162. Find Peak Element

Problem Description

A peak element is an element that is strictly greater than its neighbors.

Given an integer array nums, find a peak element, and return its index. If the array contains multiple peaks, return the index to 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 and your function should return the index number 2.

Example 2:

Input: nums = [1,2,1,3,5,6,4]
Output: 5
Explanation: Your function can return either index number 1 where the peak element is 2, or index number 5 where the peak element is 6.

Constraints:

1 <= nums.length <= 1000
-2^31 <= nums[i] <= 2^31 - 1
nums[i] != nums[i + 1] for all valid i.

Solution

Use Binary Search to search for the peak element

Python

class Solution:
    def findPeakElement(self, nums: List[int]) -> int:
        start, end = 0, len(nums) - 1
        while (start + 1 < end):
            mid = (start + end) // 2

            # nums[mid] is one of peaks
            if nums[mid] > nums[mid - 1] and nums[mid] > nums[mid + 1]:
                return mid
            # Ascending area
            elif nums[mid] > nums[mid - 1] and nums[mid] < nums[mid + 1]:
                start = mid
            # Descending area
            else:
                end = mid

        return start if nums[start] >= nums[end] else end

Java

class Solution {
    public int findPeakElement(int[] nums) {
        int start = 0, end = nums.length - 1;
        int mid;
        while (start + 1 < end) {
            mid = (start + end) / 2;
            if (nums[mid] > nums[mid + 1] && nums[mid] > nums[mid - 1]) {
                return mid;
            } else if (nums[mid - 1] < nums[mid] && nums[mid] < nums[mid + 1]) {
                start = mid;
            } else {
                end = mid;
            }
        }
        if (nums[start] >= nums[end]) {
            return start;
        } else {
            return end;
        }
    }
}

Complexity Analysis

• Time Complexity
  • O(logn)
• Space Complexity
  • O(1)