# Maximum number of pieces in N cuts

Given a square piece and a total number of cuts available n, Find out the maximum number of rectangular or square pieces of equal size that can be obtained with n cuts. The allowed cuts are horizontal and vertical cut. **Note:** Stacking and folding is not allowed.**Examples**:

Input: n = 1Output: 2Explanation:

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Input: n = 2Output: 4Explanation:

Input: n = 3Output: 6Explanation:

Given is n which is the number of allowed cuts. As it is required to maximize number of pieces after n cuts, So number of horizontal cuts will be equal to number of vertical cuts. This can be prove using differentiation. So number of horizontal cut will be n/2. and vertical cuts will be n-n/2.

So **number of pieces = (horizontal cut + 1) * (vertical cut + 1).****Program:**

## 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)` `{` ` ` `// to maximize number of pieces` ` ` `// x is the horizontal cuts` ` ` `int` `x = n / 2;` ` ` `// Now (x) is the horizontal cuts` ` ` `// and (n-x) is vertical cuts, then` ` ` `// maximum number of pieces = (x+1)*(n-x+1)` ` ` `return` `((x + 1) * (n - x + 1));` `}` `// Driver code` `int` `main()` `{` ` ` `// Taking the maximum number of cuts allowed as 3` ` ` `int` `n = 3;` ` ` `// Finding and printing the max number of pieces` ` ` `cout << ` `"Max number of pieces for n = "` `<< n` ` ` `<< ` `" is "` `<< findMaximumPieces(3);` ` ` `return` `0;` `}` |

## Java

`// Java program to find maximum` `// no of pieces by given number` `// of cuts` `import` `java.util.*;` `class` `GFG` `{` `// Function for finding maximum` `// pieces with n cuts.` `public` `static` `int` `findMaximumPieces(` `int` `n)` `{` ` ` `// to maximize number of pieces` ` ` `// x is the horizontal cuts` ` ` `int` `x = n / ` `2` `;` ` ` `// Now (x) is the horizontal cuts` ` ` `// and (n-x) is vertical cuts, then` ` ` `// maximum number of pieces = (x+1)*(n-x+1)` ` ` `return` `((x + ` `1` `) * (n - x + ` `1` `));` `}` `// Driver code` `public` `static` `void` `main (String[] args)` `{` ` ` `// Taking the maximum number` ` ` `// of cuts allowed as 3` ` ` `int` `n = ` `3` `;` ` ` ` ` `// Finding and printing the` ` ` `// max number of pieces` ` ` `System.out.print(` `"Max number of pieces for n = "` `+` ` ` `n + ` `" is "` `+ findMaximumPieces(` `3` `));` ` ` `}` `}` `// This code is contributed by Kirti_Mangal` |

## Python 3

`# Python 3 program to find maximum no of pieces` `# by given number of cuts` ` ` `# Function for finding maximum pieces` `# with n cuts.` `def` `findMaximumPieces(n):` ` ` `# to maximize number of pieces` ` ` `# x is the horizontal cuts` ` ` `x ` `=` `n ` `/` `/` `2` ` ` ` ` `# Now (x) is the horizontal cuts` ` ` `# and (n-x) is vertical cuts, then` ` ` `# maximum number of pieces = (x+1)*(n-x+1)` ` ` `return` `((x ` `+` `1` `) ` `*` `(n ` `-` `x ` `+` `1` `))` ` ` `# Driver code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` ` ` `#Taking the maximum number of cuts allowed as 3` ` ` `n ` `=` `3` ` ` ` ` `# Finding and printing the max number of pieces` ` ` `print` `(` `"Max number of pieces for n = "` `+` `str` `( n)` ` ` `+` `" is "` `+` `str` `(findMaximumPieces(` `3` `)))` `# This code is contributed by ChitraNayal` |

## 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.` `public` `static` `int` `findMaximumPieces(` `int` `n)` `{` ` ` `// to maximize number of pieces` ` ` `// x is the horizontal cuts` ` ` `int` `x = n / 2;` ` ` `// Now (x) is the horizontal ` ` ` `// cuts and (n-x) is vertical` ` ` `// cuts, then maximum number` ` ` `// of pieces = (x+1)*(n-x+1)` ` ` `return` `((x + 1) * (n - x + 1));` `}` `// Driver code` `static` `public` `void` `Main ()` `{` ` ` `// Taking the maximum number` ` ` `// of cuts allowed as 3` ` ` `int` `n = 3;` ` ` ` ` `// Finding and printing the` ` ` `// max number of pieces` ` ` `Console.Write(` `"Max number of pieces for n = "` `+` ` ` `n + ` `" is "` `+ findMaximumPieces(3));` `}` `}` `// This code is contributed by Mahadev` |

## 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(` `$n` `)` `{` ` ` `// to maximize number of pieces` ` ` `// x is the horizontal cuts` ` ` `$x` `= (int)(` `$n` `/ 2);` ` ` `// Now (x) is the horizontal cuts` ` ` `// and (n-x) is vertical cuts, then` ` ` `// maximum number of pieces = (x+1)*(n-x+1)` ` ` `return` `((` `$x` `+ 1) * (` `$n` `- ` `$x` `+ 1));` `}` `// Driver code` `// Taking the maximum number` `// of cuts allowed as 3` `$n` `= 3;` `// Finding and printing the` `// max number of pieces` `echo` `"Max number of pieces for n = "` `.` ` ` `$n` `. ` `" is "` `. findMaximumPieces(3);` `// This code is contributed` `// by Akanksha Rai(Abby_akku)` `?>` |

## 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)` `{` ` ` `// to maximize number of pieces` ` ` `// x is the horizontal cuts` ` ` `var` `x = parseInt(n / 2);` ` ` `// Now (x) is the horizontal cuts` ` ` `// and (n-x) is vertical cuts, then` ` ` `// maximum number of pieces = (x+1)*(n-x+1)` ` ` `return` `((x + 1) * (n - x + 1));` `}` `// Driver code` `// Taking the maximum number of cuts allowed as 3` `var` `n = 3;` `// Finding and printing the max number of pieces` `document.write(` `"Max number of pieces for n = "` `+ n` ` ` `+ ` `" is "` `+ findMaximumPieces(3));` `// This code is contributed by noob2000.` `</script>` |

**Output:**

Max number of pieces for n = 3 is 6