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Pizza cut problem (Or Circle Division by Lines)

  • Difficulty Level : Basic
  • Last Updated : 24 Mar, 2021
Geek Week

Given number of cuts, find the maximum number of possible pieces.
Examples: 
 

Input  : 2
Output : 4

Input  : 3
Output : 7

 

This problem is nothing but The Lazy Caterer’s Problem and has below formula.
Maximum number of pieces = 1 + n*(n+1)/2
Refer this for proof.
 

C++




// C++ program to find maximum no of pieces
// by given number of cuts
#include<bits/stdc++.h>
using namespace std;
 
// Function for finding maximum pieces
// with n cuts.
int findMaximumPieces(int n)
{
   return 1 + n*(n+1)/2;   
}
 
// Driver code
int main()
{
   cout << findMaximumPieces(3);
   return 0;
}

Java




// Java program to find maximum no of
// pieces by given number of cuts
class GFG {
     
    // Function for finding maximum pieces
    // with n cuts.
    static int findMaximumPieces(int n)
    {
        return 1 + n * (n + 1) / 2;
    }
     
    // Driver Program to test above function
    public static void main(String arg[])
    {
         
        System.out.print(findMaximumPieces(3));
    }
}
 
// This code is contributed by Anant Agarwal.

Python3




# Python3 program to find maximum
# no. of pieces by given
# number of cuts
 
# Function for finding maximum
# pieces with n cuts.
def findMaximumPieces(n):
    return int(1 + n * (n + 1) / 2)
 
# Driver code
print(findMaximumPieces(3))
 
# This code is contributed 29AjayKumar

C#




// C# program to find maximum no of
// pieces by given number of cuts
using System;
 
class GFG {
      
    // Function for finding maximum pieces
    // with n cuts.
    static int findMaximumPieces(int n)
    {
        return 1 + n * (n + 1) / 2;
    }
      
    // Driver Program to test above function
    public static void Main()
    {
          
        Console.Write(findMaximumPieces(3));
    }
}
  
// This code is contributed by nitin mittal.

PHP




<?php
// PHP program to find maximum
// no. of pieces by given
// number of cuts
 
// Function for finding maximum
// pieces with n cuts.
function findMaximumPieces($n)
{
    return 1 + $n * ($n + 1) / 2;
}
 
// Driver code
echo findMaximumPieces(3);
 
// This code is contributed by nitin mittal.
?>

Javascript




<script>
 
// Javascript program to find maximum no of pieces
// by given number of cuts
 
// Function for finding maximum pieces
 // with n cuts.
    function findMaximumPieces(n)
    {
        return 1 + n * (n + 1) / 2;
    }
 
// Driver Code
 
    document.write(findMaximumPieces(3));
 
</script>

Output: 

7

This article is contributed by DANISH_RAZA. 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.
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