Java Program to Find Number of Rectangles in N*M Grid

Java Program to Find Number of Rectangles in N*M Grid

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In the previous article, we have seen Java Program to Find Minimum Perimeter of n Blocks

In this article we will discuss about how to find Number of Rectangles in N*M Grid using Java programming language.

Java Program to Find Number of Rectangles in N*M Grid

Before jumping into the program directly, let’s first know how can we find the number of rectangles in M*N grid.

Formula to Find Total Rectangles in M*N Grid: (M(M+1)(N)(N+1))/4
Example:

When M=2 and N=2

Number rectangles: (M(M+1)(N)(N+1))/4

                               => (2(2+1)(2)(2+1))/4=(2*3*2*3)/4

                               => 36/4 = 9

Let’s see different ways to find number of Rectangles in N*M Grid.

Method-1: Java Program to Find Number of Rectangles in N*M Grid By Using Static Value

Approach:

  1. Declare the value for ‘m‘ and ‘n‘.
  2. Then call the rectangleCount() method by passing m and n value as parameter.
  3. In this method the number of rectangle possible will be calculated using the formula  (M(M+1)(N)(N+1))/4
  4. Then print the result.

Program:

// JAVA Code to count number of  
// rectangles in N*M grid 

public class Main
{ 
    // Driver method
    public static void main(String[] args)  
    { 
       //Value of 'n' and 'm' are declared
       int n = 2, m = 2; 
       //calling the rectangleCount() user defined method
       System.out.println("Number of rectangle : "+rectangleCount(n, m)); 
    } 
    
    //rectangleCount() method to find the number of rectangles  
    public static long  rectangleCount(int n, int m) 
    { 
        return (m * n * (n + 1) * (m + 1)) / 4; 
    } 
}

Output:

Number of rectangle : 9

Method-2: Java Program to Find Number of Rectangles in N*M Grid By User Input Value

Approach:

  1. Take user input the value for ‘m‘ and ‘n‘.
  2. Then call the rectangleCount() method by passing m and n value as parameter.
  3. In this method the number of rectangle possible will be calculated using the formula  (M(M+1)(N)(N+1))/4
  4. Then print the result.

Program:

// JAVA Code to count number of  
// rectangles in N*M grid 

import java.util.*;

public class Main 
{ 
    // Driver method
    public static void main(String[] args)  
    { 
        //Scanner classobject created
    	Scanner sc=new Scanner(System.in);
    	//Taking input of 'n' value
    	System.out.println("Enter value of N : ");
    	int n=sc.nextInt();
    	//Taking input of 'm' value
    	System.out.println("Enter value of M : ");
    	int m=sc.nextInt();
    	//calling the rectangleCount() user defined method 
    	System.out.println("Number of rectangle : "+rectangleCount(n, m));
    }
    
    //rectangleCount() method to find the number of rectangles
    public static long  rectangleCount(int n, int m) 
    { 
        return (m * n * (n + 1) * (m + 1)) / 4; 
    } 
}


Output:

Enter value of N : 2
Enter value of M : 2
Number of rectangle : 9

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