What is the time and space complexity of Find Peak Element?

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

Find Peak Element

Med

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Solution Guide: Find Peak Element

Approach

Compare mid to its right neighbor. If the right neighbor is larger, a peak must exist to the right (uphill). If mid is larger, a peak exists at mid or to the left. Converge left and right until they meet at a peak.

Complexity Analysis

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

Pattern

Binary Search (Boundary Finding)

Why It Works

If the right neighbor is larger, climbing right guarantees a peak exists there (array drops to -infinity at boundaries). Same logic applies for left. Always move toward the uphill direction.

Updated Mar 2026