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.

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

思路：2个指针“遍历比较”所有线段的配对得到面积大小。对于当前区间[left,right]，不失一般性，假设height[left]<height[right]，那么left++就意味着舍弃了[left,left+1]、...、[left,right-1]这些线段对组成的面积，这是显然的，对于[left,j]（j<right），围成的面积=min(height[left],height[j])*(j-left) < height[left]*(right-left)，因此这些线段对围成的面积都是可以不用计算的，相当于遍历过，搜索空间进一步减少为[left+1,right]。最后收敛于left==right。

代码：

 1 public class Solution {
 2     public int maxArea(int[] height) {
 3         int maxarea = 0, left = 0, right = height.length - 1;
 4         while(left < right) {
 5             maxarea = Math.max(maxarea, Math.min(height[left], height[right]) * (right - left));
 6             if (height[left] < height[right]) {
 7                 left++;
 8             } else {
 9                 right--;
10             }
11         }
12         return maxarea;
13     }
14 }

G

iven 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.