162-寻找峰值

LeetCode 162. Find Peak Element

LeetCode-162

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 $O(logn)$ time.

示例 1：

输入：nums = [1,2,3,1]
输出：2
解释：3 是峰值元素，你的函数应该返回其索引 2。

示例 2：

输入：nums = [1,2,1,3,5,6,4]
输出：1 或 5 
解释：你的函数可以返回索引 1，其峰值元素为 2；
     或者返回索引 5， 其峰值元素为 6。

method: 二分模板一

如果mid比mid+1大，说明峰值在左边，所以r=mid
如果mid比mid+1小，说明峰值在右边，所以l=mid+1

考虑边界条件，l指向倒数第二个元素，r指向最后一个元素，mid是l
如果满足条件，则r = mid = l，退出，结果正确
如果不满足，则l = mid + 1 = r，退出，结果也正确

int findPeakElement(vector<int>& nums) {
    int l = 0, r = nums.size() - 1;
    while (l < r) {
        int mid = l + r >> 1;
        if (nums[mid] > nums[mid + 1]) r = mid;
        else l = mid + 1;
    }
    return r;
}

时间复杂度：$O(logn)$
空间复杂度：$O(1)$

模板二

模板二是上取整，所以和mid-1比较不会越界

int findPeakElement(vector<int>& nums) {
    int l = 0, r = nums.size() - 1;
    while (l < r) {
        int mid = l + r + 1 >> 1;
        if (nums[mid] > nums[mid - 1]) l = mid;
        else r = mid - 1;
    }
    return l;
}