LeetCode 11. Container With Most Water 单调队列

题意

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.

思路

假如有容器如下图：

那么他装满水之后一定是这个样子：

可以看出，其从中间到两边一定是呈阶梯状下降的，中间的空缺一定会被水填上的。所以我们只需要枚举上图中由蓝色组成的矩形即可。

开始做的时候竟然不会做了。然后问了下学妹，说是单调队列，发现不会写…… 真是忧伤。

代码

public class Solution {
    public int maxArea(int[] height) {
        int l = 0;
        int r = height.length - 1;
        int rlt = calcArea(l, r, height);
        while (l < r) {
            if (height[l] < height[r]) {
                l = nextLeftBoard(l, r, height);
            } else {
                r = nextRightBoard(l, r, height);
            }
            rlt = Math.max(calcArea(l, r, height), rlt);
        }
        return rlt;
    }
    
    private int nextLeftBoard(int l, int r, int[] height) {
        int rlt = l;
        while (rlt < r && height[rlt] <= height[l])
            rlt ++;
        return rlt;
    }
    
    private int nextRightBoard(int l, int r, int[] height) {
        int rlt = r;
        while (l < rlt && height[rlt] <= height[r])
            rlt --;
        return rlt;
    }
    
    private int calcArea(int l, int r, int[] height) {
        int h = Math.min(height[l], height[r]);
        return (r-l) * h;
    }
}