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;
}
}
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