# LeetCode 162. Find Peak Element

## Description

https://leetcode.com/problems/find-peak-element/

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`
• `-231 <= nums[i] <= 231 - 1`
• `nums[i] != nums[i + 1]` for all valid `i`.

## Explanation

Use binary search to find the peak element which is greater than the nearby elements.

## Python Solution

``````class Solution:
def findPeakElement(self, nums: List[int]) -> int:

start = 0
end = len(nums) - 1

while start + 1 < end:
mid = start + (end - start) // 2

if nums[mid] > nums[mid - 1] and nums[mid] > nums[mid + 1]:
return mid
elif nums[mid] < nums[mid - 1]:
end = mid
elif nums[mid] < nums[mid + 1]:
start = mid

if nums[end] > nums[start]:
return end

return start``````
• Time complexity: O(log(N)).
• Space complexity: O(1).