def __init__(self, height, width, piece_counts):
"""Assigns board size and create piece abstractions"""
self.height = height
self.width = width
self.threat_cache = ThreatCache(height, width)
self.pieces = []
# Sorted list of pieces based on how many squares will they cover
for piece in ['Q', 'R', 'B', 'K', 'N']:
self.pieces += [piece for _ in range(piece_counts[piece])]
self.elapsed_time = None # Problem resolution time in float seconds
# Unique list of simple string solutions
self.raw_solutions = set()
# List of pretty printed solutions (only showing up to MAX_SOLUTIONS)
self.solutions = []
class ChessPlayer(object):
"""Create all possible solutions for the given pieces and board size"""
MAX_SOLUTIONS = 15
def __init__(self, height, width, piece_counts):
"""Assigns board size and create piece abstractions"""
self.height = height
self.width = width
self.threat_cache = ThreatCache(height, width)
self.pieces = []
# Sorted list of pieces based on how many squares will they cover
for piece in ['Q', 'R', 'B', 'K', 'N']:
self.pieces += [piece for _ in range(piece_counts[piece])]
self.elapsed_time = None # Problem resolution time in float seconds
# Unique list of simple string solutions
self.raw_solutions = set()
# List of pretty printed solutions (only showing up to MAX_SOLUTIONS)
self.solutions = []
def run(self):
"""
Starts the backtracking algorithm process from top to down,
setting the initial state
"""
start = time.clock()
free_positions = set()
assigned_positions = ''
# Generate all board position coordinates as tuples
for i in range(self.height):
for j in range(self.width):
assigned_positions += '-'
free_positions.add((i, j))
# Start backtracking algorithm
self._solve(free_positions, set(), list(assigned_positions), 0)
self.elapsed_time = time.clock() - start
def _solve(self, free_positions, occupied_positions, assigned_positions,
piece_index):
"""
Iterates through the search tree recursively, from the root down,
in depth-first order, until it finds a valid solution or it runs
out of elegible chess positions
"""
if piece_index == len(self.pieces):
# Found solution as there are no more pieces to assign
self.raw_solutions.add(''.join(assigned_positions))
return
piece = self.pieces[piece_index] # Retrieve next chess piece
for free_position in free_positions:
# Retrieve all positions current piece threatens in this slot
threatened_positions = set(
self.threat_cache.get_threats(piece, free_position))
if threatened_positions & occupied_positions:
# Current piece threatens a previously placed one: backtrack
continue
occupied_copy = occupied_positions.copy()
assigned_copy = assigned_positions[:]
# Occupy that slot for further iterations
occupied_copy.add(free_position)
# Add new position to the current piece
assigned_copy[
free_position[0] * self.width + free_position[1]] = piece
# Recursive call with updated free, occupied and assigned slots,
# for the next piece index
self._solve(free_positions - threatened_positions - occupied_copy,
occupied_copy, assigned_copy, piece_index + 1)
def draw_boards(self):
"""Concatenates all tracked unique solution strings"""
n_solutions = len(self.raw_solutions)
output = "\nSolutions:\n\n"
if n_solutions > self.MAX_SOLUTIONS:
# Show only up to MAX_SOLUTIONS number of solutions
output += ("(only showing up to {} unique solutions)\n"
"").format(self.MAX_SOLUTIONS)
limit = self.MAX_SOLUTIONS
else:
limit = n_solutions
for _ in range(limit):
solution = self._generate_board(self.raw_solutions.pop())
self.solutions.append(solution)
output += "{}\n".format(solution)
output += "{} solutions found in {} seconds\n".format(
n_solutions, self.elapsed_time)
return output
def _generate_board(self, layout):
"""
Creates a pretty formatted string from a dictionary of piece types
assigned to one or more positions
"""
output = "* " * (self.width + 1) + "*\n"
for i in range(0, self.width * self.height, self.width):
output += "*{}*\n".format(
layout[i:i+self.width].replace('', ' '))
output += "* " * (self.width + 1) + "*\n"
return output
