ContainerWithMostWater.java

/*
Container With Most Water

Problem Description

Given n non-negative integers A[0], A[1], ..., A[n-1] , where each represents a point at coordinate (i, A[i]).

N vertical lines are drawn such that the two endpoints of line i is at (i, A[i]) 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.



Problem Constraints

0 <= N <= 105

1 <= A[i] <= 105



Input Format

Single Argument representing a 1-D array A.


Output Format

Return single Integer denoting the maximum area you can obtain.


Example Input

Input 1:

A = [1, 5, 4, 3]

Input 2:

A = [1]



Example Output

Output 1:

 6

Output 2:

 0



Example Explanation

Explanation 1:

 
5 and 3 are distance 2 apart. So size of the base = 2. Height of container = min(5, 3) = 3. 
So total area = 3 * 2 = 6

Explanation 2:

 
No container is formed.
*/

/*
Solution Approach

Description of approach 1:

    Note 1: When you consider a1 and aN, then the area is (N-1) * min(a1, aN).
    Note 2: The base (N-1) is the maximum possible.

This implies that if there was a better solution possible, it will definitely have height greater than min(a1, aN).

B * H > (N-1) * min(a1, aN)
We know that, B < (N-1)
So, H > min(a1, aN)

This means that we can discard min(a1, aN) from our set and look to solve this problem again from the start.
If a1 < aN, then the problem reduces to solving the same thing for a2, aN.
Else, it reduces to solving the same thing for a1, aN-1
*/


public class Solution {
    public int maxArea(int[] A) {
        int i=0, j=A.length-1, max = 0;
        while(i<j){
            int min = Integer.min(A[i], A[j]);
            max = Integer.max(max, (j-i)*min);
            // if(max==9336375){
            //     System.out.println(i+","+j+","+min);
            // }
            if(A[i]==min){
                i++;
            }
            else{
                j--;
            }
        }
        
        return max;
    }
}