LeetCode Container With Most Water

· 111 words · 1 minute read
2017年6月
LeetCode

11. Container With Most Water

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

方法

一开始暴力解，结果超时了，实际上该问题有O(n)的解法。设定两个收尾指针i,j进行扫描,若height[i] <= height[j], i++，若height[i] > height[j], j--为什么这样就可以判断了呢，leetcode discuss里好多用的反证法，自己可以 点击 去看。

网上还有一种比较直观的解释，就是i到j-1的容积,i到j-2]的容积，不可能比i到j的容积大，因为宽不可能大于j-i,而且高度受限于height[i]

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