What is the time and space complexity of Peak Index in Mountain Array?

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

Peak Index in Mountain Array

Med

Concept

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Solution Guide: Peak Index in Mountain Array

Approach

Because the array increases then decreases, compare mid with mid+1. If rising, peak is to the right; if falling, peak is at mid or to the left.

Complexity Analysis

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

Pattern

Binary Search (Boundary Finding)

Why It Works

The mountain shape guarantees a directional slope. Each step moves toward the slope change, so left/right bounds narrow until only the peak index remains.

Updated Feb 2026