Container With Most Water in C++

We are given an array of height of the walls of the container. The goal is to find the container that can contain the maximum volume of water. As heights of walls are elements of an array, the distance between them is considered as width between two walls. For example walls of height Arr[i] and Arr[j] have j-i width between them ( 0<=i<j<=N), where N is no. of walls or length of the array.

So the height of water will be up to the lesser height, if Arr[i] < Arr[j] height of water will be Arr[i]. Width is j-i so area for water = Arr[i] * ( j- i ).

We have to find the maximum such area.

Input

Arr[]= { 5,1,2,3,5 }

Output

Maximum water area : 20

Explanation

As shown in the figure, for wall heights 5,1,2,3 and maximum widths between walls are

Arr[0] and Arr[4] width=4, area = Arr[0]<=Arr[4] → 5*4=20
Arr[1] and Arr[4] width=3, area = Arr[1]<=Arr[4] → 1*4=4
Arr[2] and Arr[0] or Arr[4] width=4, area = Arr[0]<=Arr[0] → 2*2=4
Arr3] and Arr[0] width=3, area = Arr[0]<=Arr[0] → 3*3=9
Arr[4] and Arr[0] width=4, area = Arr[0]<=Arr[4] → 5*4=20

Maximum area container will have maximum water, area=20, walls Arr[0] and Arr[4]

Input

Arr[]= { 1, 5, 4, 3, 2, 4 }

Output

Maximum water area : 16

Explanation

Arr[0] and Arr[5] width=5, area = Arr[0]<=Arr[5] → 1*5= 5
Arr[1] and Arr[5] width=4, area = Arr[1]<=Arr[5] → 4*4=16
Arr[2] and Arr[5] width=3, area = Arr[2]<=Arr[5] → 3*4=12
Arr[3] and Arr[1] width=2, area = Arr[3]<=Arr[1] → 3*2=6
Arr[4] and Arr[1] width=3, area = Arr[1]<=Arr[4] → 2*3=6
Arr[5] and Arr[1] width=4, area = Arr[1]<=Arr[4] → 4*4=16

Maximum area container will have maximum water, area=16, walls Arr[0] and Arr[4]

Approach used in the below program is as follows

• The integer array walls[] contains heights of walls.

• Function mostwater(int A[], int len) takes array of heights and the no. of elements in it and returns the area of container with most water as only height and width are available.

• We take two indexes r=len-1 and l=0 to start traversing the array from both ends.

• Integers area and maxarea are used to store area of current container and maximum container area found so far respectively. Initially 0

• int minwall,lwall,rwall stores the height of left wall ( A[l] ), right wall ( A[r] ), and minimum height of lwall and rwall;

• While ( l<r ) traverse array and for each A[l] and A[r], height of water will be minimum of two. Whichever is minimum store in minwall

• Width between two walls is difference of indexes ( r-l )

• Calculate area of water/container as minwall* ( r-l ) and update area.

• Do this for all walls, if current area is maximum so far update maxarea.

• In the end maxarea will have the desired area of container with most water.

• Return maxarea as result.

Example

 Live Demo

#include<iostream>
using namespace std;
int mostwater(int A[], int len){
   int r=len-1; //index of right wall of container
   int l=0; //index of left wall of container
   int area=0,maxarea=0;
   int minwall,lwall,rwall;
   // int area = 0;
   while (l < r){
      // Calculating the max area
      lwall = A[l]; //height of left wall of container
      rwall =A[r]; //height of right wall of container
      minwall=lwall<=rwall?lwall:rwall; //min. of two walls is height of water
      area=minwall*(r-l); // area is min wall* widht(r-l)
      maxarea=area>=maxarea?area:maxarea;
      if (l < r)
         l += 1;
      else
         r -= 1;
   }
   return maxarea;
}
int main(){
   int walls[] = {1, 5, 4, 3, 2, 4};
   int num = sizeof(walls) / sizeof(walls[0]);
   cout << endl <<"Container with Most water has area:"<< mostwater(walls,num);
}

Output

Container with Most water has area:16