# 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 = 1
Output : 2
Explanation : ``` ```Input : n = 2
Output : 4
Explanation : ``` ```Input : n = 3
Output : 6
Explanation : ``` ` `

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 ` `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

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## Javascript

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Output:

`Max number of pieces for n = 3 is 6`

Time Complexity: O(1)
Auxiliary Space: O(1)

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