Programming Contest Question: Counting Polyominos

Question

Please see my own answer, I think I did it!

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Hi,

An example question for a programming contest was to write a program that finds out ho

Answer 1

Just solved this as well in java. Since all here appear to have performance issues. I give you mine as well.

Board reprsentation:

2 arrays of integers. 1 for the rows and 1 for the columns.

• Rotation: column[i]=row[size-(i+1)], row[i] = reverse(column[i]) where reverse is the bits reversed according to the size (for size = 4 and first 2 bits are taken: rev(1100) = 0011)
• Shifting block: row[i-1] = row[i], col[i]<<=1
• Check if bit is set: (row[r] & (1<<c)) > 0
• Board uniqueness: The board is unique when the array row is unique.
• Board hash: Hashcode of the array row
• ..

So this makes all operations fast. Many of them would have been O(size²) in the 2D array representation instead of now O(size).

Algorithm:

• Start with the block of size 1
• For each size start from the blocks with 1 stone less.
• If it's possible to add the stone. Check if it was already added to the set.
• If it's not yet added. Add it to the solution of this size.
  • add the block to the set and all its rotations. (3 rotations, 4 in total)
  • Important, after each rotation shift the block as left/top as possible.
• +Special cases: do the same logic for the next 2 cases
  • shift block one to the right and add stone in first column
  • shift block one to the bottom and add stone in first row

Performance:

• N=5 , time: 3ms
• N=10, time: 58ms
• N=11, time: 166ms
• N=12, time: 538ms
• N=13, time: 2893ms
• N=14, time:17266ms
• N=15, NA (out of heapspace)

Code: https://github.com/Samjayyy/logicpuzzles/tree/master/polyominos