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Maximum number of pieces in N cuts

  • Difficulty Level : Medium
  • Last Updated : 20 Apr, 2021

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 <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

 


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