Paper cutting programs

rani m mk

Hi,

Please help me write a logic for the below:

A square paper is cut into 16 square pieces. Arrange the pieces to get the original form.

7 Replies

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Vulpes14y ago
Accepted answer
If all the pieces are of the same size, then it follows that they must be arranged in four rows of four pieces each as that's the only arrangement which is symmetrical.

If we assume that the pieces are numbered 1 to 16 (1 to 4 in the first row, 2 to 7 in the second row etc) and that they've all been shuffled so they are now in random order, we can solve the problem as follows:

using System;

class Paper
{
static Random rand = new Random();
static int[] pieces = new int[16];

static void Main()
{

while(true)
{
Array.Clear(pieces, 0, 16); // resets all elements to 0

// fill the pieces array in a random fashion
int index = 0;
int number;

while (index < 16)
{
number = rand.Next(1, 17); // gets random number between 1 to 16 (excludes endpoint);
// check if it's already been drawn and, if it hasn't put it in the array
if (Array.IndexOf(pieces, number) == -1)
{
pieces[index] = number;
index++;
}
}

// print out random pieces
Console.WriteLine("The unsorted pieces are : \n");
PrintPieces();

// now we need to sort the array to restore the original arrangement
Array.Sort(pieces);
Console.WriteLine("\nThe rearranged pieces are :\n");
PrintPieces();

Console.Write("\nDo another y/n : ");
string yn = Console.ReadLine();
if (yn == "n") return;
Console.WriteLine();
}
}

static void PrintPieces()
{
for (int row = 0; row < 4; row++)
{
for(int col = 0; col < 4; col++)
{
Console.Write(" {0,2} ", pieces[row * 4 + col]);
}
Console.WriteLine();
}
}
}
Vulpes14y ago
Here's a simple example of recursion.

The following program computes the numbers in the Fibonacci series (see link below) for values of n from 0 to 35 inclusive:

http://en.wikipedia.org/wiki/Fibonacci_number

using System;

public class Test
{

public static long Fibonacci(int n)
{
if (n < 0)
{
throw new ArgumentException("Argument can't be less than zero");
}
else if (n < 2)
{
return n;
}
else
{
return Fibonacci(n - 1) + Fibonacci(n - 2);
}
}

static void Main()
{

for (int i = 0; i < 36; i++)
{
Console.WriteLine("n = {0} => {1}", i, Fibonacci(i));
}

Console.ReadKey();
}
}

Notice how the Fibonacci method is calling itself recursively in this line:

return Fibonacci(n - 1) + Fibonacci(n - 2);

As I said earlier, I can't see how you could use recursion to solve this 'paper-cutting' problem but if anyone else has any ideas, I'd be interested to hear them.
rani m mk14y ago
Vulpes,

I thought we could use recursion,but i don`t know much about that so thought someone would guide..
Vulpes14y ago
Well, recursion is when a method calls itself.

Although you can sometimes rewrite code to use recursion rather than iteration, I don't see how you could do that in any meaningful way here.
rani m mk14y ago
Can recursion be used for this? If yes how can we use?
rani m mk14y ago
Yes Vulpes, All pieces are of same size and cut into 16 pieces.. How do we write the logic to get the original form of the paper(original form being square)
Vulpes14y ago
Is there some more information on this question - for example, whether we can assume that the pieces are all the same size and are numbered in some way?

If the square pieces can be of arbitrary size (subject to them fitting into the square paper), the question seems far too hard for a beginner or me for that matter!