Leetcode 162. Find Peak Element

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.

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Note:

Your solution should be in logarithmic complexity.

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解题思路：

一看complexity 要求，立即想到binary search.

如果中间元素大于其相邻后续元素，则中间元素左侧(包含该中间元素）必包含一个局部最大值。

如果中间元素小于其相邻后续元素，则中间元素右侧必包含一个局部最大值。

 

九章算法：

当找到一个下坡，我们往左移动，当找到一个上坡，我们往右移动，这样我们就可以达到顶峰。

如果找到一个山谷，则向任意方向移动即可。

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Java code:

public class Solution {
    public int findPeakElement(int[] nums) {
        int left = 0, right = nums.length-1;
        while(left < right){
            int mid = left + (right - left )/2;
            if(nums[mid] < nums[mid+1]) {
                left = mid + 1;
            }else {
                right = mid;
            }
        }
        return left;
    }
}

2. 九章算法方法 2016.01.18

public class Solution {
    public int findPeakElement(int[] nums) {
        int start = 0, end = nums.length - 1;
        int mid;
        while(start + 1 < end) {
            mid = start + (end - start) / 2;
            if(nums[mid] < nums[mid-1]){
                end = mid;
            }else if(nums[mid] > nums[mid-1]){
                start = mid;
            }else {
                end = mid;
            }
        }
        if(nums[start] > nums[end]){
            return start;
        }else {
            return end;
        }
    }
}

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Reference：

1. http://blog.csdn.net/u010367506/article/details/41943309

2. https://leetcode.com/discuss/56031/java-short-and-neat-code-10-line