Find Peak Element — DSA Visualizer

Problem

A peak element is an element that is strictly greater than its neighbors. Given a 0-indexed integer array nums, find a peak element and return its index. If the array contains multiple peaks, return the index of any of the peaks. You may imagine that nums[-1] = nums[n] = -∞. You must write an algorithm that runs in O(log n) time.

Example 1

Input: nums = [1,2,3,1]

Output: 2

Explanation: 3 is a peak element at index 2 (3 > 2 and 3 > 1).

Example 2

Input: nums = [1,2,1,3,5,6,4]

Output: 5 (or 1)

Explanation: Index 1 (value 2) and index 5 (value 6) are both peaks.

Constraints: 1 ≤ nums.length ≤ 1000 | -2³¹ ≤ nums[i] ≤ 2³¹−1 | nums[i] ≠ nums[i+1]

Bar Chart — Find the Peak

State Variables

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mid

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nums[mid]

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nums[mid+1]

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direction

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Step Logic

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Algorithm

Init lo = 0, hi = n−1

While lo < hi: compute mid = lo + (hi−lo)/2

If nums[mid] < nums[mid+1]: slope goes UP → peak is RIGHT → lo = mid+1

Else: slope goes DOWN (or plateau) → peak is at mid or LEFT → hi = mid

Loop ends when lo == hi → that index is the peak → return lo

Time

O(log n)

Space

O(1)

Why It Works

Because the array has no equal adjacent elements and the virtual boundaries are −∞, a peak must exist. At any mid, if nums[mid] < nums[mid+1] the right side is going up — there's definitely a peak somewhere to the right (at minimum the next element is higher, and since the array must come back down, a local max exists). We safely eliminate the left half. The symmetric argument applies for the down slope.