LeetCode/solutions/162. Find Peak Element.md

# [162. Find Peak Element](https://leetcode.com/problems/find-peak-element/)
# 思路
寻找一个数组中的极大值. 由于要求对数复杂度, 所以我们很容易想到二分法. 
由于题目说了nums[-1]和nums[n]为负无穷, 那么极大值一定存在(想象一下被山谷包围的山脉). 

那么在二分的循环中:
1. 若`mid == 0 || nums[mid-1] < nums[mid]`, 即mid左边是上升趋势, 那么mid或者其右边一定存在极大值;
2. 满足1且`mid == n - 1 || nums[mid] > nums[mid+1]`, 即mid就是极大值;
3. 满足1但不满足2, 那么其右边一定存在极大值, 此时更新`low = mid + 1`;
4. 否则, mid左边一定存在极大值, 此时更新`high = mid - 1`;

# C++
``` C++
class Solution {
public:
    int findPeakElement(vector<int>& nums) {
        int n = nums.size();
        int low = 0, high = n - 1, mid;
        while(low < high){
            mid = low + (high - low) / 2;
            if(mid == 0 || nums[mid-1] < nums[mid]){
                if(mid == n - 1 || nums[mid] > nums[mid+1]) return mid; // 找到
                else low = mid + 1;
            }
            else high = mid - 1;
        }
        return low;
    }
};
```