examples/notebook/contrib/crossword2.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Crosswords in Google CP Solver.
This is a standard example for constraint logic programming. See e.g.
http://www.cis.temple.edu/~ingargio/cis587/readings/constraints.html ''' We are to complete the puzzle
1 2 3 4 5
+---+---+---+---+---+ Given the list of words: 1 | 1 | | 2 | | 3 | AFT LASER +---+---+---+---+---+ ALE LEE 2 | # | # | | # | | EEL LINE +---+---+---+---+---+ HEEL SAILS 3 | # | 4 | | 5 | | HIKE SHEET +---+---+---+---+---+ HOSES STEER 4 | 6 | # | 7 | | | KEEL TIE +---+---+---+---+---+ KNOT 5 | 8 | | | | | +---+---+---+---+---+ 6 | | # | # | | # | The numbers 1,2,3,4,5,6,7,8 in the crossword +---+---+---+---+---+ puzzle correspond to the words that will start at those locations. '''
The model was inspired by Sebastian Brand's Array Constraint cross word example http://www.cs.mu.oz.au/~sbrand/project/ac/ http://www.cs.mu.oz.au/~sbrand/project/ac/examples.pl
Also, see the following models:
This model was created by Hakan Kjellerstrand ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
from ortools.constraint_solver import pywrapcp
def main():
# Create the solver.
solver = pywrapcp.Solver("Problem")
#
# data
#
alpha = "_abcdefghijklmnopqrstuvwxyz"
a = 1
b = 2
c = 3
d = 4
e = 5
f = 6
g = 7
h = 8
i = 9
j = 10
k = 11
l = 12
m = 13
n = 14
o = 15
p = 16
q = 17
r = 18
s = 19
t = 20
u = 21
v = 22
w = 23
x = 24
y = 25
z = 26
num_words = 15
word_len = 5
AA = [
[h, o, s, e, s], # HOSES
[l, a, s, e, r], # LASER
[s, a, i, l, s], # SAILS
[s, h, e, e, t], # SHEET
[s, t, e, e, r], # STEER
[h, e, e, l, 0], # HEEL
[h, i, k, e, 0], # HIKE
[k, e, e, l, 0], # KEEL
[k, n, o, t, 0], # KNOT
[l, i, n, e, 0], # LINE
[a, f, t, 0, 0], # AFT
[a, l, e, 0, 0], # ALE
[e, e, l, 0, 0], # EEL
[l, e, e, 0, 0], # LEE
[t, i, e, 0, 0] # TIE
]
num_overlapping = 12
overlapping = [
[0, 2, 1, 0], # s
[0, 4, 2, 0], # s
[3, 1, 1, 2], # i
[3, 2, 4, 0], # k
[3, 3, 2, 2], # e
[6, 0, 1, 3], # l
[6, 1, 4, 1], # e
[6, 2, 2, 3], # e
[7, 0, 5, 1], # l
[7, 2, 1, 4], # s
[7, 3, 4, 2], # e
[7, 4, 2, 4] # r
]
n = 8
# declare variables
A = {}
for I in range(num_words):
for J in range(word_len):
A[(I, J)] = solver.IntVar(0, 26, "A(%i,%i)" % (I, J))
A_flat = [A[(I, J)] for I in range(num_words) for J in range(word_len)]
E = [solver.IntVar(0, num_words, "E%i" % I) for I in range(n)]
#
# constraints
#
solver.Add(solver.AllDifferent(E))
for I in range(num_words):
for J in range(word_len):
solver.Add(A[(I, J)] == AA[I][J])
for I in range(num_overlapping):
# This is what I would do:
# solver.Add(A[(E[overlapping[I][0]], overlapping[I][1])] == A[(E[overlapping[I][2]], overlapping[I][3])])
# But we must use Element explicitly
solver.Add(
solver.Element(A_flat, E[overlapping[I][0]] * word_len +
overlapping[I][1]) == solver
.Element(A_flat, E[overlapping[I][2]] * word_len + overlapping[I][3]))
#
# solution and search
#
solution = solver.Assignment()
solution.Add(E)
# db: DecisionBuilder
db = solver.Phase(E + A_flat, solver.INT_VAR_SIMPLE, solver.ASSIGN_MIN_VALUE)
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
print(E)
print_solution(A, E, alpha, n, word_len)
num_solutions += 1
solver.EndSearch()
print()
print("num_solutions:", num_solutions)
print("failures:", solver.Failures())
print("branches:", solver.Branches())
print("WallTime:", solver.WallTime())
def print_solution(A, E, alpha, n, word_len):
for ee in range(n):
print("%i: (%2i)" % (ee, E[ee].Value()), end=" ")
print("".join(
["%s" % (alpha[A[ee, ii].Value()]) for ii in range(word_len)]))
main()