Program for Minimum Perimeter of n Blocks

Python Program for Minimum Perimeter of n Blocks

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In the previous article, we have discussed Python Program To Find Area of a Circular Sector
Given n blocks of size 1*1, the task is to find the minimum perimeter of the grid made by these given n blocks in python.

Examples:

Example1:

Input:

Given n value = 6

Output:

The minimum perimeter of the grid made by the given n blocks{ 6 } =  11

Example2:

Input:

Given n value = 9

Output:

The minimum perimeter of the grid made by the given n blocks{ 9 } =  12

Program for Minimum Perimeter of n Blocks in Python

Below are the ways to find the minimum perimeter of the grid made by these given n blocks in python:

Method #1: Using Mathematical Approach (Static Input)

Approach:

  • Import math module using the import keyword.
  • Give the n value as static input and store it in a variable.
  • Create a function to say Minimum_perimtr() which takes the given n value as an argument and returns the minimum perimeter of the grid made by these given n blocks.
  • Calculate the square root of the given n value using the math.sqrt() function and store it in a variable say sqrt_val.
  • Multiply the above result with itself and store it in another variable.
  • Check if the given n value is a perfect square by using the if conditional statement.
  • If it is true, then return the value of above sqrt_val multiplied by 4.
  • Else calculate the number of rows by dividing the given n value by sqrt_val.
  • Add the above sqrt_val with the number of rows obtained and multiply the result by 2 to get the perimeter of the rectangular grid.
  • Store it in another variable.
  • Check whether there are any blocks left using the if conditional statement.
  • If it is true, then add 2 to the above-obtained perimeter of the rectangular grid and store it in the same variable.
  • Return the minimum perimeter of the grid made by the given n blocks.
  • Pass the given n value as an argument to the Minimum_perimtr() function, convert it into an integer using the int() function and store it in another variable.
  • Print the above result which is the minimum perimeter of the grid made by the given n blocks.
  • The Exit of the Program.

Below is the implementation:

# Import math module using the import keyword.
import math

# Create a function to say Minimum_perimtr() which takes the given n value as an
# argument and returns the minimum perimeter of the grid made by these given n blocks.


def Minimum_perimtr(gvn_n_val):
    # Calculate the square root of the given n value using the math.sqrt() function
    # and store it in a variable say sqrt_val.
    sqrt_val = math.sqrt(gvn_n_val)
    # Multiply the above result with itself and store it in another variable.
    sqre_rslt = sqrt_val * sqrt_val

    # Check if the given n value is a perfect square by using the if
    # conditional statement.
    if (sqre_rslt == gvn_n_val):
        # If it is true, then return the value of above sqrt_val multiplied by 4.
        return sqrt_val * 4
    else:
        # Else calculate the number of rows by dividing the given n value by sqrt_val.
        no_of_rows = gvn_n_val / sqrt_val

        # Add the above sqrt_val with the number of rows obtained and multiply the result
        # by 2 to get the perimeter of the rectangular grid.
        # Store it in another variable.
        rslt_perimetr = 2 * (sqrt_val + no_of_rows)

        # Check whether there are any blocks left using the if conditional statement.
        if (gvn_n_val % sqrt_val != 0):
            # If it is true, then add 2 to the above-obtained perimeter of the rectangular
                    # grid and store it in the same variable.
            rslt_perimetr += 2
        # Return the minimum perimeter of the grid made by the given n blocks.
        return rslt_perimetr


# Give the n value as static input and store it in a variable.
gvn_n_val = 6
# Pass the given n value as an argument to the Minimum_perimtr() function, convert
# it into an integer using the int() function and store it in another variable.
fnl_rslt = int(Minimum_perimtr(gvn_n_val))
# Print the above result which is the minimum perimeter of the grid made by the
# given n blocks.
print(
    "The minimum perimeter of the grid made by the given n blocks{", gvn_n_val, "} = ", fnl_rslt)

#include <iostream>
#include<math.h>
using namespace std;
int Minimum_perimtr ( int gvn_n_val ) {
  int sqrt_val = sqrt ( gvn_n_val );
  int sqre_rslt = sqrt_val * sqrt_val;
  if (  sqre_rslt == gvn_n_val  ) {
    return sqrt_val * 4;
  }
  else {
    int no_of_rows = gvn_n_val / sqrt_val;
    int rslt_perimetr = 2 * ( sqrt_val + no_of_rows );
    if ( ( gvn_n_val % sqrt_val != 0 )  ) {
      rslt_perimetr += 2;
    }
    return rslt_perimetr;
  }
}
int main() {
   int gvn_n_val = 6;
 int fnl_rslt = ( int ) Minimum_perimtr ( gvn_n_val );
  cout << "The minimum perimeter of the grid made by the given n blocks{" << gvn_n_val << "} = " << fnl_rslt << endl;
  return 0;
}

Output:

The minimum perimeter of the grid made by the given n blocks{ 6 } =  11

Method #2: Using Mathematical Approach (User Input)

Approach:

  • Import math module using the import keyword.
  • Give the n value as user input using the int(input()) function input and store it in a variable.
  • Create a function to say Minimum_perimtr() which takes the given n value as an argument and returns the minimum perimeter of the grid made by these given n blocks.
  • Calculate the square root of the given n value using the math.sqrt() function and store it in a variable say sqrt_val.
  • Multiply the above result with itself and store it in another variable.
  • Check if the given n value is a perfect square by using the if conditional statement.
  • If it is true, then return the value of above sqrt_val multiplied by 4.
  • Else calculate the number of rows by dividing the given n value by sqrt_val.
  • Add the above sqrt_val with the number of rows obtained and multiply the result by 2 to get the perimeter of the rectangular grid.
  • Store it in another variable.
  • Check whether there are any blocks left using the if conditional statement.
  • If it is true, then add 2 to the above-obtained perimeter of the rectangular grid and store it in the same variable.
  • Return the minimum perimeter of the grid made by the given n blocks.
  • Pass the given n value as an argument to the Minimum_perimtr() function, convert it into an integer using the int() function and store it in another variable.
  • Print the above result which is the minimum perimeter of the grid made by the given n blocks.
  • The Exit of the Program.

Below is the implementation:

# Import math module using the import keyword.
import math

# Create a function to say Minimum_perimtr() which takes the given n value as an
# argument and returns the minimum perimeter of the grid made by these given n blocks.


def Minimum_perimtr(gvn_n_val):
    # Calculate the square root of the given n value using the math.sqrt() function
    # and store it in a variable say sqrt_val.
    sqrt_val = math.sqrt(gvn_n_val)
    # Multiply the above result with itself and store it in another variable.
    sqre_rslt = sqrt_val * sqrt_val

    # Check if the given n value is a perfect square by using the if
    # conditional statement.
    if (sqre_rslt == gvn_n_val):
        # If it is true, then return the value of above sqrt_val multiplied by 4.
        return sqrt_val * 4
    else:
        # Else calculate the number of rows by dividing the given n value by sqrt_val.
        no_of_rows = gvn_n_val / sqrt_val

        # Add the above sqrt_val with the number of rows obtained and multiply the result
        # by 2 to get the perimeter of the rectangular grid.
        # Store it in another variable.
        rslt_perimetr = 2 * (sqrt_val + no_of_rows)

        # Check whether there are any blocks left using the if conditional statement.
        if (gvn_n_val % sqrt_val != 0):
            # If it is true, then add 2 to the above-obtained perimeter of the rectangular
                    # grid and store it in the same variable.
            rslt_perimetr += 2
        # Return the minimum perimeter of the grid made by the given n blocks.
        return rslt_perimetr


# Give the n value as user input using the int(input()) function input and
# store it in a variable.
gvn_n_val = int(input("Enter some random number = "))
# Pass the given n value as an argument to the Minimum_perimtr() function, convert
# it into an integer using the int() function and store it in another variable.
fnl_rslt = int(Minimum_perimtr(gvn_n_val))
# Print the above result which is the minimum perimeter of the grid made by the
# given n blocks.
print(
    "The minimum perimeter of the grid made by the given n blocks{", gvn_n_val, "} = ", fnl_rslt)

Output:

Enter some random number = 9
The minimum perimeter of the grid made by the given n blocks{ 9 } = 12

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