# 162    Find Peak Element

## 162. [Find Peak Element](https://leetcode.com/problems/find-peak-element/description/)

## 1. Question

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

Given an input array where`num[i] ≠ num[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`num[-1] = num[n] = -∞`.

For example, in array`[1, 2, 3, 1]`, 3 is a peak element and your function should return the index number 2.

## 2. Implementation

**(1) Binary Search**

```java
class Solution {
    public int findPeakElement(int[] nums) {
        if (nums.length <= 1) {
            return 0;
        }

        int start = 0, end = nums.length - 1, mid = 0;

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

            if (nums[mid - 1] < nums[mid] && nums[mid] > nums[mid + 1]) {
                return mid;
            }
            else if (nums[mid - 1] < nums[mid] && nums[mid] < nums[mid + 1]) {
                start = mid + 1;
            }
            else {
                end = mid - 1;
            }
        }

        return nums[start] > nums[end] ? start : end;
    }
}
```

## 3. Time & Space Complexity

**Binary Search:** 时间复杂度O(logn), 空间复杂度O(1)


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