many Times an Array Has Been Rotated

Easy · Algorithms · Topics: binary search, rotated array

The problem

A sorted playlist was shifted to the right K times by a buggy "shuffle" button (each shift moves the last song to the front), and the app wants to know K so it can undo the damage. For an increasing array with distinct values, K is exactly the index of the minimum element: the smallest value started at index 0, and every right rotation moves it one step further. So the problem reduces to finding the minimum of a rotated sorted array, in O(log n).

Example: [4, 5, 1, 2, 3] → 2 (it's [1, 2, 3, 4, 5] rotated right twice).

Function signature

int countRotations(const vector<int>& a);  // distinct values; number of right rotations

Test cases

Input `a`	Output	Explanation
`[5, 1, 2, 3, 4]`	1	The minimum is at index 1
`[4, 5, 1, 2, 3]`	2
`[1, 2, 3, 4, 5]`	0	Not rotated
`[2, 1]`	1
`[7]`	0

(Confirm: the original array was sorted increasingly with distinct values and rotated to the right K times, with 0 ≤ K < n.)

How interviewers phrase it

"Find the number of times a sorted array has been rotated" (GeeksforGeeks "Rotation").
Sometimes phrased as "find the rotation point" or "find the index of the minimum".

Clarifying questions to ask

Was it rotated to the right (clockwise) or to the left? (For a left rotation, the answer is (n − index) mod n.)
Are the values distinct?
Is O(log n) required?

Follow-ups to expect

"Why is the rotation count the index of the minimum?"
"How do you find that index?"
"With duplicates?"
"Complexity?"

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