# LeetCode 162. Find Peak Element

## Description

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

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

Given an input array `nums`, where `nums[i] ≠ nums[i+1]`, find a peak element and return its index.

The array may contain multiple peaks, in that case return the index to any one of the peaks is fine.

You may imagine that `nums[-1] = nums[n] = -∞`.

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: 1 or 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.
```

Note:

Your solution should be in logarithmic complexity.

## Explanation

Use binary search to find

## 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 - 1] < nums[mid] and nums[mid] > nums[mid + 1]:
return mid
elif nums[mid - 1] > nums[mid]:
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).