examples/notebook/contrib/hidato.ipynb
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http://www.apache.org/licenses/LICENSE-2.0
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First, you must install ortools package in this colab.
%pip install ortools
Hidato puzzle in Google CP Solver.
http://www.shockwave.com/gamelanding/hidato.jsp http://www.hidato.com/ ''' Puzzles start semi-filled with numbered tiles. The first and last numbers are circled. Connect the numbers together to win. Consecutive number must touch horizontally, vertically, or diagonally. '''
Compare with the following models:
Note: This model is very slow. Please see Laurent Perron's much faster (and more elegant) model: hidato_table.py .
This model was created by Hakan Kjellerstrand ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
import sys
from ortools.constraint_solver import pywrapcp
def main(r, c):
# Create the solver.
solver = pywrapcp.Solver("hidato")
# data
# Simple problem
if r == 3 and c == 3:
puzzle = [[6, 0, 9], [0, 2, 8], [1, 0, 0]]
if r == 7 and c == 7:
puzzle = [[0, 44, 41, 0, 0, 0, 0], [0, 43, 0, 28, 29, 0, 0],
[0, 1, 0, 0, 0, 33, 0], [0, 2, 25, 4, 34, 0, 36],
[49, 16, 0, 23, 0, 0, 0], [0, 19, 0, 0, 12, 7, 0],
[0, 0, 0, 14, 0, 0, 0]]
# Problems from the book:
# Gyora Bededek: "Hidato: 2000 Pure Logic Puzzles"
# Problem 1 (Practice)
# r = 5
# c = r
# puzzle = [
# [ 0, 0,20, 0, 0],
# [ 0, 0, 0,16,18],
# [22, 0,15, 0, 0],
# [23, 0, 1,14,11],
# [ 0,25, 0, 0,12],
# ]
# Problem 2 (Practice)
if r == 5 and c == 5:
puzzle = [
[0, 0, 0, 0, 14],
[0, 18, 12, 0, 0],
[0, 0, 17, 4, 5],
[0, 0, 7, 0, 0],
[9, 8, 25, 1, 0],
]
# Problem 3 (Beginner)
if r == 6 and c == 6:
puzzle = [[0, 26, 0, 0, 0, 18], [0, 0, 27, 0, 0, 19], [31, 23, 0, 0, 14, 0],
[0, 33, 8, 0, 15, 1], [0, 0, 0, 5, 0, 0], [35, 36, 0, 10, 0, 0]]
# Problem 15 (Intermediate)
# Note: This takes very long time to solve...
if r == 8 and c == 8:
puzzle = [[64, 0, 0, 0, 0, 0, 0, 0], [1, 63, 0, 59, 15, 57, 53, 0],
[0, 4, 0, 14, 0, 0, 0, 0], [3, 0, 11, 0, 20, 19, 0, 50],
[0, 0, 0, 0, 22, 0, 48, 40], [9, 0, 0, 32, 23, 0, 0, 41],
[27, 0, 0, 0, 36, 0, 46, 0], [28, 30, 0, 35, 0, 0, 0, 0]]
print_game(puzzle, r, c)
#
# declare variables
#
x = {}
for i in range(r):
for j in range(c):
x[(i, j)] = solver.IntVar(1, r * c, "dice(%i,%i)" % (i, j))
x_flat = [x[(i, j)] for i in range(r) for j in range(c)]
#
# constraints
#
solver.Add(solver.AllDifferent(x_flat))
#
# Fill in the clues
#
for i in range(r):
for j in range(c):
if puzzle[i][j] > 0:
solver.Add(x[(i, j)] == puzzle[i][j])
# From the numbers k = 1 to r*c-1, find this position,
# and then the position of k+1
for k in range(1, r * c):
i = solver.IntVar(0, r)
j = solver.IntVar(0, c)
a = solver.IntVar(-1, 1)
b = solver.IntVar(-1, 1)
# 1) First: fix "this" k
# 2) and then find the position of the next value (k+1)
# solver.Add(k == x[(i,j)])
solver.Add(k == solver.Element(x_flat, i * c + j))
# solver.Add(k + 1 == x[(i+a,j+b)])
solver.Add(k + 1 == solver.Element(x_flat, (i + a) * c + (j + b)))
solver.Add(i + a >= 0)
solver.Add(j + b >= 0)
solver.Add(i + a < r)
solver.Add(j + b < c)
# solver.Add(((a != 0) | (b != 0)))
a_nz = solver.BoolVar()
b_nz = solver.BoolVar()
solver.Add(a_nz == solver.IsDifferentCstVar(a, 0))
solver.Add(b_nz == solver.IsDifferentCstVar(b, 0))
solver.Add(a_nz + b_nz >= 1)
#
# solution and search
#
solution = solver.Assignment()
solution.Add(x_flat)
# db: DecisionBuilder
db = solver.Phase(
x_flat,
# solver.INT_VAR_DEFAULT
# solver.INT_VAR_SIMPLE
# solver.CHOOSE_RANDOM
# solver.CHOOSE_MIN_SIZE_LOWEST_MIN
# solver.CHOOSE_MIN_SIZE_HIGHEST_MIN
# solver.CHOOSE_MIN_SIZE_LOWEST_MAX
# solver.CHOOSE_MIN_SIZE_HIGHEST_MAX
# solver.CHOOSE_PATH
solver.CHOOSE_FIRST_UNBOUND,
# solver.INT_VALUE_DEFAULT
# solver.INT_VALUE_SIMPLE
# solver.ASSIGN_MAX_VALUE
# solver.ASSIGN_RANDOM_VALUE
# solver.ASSIGN_CENTER_VALUE
solver.ASSIGN_MIN_VALUE)
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
num_solutions += 1
print("\nSolution:", num_solutions)
print_board(x, r, c)
print()
solver.EndSearch()
print()
print("num_solutions:", num_solutions)
print("failures:", solver.Failures())
print("branches:", solver.Branches())
print("WallTime:", solver.WallTime())
def print_board(x, rows, cols):
for i in range(rows):
for j in range(cols):
print("% 2s" % x[i, j].Value(), end=" ")
print("")
def print_game(game, rows, cols):
for i in range(rows):
for j in range(cols):
print("% 2s" % game[i][j], end=" ")
print("")
# data
r = 3
c = r
if len(sys.argv) > 1:
r = int(sys.argv[1])
c = r
if len(sys.argv) > 2:
c = int(sys.argv[2])
main(r, c)