Container With Most Water

题目

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

该问题可在O(n)O(n)时间内解决.

在计算区域面积时，我们以min(height[i], height[j])作为高，假如height[i] < height[j]，因为对于任意的j，min(height[i], height[j])所能返回的最大值为height[i]，所以我们可以忽略line i与区间[i,j]内其他line组成的区域的计算；同理当height[i] > height[j]时，可以忽略line j与区间[i,j]内其他line组成的区域

代码

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