Pizza cut problem (Or Circle Division by Lines)

• Difficulty Level : Easy
• 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 Catererâ€™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``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

 ``

Javascript

 ``

Output:

`7`

Time Complexity: O(1)

Auxiliary Space: O(1)

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