Minimize rooms with K seats to accommodate N girls and M boys

Given three positive integers N, M, and K, the task is to find the minimum number of rooms required to accommodate all students if there are N girls and M boys, and each room has K seats. It is not allowed for a boy and a girl to stay in the same room.

Examples:

Input: N = 13, M = 7, K = 2
Output: 11
Explanation: Room required for girls = 7 (2 + 2 + 2 + 2 + 2 + 2 + 1) Room required for boys = 4 (2 + 2 + 2 + 1)

Input: N = 5, M = 5, K = 3
Output: 4
Explanation: Rooms required for girls = 2 (3 + 2) Room required for boys = 2 (3 + 2). So, we output total seats 2 + 2 = 4

Approach: This can be solved with the following idea:

This can be solved by mathematical observation. Calculating rooms required for boys and girls separately.

Steps involved in the implementation of code:

• If the number of students in a particular gender is exactly divisible by the number of seats in a room, then the number of rooms required for that gender can be calculated as the integer division of the number of students in that gender by the number of seats in a room.
• If the number of students in a particular gender is not exactly divisible by the number of seats in a room, then the number of rooms required for that gender can be calculated as the integer division of the number of students in that gender by the number of seats in a room, plus one. This is because an additional room is required to accommodate the remaining students.
• Steps 1 and 2 can be applied separately for boys and girls to calculate the minimum number of rooms required for each gender.
• The minimum number of rooms required to accommodate all students can be calculated as the maximum of the minimum number of rooms required for boys and girls, i.e., answer = max(ceil(M/K), ceil(N/K)).
• Finally, return the answer as the minimum number of rooms required to accommodate all students.

Below is the implementation of the code:

C++14

// C++ Implementation
#include <iostream>
using namespace std;

// Function to calculate rooms required
int totalRooms(int n, int m, int k)
{

    int count = 0;

    // For girls
    count += (n / k);

    // Extra space required
    if (n % k != 0) {
        count++;
    }

    // For boys
    count += (m / k);

    // Extra space required
    if (m % k != 0) {
        count++;
    }

    return count;
}

// Driver code
int main()
{

    int n = 13;
    int m = 7;
    int k = 2;

    // Function call
    cout << totalRooms(n, m, k);
    return 0;
}

Java

import java.util.*;

class Main {
    public static void main(String[] args)
    {
        int n = 13;
        int m = 7;
        int k = 2;

        // Function to calculate rooms required
        int count = 0;

        // For girls
        count += (n / k);

        // Extra space required
        if (n % k != 0) {
            count++;
        }

        // For boys
        count += (m / k);

        // Extra space required
        if (m % k != 0) {
            count++;
        }

        // Print the total number of rooms required
        System.out.println(count);
    }
}

Python

n = 13 # n=girl
m = 7 # m=boy
k = 2 # k=number of seats in each room

count = 0 # declearing count variable

''' Checking for girls '''

count += (n//k)

if (n%k !=0):
    count+=1


''' Checking for boys '''

count += (m//k)

if (m % k != 0):
    count+=1

print(count) # print the count

C#

// C# Implementation
using System;

public class GFG {
    public static void Main()
    {
        int n = 13;
        int m = 7;
        int k = 2;

        // Function to calculate rooms required
        int count = 0;

        // For girls
        count += (n / k);

        // Extra space required
        if (n % k != 0) {
            count++;
        }

        // For boys
        count += (m / k);

        // Extra space required
        if (m % k != 0) {
            count++;
        }

        // Print the total number of rooms required
        Console.WriteLine(count);
    }
}

// This code is contributed by Pushpesh Raj

Javascript

function totalRooms(n, m, k) {
  let count = 0;

  // For girls
  count += Math.floor(n / k);

  // Extra space required
  if (n % k !== 0) {
    count++;
  }

  // For boys
  count += Math.floor(m / k);

  // Extra space required
  if (m % k !== 0) {
    count++;
  }

  return count;
}

// Driver code
const n = 13;
const m = 7;
const k = 2;

// Function call
console.log(totalRooms(n, m, k));

Output

11

Time Complexity: O(1)
Auxiliary Space: O(1)