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

In the previous article, we have discussed Python Program for Minimum Perimeter of n Blocks
Given a grid of size N*M the task is to find the number of rectangles in the given grid in Python, Number of rectangles in a 4×4 grid, Number of rectangles formula, number of rectangles in a 3×3 grid, number of squares in mn grid, number of rectangles in the grid shown which are not squares is, count number of rectangles given points, number of rectangles in a grid leetcode, formula for number of squares in a grid, number of squares in m*n grid, number of rectangles in mxn grid, python program to find area of rectangle, you will get an idea.

Examples:

Example1:

Input:

Given N = 6
Given M = 4

Output:

Number of Rectangles in the grid of size { 6 * 4 } : 210

Example2:

Input:

Given N = 4
Given M = 2

Output:

Number of Rectangles in the grid of size { 4 * 2 } : 30

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

Below are the ways to find the number of rectangles in the given N*M:

Using Mathematical Formula (Static Input)
Using Mathematical Formula (User Input)

Let’s try to come up with a formula for the number of rectangles.

There is one rectangle in a grid of 1*1

There will be 2 + 1 = 3 rectangles if the grid is 2*1.

There will be 3 + 2 + 1 = 6 rectangles if the grid is 3*1

The formula for Number of Rectangles = M(M+1)(N)(N+1)/4

Method #1: Using Mathematical Formula (Static Input)

Approach:

Give the number N as static input and store it in a variable.
Give the number M as static input and store it in another variable.
Create a function getCountRect() which accepts given N, M grid sides as arguments and returns the number of rectangles.
Inside the getCountRect() function Calculate the number of rectangles using the MatheMatical Formula M(M+1)(N)(N+1)/4 and store it in a variable say reslt.
Return the reslt value.
Inside the Main Function.
Pass the given N, M as arguments to getCountRect() function and store the result returned from the function in a variable say countRect.
Print the countRect value.
The Exit of the Program.

Below is the implementation:

# Create a function getCountRect() which accepts given N, M grid sides
# as arguments and returns the number of rectangles.


def getCountRect(nVal, mVal):
        # Inside the getCountRect() function Calculate the number of rectangles
    # using the MatheMatical Formula M(M+1)(N)(N+1)/4 
    # and store it in a variable say reslt.
    reslt = (mVal * nVal * (nVal + 1) * (mVal + 1)) / 4
    # Return the reslt value.
    return reslt


# Inside the Main Function.
# Give the number N as static input and store it in a variable.
nVal = 6
# Give the number M as static input and store it in another variable.
mVal = 4
# Pass the given N, M as arguments to getCountRect() function
# and store the result returned from the function in a variable say countRect.
countRect = int(getCountRect(nVal, mVal))
# Print the countRect value.
print(
    'Number of Rectangles in the grid of size {', nVal, '*', mVal, '} :', countRect)

#include <iostream>

using namespace std;
int getCountRect ( int nVal, int mVal ) {
  int reslt = ( mVal * nVal * ( nVal + 1 ) * ( mVal + 1 ) ) / 4;
  return reslt;
}
int main() {
    int nVal = 6;
  int mVal = 4;
  int countRect = ( int ) getCountRect ( nVal, mVal );
  cout << "Number of Rectangles in the grid of size {" << nVal << '*' << mVal << " } is: " << countRect << endl;
  return 0;
}

Output:

Number of Rectangles in the grid of size { 6 * 4 } : 210

Method #2: Using Mathematical Formula (User Input)

Approach:

Give the number N as user input using the int(input()) function and store it in a variable.
Give the number M as user input using the int(input()) function and store it in another variable.
Create a function getCountRect() which accepts given N, M grid sides as arguments and returns the number of rectangles.
Inside the getCountRect() function Calculate the number of rectangles using the MatheMatical Formula M(M+1)(N)(N+1)/4 and store it in a variable say reslt.
Return the reslt value.
Inside the Main Function.
Pass the given N, M as arguments to getCountRect() function and store the result returned from the function in a variable say countRect.
Print the countRect value.
The Exit of the Program.

Below is the implementation:

# Create a function getCountRect() which accepts given N, M grid sides
# as arguments and returns the number of rectangles.


def getCountRect(nVal, mVal):
        # Inside the getCountRect() function Calculate the number of rectangles
    # using the MatheMatical Formula M(M+1)(N)(N+1)/4 
    # and store it in a variable say reslt.
    reslt = (mVal * nVal * (nVal + 1) * (mVal + 1)) / 4
    # Return the reslt value.
    return reslt


# Inside the Main Function.
# Give the number N as user input using the int(input()) function and store it in a variable.
nVal = int(input('Enter Some Random N value = '))
# Give the number M as static input and store it in another variable.
mVal = int(input('Enter Some Random M value = '))
# Pass the given N, M as arguments to getCountRect() function
# and store the result returned from the function in a variable say countRect.
countRect = int(getCountRect(nVal, mVal))
# Print the countRect value.
print(
    'Number of Rectangles in the grid of size {', nVal, '*', mVal, '} :', countRect)

Output:

Enter Some Random N value = 4
Enter Some Random M value = 2
Number of Rectangles in the grid of size { 4 * 2 } : 30

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