Cake Distribution Problem

Given two integers N and M, where N is the number of friends sitting in a clockwise manner in a circle and M is the number of cakes. The task is to calculate the left number of cakes after distributing i cakes to i’th friend. The distribution of cakes will stop if the count of cakes is less than the required amount.

Examples:

Input: N = 4, M = 11
Output: 0
1st round:
The 1st friend gets 1 cake, 2nd gets 2 cakes,
3rd get 3 and 4th gets 4 cakes.
Remaining cakes = 11 – (1 + 2 + 3 + 4) = 1
2nd round:
This time only 1st friend gets the left 1 cake.
Remaining cakes = 1 – 1 = 0

Input: N = 3, M = 8
Output: 1
1st round:
The 1st friend gets 1 cake, 2nd gets 2 cakes,
and 3rd get 3 cakes.
Remaining cakes = 8 – (1 + 2 + 3) = 2
2nd round:
This time only 1st friend gets the left 1 cake,
and then there is no cake left for 2nd friend.
Remaining cakes = 2 – 1 = 1

Approach:



  • Check how many cycles of distribution of cakes are possible from m number of cakes.
  • Calculate the number of cakes for 1 cycle which is
    sum = n * (n + 1) / 2
  • Now diving M by sum we get cycle count + some remainder.
  • Now check how many remaining cakes are again possible to distribute to x friends.
  • The value of x can be easily achieved by solving quadratic equation
    remainder = x * (x + 1) / 2

Below is the implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ implementation of the approach 
#include<bits/stdc++.h>
using namespace std;
  
// Function to return the 
// remaining count of cakes 
int cntCakes(int n, int m)
  
    // Sum for 1 cycle 
    int sum = (n * (n + 1)) / 2;
  
    // no. of full cycle and remainder 
    int quo = m/sum ;
    int rem = m % sum ;
    double ans = m - quo * sum ;
  
    double x = (-1 + pow((8 * rem) + 1, 0.5)) / 2;
      
    ans = ans - x * (x + 1) / 2;
  
    return int(ans);
}
  
// Driver Code
int main () 
{
    int n = 3;
    int m = 8; 
    int ans = cntCakes(n, m);
    cout << (ans);
}
  
// This code is contributed by Surendra_Gangwar

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java implementation of the approach 
class GFG 
{
      
    // Function to return the 
    // remaining count of cakes 
    static int cntCakes(int n, int m)
    
      
        // Sum for 1 cycle 
        int sum = (n * (n + 1)) / 2;
      
        // no. of full cycle and remainder 
        int quo = m/sum ;
        int rem = m % sum ;
        double ans = m - quo * sum ;
      
        double x = (-1 + Math.pow((8 * rem) + 1, 0.5)) / 2;
          
        ans = ans - x * (x + 1) / 2;
      
        return (int)ans;
    }
  
    // Driver Code
    public static void main (String[] args) 
    {
        int n = 3;
        int m = 8
        int ans = cntCakes(n, m);
        System.out.println(ans);
    }
}
  
// This code is contributed by AnkitRai01

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 implementation of the approach
  
# Function to return the 
# remaining count of cakes
def cntCakes(n, m):
  
    # Sum for 1 cycle
    sum = (n*(n + 1))//2
  
    # no. of full cycle and remainder
    quo, rem = m//sum, m % sum
    ans = m - quo * sum
  
    x = int((-1 + (8 * rem + 1)**0.5)/2)
    ans = ans - x*(x + 1)//2
  
    return ans
  
# Driver code
def main():
  n = 4
  m = 11
  ans = cntCakes(n, m)
  print(ans)
  
main()

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# implementation of the approach
using System;
  
class GFG
{
    // Function to return the 
    // remaining count of cakes 
    static int cntCakes(int n, int m)
    
      
        // Sum for 1 cycle 
        int sum = (n * (n + 1)) / 2;
      
        // no. of full cycle and remainder 
        int quo = m/sum ;
        int rem = m % sum ;
        double ans = m - quo * sum ;
      
        double x = (-1 + Math.Pow((8 * rem) + 1, 0.5)) / 2;
          
        ans = ans - x * (x + 1) / 2;
      
        return (int)ans;
    }
  
    // Driver Code
    static public void Main ()
    {
        int n = 3;
        int m = 8; 
        int ans = cntCakes(n, m);
        Console.Write(ans);
    }
}
  
// This code is contributed by ajit.

chevron_right


Output:

0

Time Complexity: O(1)

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.




My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Article Tags :
Practice Tags :


Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.