What is the time and space complexity of Find Minimum in Rotated Sorted Array?

Time complexity: O(log n). Space complexity: O(1).

Find Minimum in Rotated Sorted Array

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Solution Guide: Find Minimum in Rotated Sorted Array

Approach

Compare mid element to the rightmost element. If mid is greater, the rotation point (minimum) must be to the right. Otherwise, it is at mid or to the left. Narrow until left meets right.

Complexity Analysis

Time: O(log n)
Space: O(1)

Pattern

Binary Search (Rotated Array)

Why It Works

If mid element is greater than right element, the minimum must be in the right half (the rotation point is there). Otherwise, it is in the left half including mid.

Updated Feb 2026