11. Container With Most Water (JAVA)

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.

Example:

Input: [1,8,6,2,5,4,8,3,7]
Output: 49

class Solution {
    public int maxArea(int[] height) {
        return calMax(height, 0, height.length-1, 0);
    }
    
    public int calMax(int[] height, int left, int right, int max){
        if(left >= right) return max;

        if(height[left] > height[right]){
            int area = (right-left) * height[right];
            return calMax(height, left, right-1, Math.max(area,max));
        }
        else{
            int area = (right-left) * height[left];
            return calMax(height, left+1, right, Math.max(area,max));
        }
    }
}

解题思路：两个指针分别指向左右两个位置，保留高的那个，矮的那个往中间移动。（Greedy：总是寻找高的柱子）