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kakuro.py
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from csp import *
from time import time
from itertools import permutations
######### Kakuro puzzles
# Given, 4x3
kakuro_given4x3 = [
['*', '*', '*', [6, ''], [3, '']],
['*', [4, ''], [3, 3], '_', '_'],
[['', 10], '_', '_', '_', '_'],
[['', 3], '_', '_', '*', '*']
]
#Given, 5x7
kakuro_given5x7 = [
['*', [17, ''], [28, ''], '*', [42, ''], [22, '']],
[['', 9], '_', '_', [31, 14], '_', '_'],
[['', 20], '_', '_', '_', '_', '_'],
['*', ['', 30], '_', '_', '_', '_'],
['*', [22, 24], '_', '_', '_', '*'],
[['', 25], '_', '_', '_', '_', [11, '']],
[['', 20], '_', '_', '_', '_', '_'],
[['', 14], '_', '_', ['', 17], '_', '_']
]
# Given, 14x14
kakuro_given14x14 = [
['*', '*', '*', '*', '*', [4, ''], [24, ''], [11, ''], '*', '*', '*', [11, ''], [17, ''], '*', '*'],
['*', '*', '*', [17, ''], [11, 12], '_', '_', '_', '*', '*', [24, 10], '_', '_', [11, ''], '*'],
['*', [4, ''], [16, 26], '_', '_', '_', '_', '_', '*', ['', 20], '_', '_', '_', '_', [16, '']],
[['', 20], '_', '_', '_', '_', [24, 13], '_', '_', [16, ''], ['', 12], '_', '_', [23, 10], '_', '_'],
[['', 10], '_', '_', [24, 12], '_', '_', [16, 5], '_', '_', [16, 30], '_', '_', '_', '_', '_'],
['*', '*', [3, 26], '_', '_', '_', '_', ['', 12], '_', '_', [4, ''], [16, 14], '_', '_', '*'],
['*', ['', 8], '_', '_', ['', 15], '_', '_', [34, 26], '_', '_', '_', '_', '_', '*', '*'],
['*', ['', 11], '_', '_', [3, ''], [17, ''], ['', 14], '_', '_', ['', 8], '_', '_', [7, ''], [17, ''], '*'],
['*', '*', '*', [23, 10], '_', '_', [3, 9], '_', '_', [4, ''], [23, ''], ['', 13], '_', '_', '*'],
['*', '*', [10, 26], '_', '_', '_', '_', '_', ['', 7], '_', '_', [30, 9], '_', '_', '*'],
['*', [17, 11], '_', '_', [11, ''], [24, 8], '_', '_', [11, 21], '_', '_', '_', '_', [16, ''], [17, '']],
[['', 29], '_', '_', '_', '_', '_', ['', 7], '_', '_', [23, 14], '_', '_', [3, 17], '_', '_'],
[['', 10], '_', '_', [3, 10], '_', '_', '*', ['', 8], '_', '_', [4, 25], '_', '_', '_', '_'],
['*', ['', 16], '_', '_', '_', '_', '*', ['', 23], '_', '_', '_', '_', '_', '*', '*'],
['*', '*', ['', 6], '_', '_', '*', '*', ['', 15], '_', '_', '_', '*', '*', '*', '*']
]
# Easy, 6x6
kakuro_intermediate6x6 = [
['*', [11, ''], [16, ''], [30, ''], '*', [24, ''], [11, '']],
[['', 24], '_', '_', '_', ['', 9], '_', '_'],
[['', 16], '_', '_', '_', [14, 17], '_', '_'],
['*', '*', [22, 20], '_', '_', '_', '*'],
['*', [3, 24], '_', '_', '_', [10, ''], [13, '']],
[['', 7], '_', '_', ['', 19], '_', '_', '_'],
[['', 11], '_', '_', ['', 7], '_', '_', '_']
]
# Hard, 8x8
kakuro_hard8x8 = [
['*', [28, ''], [15, ''], '*', [9, ''], [15, ''], '*', [9, ''], [12, '']],
[['', 10], '_', '_', [15, 6], '_', '_', [10, 4], '_', '_'],
[['', 38], '_', '_', '_', '_', '_', '_', '_', '_'],
[['', 17], '_', '_', '_', ['', 4], '_', '_', [27, ''], '*'],
[['', 13], '_', '_', [7, ''], [17, 19], '_', '_', '_', [15, '']],
['*', ['', 8], '_', '_', '_', '*', [16, 3], '_', '_'],
['*', [11, ''], [4, 4], '_', '_', [3, 24], '_', '_', '_'],
[['', 44], '_', '_', '_', '_', '_', '_', '_', '_'],
[['', 3], '_', '_', ['', 6], '_', '_', ['', 10], '_', '_']
]
######### Kakuro class implementation
class Kakuro(CSP):
""" Constructor method given the kakuro puzzle to be solved as argument """
def __init__(self, kakuro_puzzle):
variables = [] # A list of variables; each is atomic
domains = {} # A dict of {var:[possible_value, ...]} entries
neighbors = {} # A dict of {var:[var,...]} that for each variable lists
# the other variables that participate in constraints.
self.puzzle = kakuro_puzzle
for i in range(len(kakuro_puzzle)): # Index for each line
for j in range(len(kakuro_puzzle[i])): # Index for each cell in each line
# Find empty cells
if kakuro_puzzle[i][j] == "_":
var = "X" + str(i) + "," + str(j)
variables.append(var) # Add variable var
domains[var] = list(map(str, list(range(1, 10)))) # Add domain of variable var
# Find slash cells
if kakuro_puzzle[i][j] != '_' and kakuro_puzzle[i][j] != '*':
# Sum of cells down
if kakuro_puzzle[i][j][0] != "":
hidden_var = "C_d" + str(i) + "," + str(j)
variables.append(hidden_var) # Add hidden variable to convert n-ary sum constraint to binary
cell_counter = 0
for m in range(i + 1, len(kakuro_puzzle)):
if kakuro_puzzle[m][j] != "_":
break
nei = "X" + str(m) + "," + str(j)
if hidden_var not in neighbors:
neighbors[hidden_var] = []
neighbors[hidden_var].append(nei)
if nei not in neighbors:
neighbors[nei] = []
neighbors[nei].append(hidden_var)
cell_counter += 1
perms = list(map("".join, permutations('123456789', cell_counter)))
domains[hidden_var] = [perm for perm in perms if sum(int(x) for x in perm) == kakuro_puzzle[i][j][0]]
# Sum of cells right
if kakuro_puzzle[i][j][1] != "":
hidden_var = "C_r" + str(i) + "," + str(j)
variables.append(hidden_var) # Add hidden variable to convert n-ary constraint of sum to binary
cell_counter = 0
for k in range(j + 1, len(kakuro_puzzle[i])):
if kakuro_puzzle[i][k] != "_":
break
nei = "X" + str(i) + "," + str(k)
if hidden_var not in neighbors:
neighbors[hidden_var] = []
neighbors[hidden_var].append(nei)
if nei not in neighbors:
neighbors[nei] = []
neighbors[nei].append(hidden_var)
cell_counter += 1
perms = list(map("".join, permutations('123456789', cell_counter)))
domains[hidden_var] = [perm for perm in perms if sum(int(x) for x in perm) == kakuro_puzzle[i][j][1]]
CSP.__init__(self, variables, domains, neighbors, self.kakuro_constraint)
""" A function that returns true if neighbors A, B satisfy
kakuro's constraints when they have values A = a, B = b """
def kakuro_constraint(self, A, a, B, b):
if A[0] == "X" and B[0] == "C":
X_i = int(A[1 : A.index(",")])
X_j = int(A[A.index(",") + 1 :])
C_i = int(B[3 : B.index(",")])
C_j = int(B[B.index(",") + 1 :])
if B[2] == "d":
ind = X_i - C_i - 1 # Index of character to be checked
hidden_var = "C_d" + str(C_i) + "," + str(C_j)
if b[ind] == a: #and sum(int(x) for x in b) == self.sums[hidden_var]:
return True
else: # B[2] == "r":
ind = X_j - C_j - 1 # Index of character to be checked
hidden_var = "C_r" + str(C_i) + "," + str(C_j)
if b[ind] == a: #and sum(int(x) for x in b) == self.sums[hidden_var]:
return True
elif A[0] == "C" and B[0] == "X":
C_i = int(A[3 : A.index(",")])
C_j = int(A[A.index(",") + 1 :])
X_i = int(B[1 : B.index(",")])
X_j = int(B[B.index(",") + 1 :])
if A[2] == "d":
ind = X_i - C_i - 1 # Index of character to be checked
hidden_var = "C_d" + str(C_i) + "," + str(C_j)
if a[ind] == b:# and sum(int(x) for x in a) == self.sums[hidden_var]:
return True
else: # A[2] == "r":
ind = X_j - C_j - 1 # Index of character to be checked
hidden_var = "C_r" + str(C_i) + "," + str(C_j)
if a[ind] == b:# and sum(int(x) for x in a) == self.sums[hidden_var]:
return True
return False
def display(self, assignment=None):
for i in range(len(self.puzzle)): # Index for each line
line = ""
for j in range(len(self.puzzle[i])): # Index for each cell in each line
if self.puzzle[i][j] == '*':
line += " * \t"
elif self.puzzle[i][j] == "_":
var = "X" + str(i) + "," + str(j)
if assignment != None:
if var in assignment:
line += " " + assignment[var] + " \t"
else:
line += " _ \t"
else:
line += " _ \t"
else:
sum1 = str(self.puzzle[i][j][0]) if self.puzzle[i][j][0] else " "
sum2 = str(self.puzzle[i][j][1]) if self.puzzle[i][j][1] else " "
line += sum1 + "\\" + sum2 + "\t"
print(line)
print()
######### Solution of Kakuro Puzzle: Given, 4x3
print("Kakuro puzzle: Given, 4x3\n")
# BT + FC + MRV
Kakuro_problem = Kakuro(kakuro_given4x3)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, inference=forward_checking)
total_time = time() - start_time
Kakuro_problem.display(assignments)
print("\tHeuristic algorithms: BT + FC + MRV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + MAC + MRV
Kakuro_problem = Kakuro(kakuro_given4x3)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, inference=mac)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + MAC + MRV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + FC + MRV + LCV
Kakuro_problem = Kakuro(kakuro_given4x3)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, order_domain_values=lcv, inference=forward_checking)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + FC + MRV + LCV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + MAC + MRV + LCV
Kakuro_problem = Kakuro(kakuro_given4x3)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, order_domain_values=lcv, inference=mac)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + MAC + MRV + LCV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.")
######### Solution of Kakuro Puzzle: Given, 5x7
print("\n\nKakuro puzzle: Given, 5x7\n")
# BT + FC + MRV
Kakuro_problem = Kakuro(kakuro_given5x7)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, inference=forward_checking)
total_time = time() - start_time
Kakuro_problem.display(assignments)
print("\tHeuristic algorithms: BT + FC + MRV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + MAC + MRV
Kakuro_problem = Kakuro(kakuro_given5x7)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, inference=mac)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + MAC + MRV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + FC + MRV + LCV
Kakuro_problem = Kakuro(kakuro_given5x7)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, order_domain_values=lcv, inference=forward_checking)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + FC + MRV + LCV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + MAC + MRV + LCV
Kakuro_problem = Kakuro(kakuro_given5x7)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, order_domain_values=lcv, inference=mac)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + MAC + MRV + LCV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.")
######### Solution of Kakuro Puzzle: Given, 14x14
print("\n\nKakuro puzzle: Given, 14x14\n")
# BT + FC + MRV
Kakuro_problem = Kakuro(kakuro_given14x14)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, inference=forward_checking)
total_time = time() - start_time
Kakuro_problem.display(assignments)
print("\tHeuristic algorithms: BT + FC + MRV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + MAC + MRV
Kakuro_problem = Kakuro(kakuro_given14x14)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, inference=mac)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + MAC + MRV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + FC + MRV + LCV
Kakuro_problem = Kakuro(kakuro_given14x14)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, order_domain_values=lcv, inference=forward_checking)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + FC + MRV + LCV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + MAC + MRV + LCV
Kakuro_problem = Kakuro(kakuro_given14x14)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, order_domain_values=lcv, inference=mac)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + MAC + MRV + LCV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.")
######### Solution of Kakuro Puzzle: Intermediate, 6x6
print("\n\nKakuro puzzle: Intermediate, 6x6\n")
# BT + FC + MRV
Kakuro_problem = Kakuro(kakuro_intermediate6x6)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, inference=forward_checking)
total_time = time() - start_time
Kakuro_problem.display(assignments)
print("\tHeuristic algorithms: BT + FC + MRV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + MAC + MRV
Kakuro_problem = Kakuro(kakuro_intermediate6x6)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, inference=mac)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + MAC + MRV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + FC + MRV + LCV
Kakuro_problem = Kakuro(kakuro_intermediate6x6)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, order_domain_values=lcv, inference=forward_checking)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + FC + MRV + LCV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + MAC + MRV + LCV
Kakuro_problem = Kakuro(kakuro_intermediate6x6)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, order_domain_values=lcv, inference=mac)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + MAC + MRV + LCV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
######### Solution of Kakuro Puzzle: Hard, 8x8
print("\n\nKakuro puzzle: Hard, 8x8\n")
# BT + FC + MRV
Kakuro_problem = Kakuro(kakuro_hard8x8)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, inference=forward_checking)
total_time = time() - start_time
Kakuro_problem.display(assignments)
print("\tHeuristic algorithms: BT + FC + MRV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + MAC + MRV
Kakuro_problem = Kakuro(kakuro_hard8x8)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, inference=mac)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + MAC + MRV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + FC + MRV + LCV
Kakuro_problem = Kakuro(kakuro_hard8x8)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, order_domain_values=lcv, inference=forward_checking)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + FC + MRV + LCV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.\n")
# BT + MAC + MRV + LCV
Kakuro_problem = Kakuro(kakuro_hard8x8)
start_time = time()
assignments = backtracking_search(Kakuro_problem, select_unassigned_variable=mrv, order_domain_values=lcv, inference=mac)
total_time = time() - start_time
print("\tHeuristic algorithms: BT + MAC + MRV + LCV")
print("\tSolved in", total_time, "seconds.")
print("\tMade", Kakuro_problem.nassigns, "assignments.")