Pizza cut problem (Or Circle Division by Lines)

Last Updated : 16 Jun, 2022

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# 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:

Time Complexity: O(1)

Auxiliary Space: O(1)

Angular Sweep (Maximum points that can be enclosed in a circle of given radius)

kartik

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Geometric

Pizza cut problem (Or Circle Division by Lines)

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