#162 - Find Peak Element

MediumBinary Search

A peak element is strictly greater than its neighbors. Given an integer array nums where nums[i] ≠ nums[i + 1], find any peak element and return its index. The array may contain multiple peaks. You must solve in O(log n) time. Assume nums[-1] = nums[n] = -∞.

Input	Output
nums = [1,2,3,1]	2
nums = [1,2,1,3,5,6,4]	5 (or 1)

Solution Space

Try it

/**
 * Finds any peak element index using binary search.
 * If mid < mid+1, a peak must exist to the right; otherwise to the left.
 *
 * @param nums Array where adjacent elements differ
 * @returns    Index of any peak element
 */
export function findPeakElement(nums: number[]): number {
  let lo = 0;
  let hi = nums.length - 1;

  while (lo < hi) {
    const mid = lo + Math.floor((hi - lo) / 2);

    if (nums[mid] < nums[mid + 1]) {
      lo = mid + 1; // ascending → peak is to the right
    } else {
      hi = mid; // descending or at peak → search left half (inclusive)
    }
  }

  return lo;
}

Approach: binary search on slope – since `nums[-1] = nums[n] = -∞`, a rising slope guarantees a peak to the right. Converge to a peak by always moving toward the higher neighbor.

Time: O(log n) – halves the search space each iteration.

Space: O(1) – only a few variables.

#2542 Maximum Subsequence Score

#374 Guess Number Higher or Lower