Polyomino puzzle solver

Given a "building set" of polyominos and a universe polyomino, program outputs whether it is possible to build the universe polyomino with polyominos from the building set.

This problem is actually just a restricted version of the exact cover problem, and as such it is solved using Knuth's Algorithm X.

Requirements

A working ghc compiler or any online Haskell compiler.

Usage

Compile Main

ghc Main.hs

Run program

./Main "input.txt"

Input

Program accepts text inputs of the polyominos as shapes built from points on the plane, in the following format:

 (u0_x,u0_y) (u1_x,u1_y) ... (un_x,un_y)

 (pA0_x,pA0_y) (pA1_x,pA1_y) ... (pAn_x,pAn_y)

 ...

 (pN0_x,pN0_y) (pN1_x,pN1_y) ... (pNn_x,pNn_y)

Where u0, u1 etc. are points forming the universe polyomino and pA0, ..., pAn are points forming polyomino A from the polyomino set (and so on until the N polyomino).

Example input

(0,0) (0,1) (0,2) (1,0) (1,1) (1,2) (2,0) (2,1) (2,2)

(0,0) (0,1) (1,0)

(0,0) (1,0)

(1,0) (1,1) (0,1) (1,2)

Test inputs can be found in tests

Output

Program outputs the graphical representation of the inputted universe polyomino, all the polyominos from building set, and a boolean answer to the puzzle.

Output for the example input

Your universe:

ooo

ooo

ooo


Your polyominos:

oo

o 


oo


 o
 
oo

 o


Solution to the problem: True.