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require 'matrix'
BASIC_ROTATIONS = {
:x => Matrix[
[1, 0, 0],
[0, 0, -1],
[0, 1, 0]
],
:y => Matrix[
[0, 0, 1],
[0, 1, 0],
[-1, 0, 0]
],
:z => Matrix[
[0, -1, 0],
[1, 0, 0],
[0, 0, 1]
]
}
ROTATIONS = []
(0..3).each do |i|
power = BASIC_ROTATIONS[:z] ** i
ROTATIONS << power
ROTATIONS << power * (BASIC_ROTATIONS[:x] ** 2)
end
(0..3).each do |i|
power = BASIC_ROTATIONS[:y] ** i
ROTATIONS << power * BASIC_ROTATIONS[:x]
ROTATIONS << power * (BASIC_ROTATIONS[:x] ** 3)
end
(0..3).each do |i|
power = BASIC_ROTATIONS[:x] ** i
ROTATIONS << power * BASIC_ROTATIONS[:y]
ROTATIONS << power * (BASIC_ROTATIONS[:y] ** 3)
end
pieces = [
[Vector[0, -1, -1], Vector[-1, 0, -1], Vector[0, 0, -1], Vector[0, -1, 0], Vector[1, -1, 0]],
[Vector[-1, -1, -1], Vector[0, -1, -1], Vector[0, 0, -1], Vector[0, 0, 0]],
[Vector[-1, -1, -1], Vector[0, -1, -1], Vector[1, -1, -1], Vector[-1, 0, -1], Vector[-1, 0, 0]],
[Vector[-1, -1, -1], Vector[0, -1, -1], Vector[1, -1, -1], Vector[-1, 0, -1], Vector[0, -1, 0]],
[Vector[-1, -1, -1], Vector[0, -1, -1], Vector[-1, 0, -1], Vector[-1, 0, 0]],
[Vector[-1, -1, -1], Vector[0, -1, -1], Vector[1, -1, -1], Vector[-1, 0, -1]]
]
cells = []
(-1..1).each do |x|
(-1..1).each do |y|
(-1..1).each do |z|
cells << Vector[x, y, z]
end
end
end
def check_single(cells, piece, rotation, translation)
new_cells = cells.clone
piece.each do |cube|
after_cube = rotation * cube + translation
if after_cube.all?{|s| s.between?(-1, 1)}
if cells.include?(after_cube)
new_cells.delete(after_cube)
else
return nil
end
else
return nil
end
end
return new_cells
end
def check(cells, pieces, result)
return result if pieces.empty?
piece = pieces[0]
ROTATIONS.each do |rotation|
first_cube = rotation * piece[0]
cells.each do |cell|
translation = cell - first_cube
new_cells = check_single(cells, piece, rotation, translation)
if new_cells
new_result = result + [new_cells]
final_result = check(new_cells, pieces.reject{|s| s == piece}, new_result)
if final_result
return final_result
end
end
end
end
return nil
end
def output(cells)
(-1..1).each do |z|
(-1..1).each do |y|
print("[")
(-1..1).each do |x|
if cells.include?(Vector[x, y, z])
print(" ")
else
print("#")
end
end
puts("]")
end
end
end
result = check(cells, pieces, [])
if result
result.each do |each_result|
output(each_result)
puts("---")
end
else
puts("impossible")
end
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