// Source : https://oj.leetcode.com/problems/container-with-most-water/
// Author : Hao Chen
// Date   : 2014-06-22

/********************************************************************************** 
* 
* 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.
* 
*               
**********************************************************************************/

class Solution {
public:
    int maxArea(vector<int> &height) {
        int area = 0;
        int i = 0; 
        int j = height.size()-1;
        
        while(i<j){
            int a = (j-i)* (height[i]>height[j] ? height[j] : height[i]);
            area = a>area ? a : area;
            height[i]>height[j] ? j-- : i++;
        }
        
        return area;
    }
};

// Source : https://oj.leetcode.com/problems/container-with-most-water/
// Author : Hao Chen
// Date   : 2014-06-22

/********************************************************************************** 
* 
* 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.
* 
*               
**********************************************************************************/

class Solution {
public:
    int maxArea(vector<int> &height) {

        int maxArea = 0;
        // two pointers scan from two sides to middle
        int left = 0; 
        int right = height.size()-1;

        int area; 
        while ( left < right ){
            //calculate the area
            area = (right - left) * ( height[left] < height[right] ? height[left] : height[right]);
            //tracking the maxium area
            maxArea = area > maxArea ? area : maxArea;
            // because the area is decided by the shorter edge
            // so we increase the area is to increase the shorter edge
            height[left] < height[right] ? left++ : right-- ;
        }
        
        return maxArea;
    }
};

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