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Ind_04-20. 50520 - Filling a Matrix Randomly

IMPC-2014-15 Questions

Start: Nov.22.2014 at 03:00:00 PM
Finish: Nov.22.2014 at 08:00:00 PM
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Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
Question by Ibrahim Mesecan.

Filling a Matrix Randomly

Your physics professor, wants to analyze the effect of a random variable on a range. For that he wants fill a range with random colors in such a way that no adjacent two cells (4 sides: Up, Down, Right, Left) will have the same colors.

Question: Write a program that is going to fill a range with the given number of colors complying the given condition above.

Input specification
You will be given only three integers:

  • The number of rows (m) for the given range
  • The number of cols (n) for the given range
  • The number of colors (c) where you can use the colors from 1 to c
where m and n are integers between 0 and 500, and c is an integer between 1 and 100.

Output specification
If possible, fill the given shape with the given colors randomly. Show -1, if it's not possible to fill comply the given criterion. Note: All the colors have to be used at least once.

Sample Input I
5 4 4
Sample Input II
3 4 5
Sample Output I
4 1 4 2
1 4 2 4
2 3 4 3
3 4 1 4
4 1 3 1
Sample Output II
5 3 4 1
3 4 1 3
4 2 3 1


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