【LeetCode】11. Container With Most Water

问题描述

Given n non-negative integers a1, a2, ..., an, where each represents a point at coordinate (i, ai). n vertical lines are drawn such that the two endpoints of line i is at (i, ai) and (i, 0). Find two lines, which together with x-axis forms a container, such that the container contains the most water.

水桶装水求容积，实际上是求各条线组成的长方形的面积。

问题分析

保留左右两个指针，每次计算出当前长方形的面积（高是短的那条线，宽是两个指针的距离），然后与当前最大值进行比较，如果大于当前最大值就替换掉；然后比较两个指针指向的值，移动值小的指针，即移动决定高的。

可以理解为最开始就把宽设为最大，然后不断缩小宽，增长高。

代码

class Solution {
public:
    int maxArea(vector<int>& height) {
    	if(height.size()<=1) return 0;
		int left=0;
		int right = height.size()-1;
		int max_area = 0;
		while(left<right) {
			max_area = max(max_area, 
				min(height[left],height[right])*(right-left));
			if(height[left]>=height[right]) {
				right--;
			} else {
				left++;
			}
		}
		return max_area;
    }
};