011_LeetCode_11 Container With Most Water 题解

Description

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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.

Note: You may not slant the container and n is at least 2.

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给定一个数组，第i个值代表第i个位置的高度，求这些值中，任意两个值与x的垂直线与x轴组成的桶中，最多能乘多少水

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解：

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• 方法一：暴力递归，时间复杂度为O(n2).
• 方法二：分别设置头尾两个指针l和r，当l较小时，l向r移动，此时l与l+1到r之间所有的线组成的桶全部被忽略。（因为，此时l的高度比r的小，与其余点的的面积由l的高度或者比l更小的高度决定，同时他们之间的距离肯定没有l到r大，因此这种方法可行）。r较小时同理移动，知道l和r重合，移动的过程中记录最大的乘水量即可。

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java代码：

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class Solution {    public int maxArea(int[] height) {        if (height.length < 2)            return 0;        int l = 0, r = height.length - 1;        int max = 0;        int now;        while (l < r){            now = (r - l) * Math.min(height[l], height[r]);            max = Math.max(now, max);            if (height[l] < height[r])                l++;            else                r--;        }        return max;    }}