examples/notebook/contrib/seseman.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Seseman Convent problem in Google CP Solver.
n is the length of a border There are (n-2)^2 "holes", i.e. there are n^2 - (n-2)^2 variables to find out.
The simplest problem, n = 3 (n x n matrix) which is represented by the following matrix:
a b c d e f g h
Where the following constraints must hold:
a + b + c = border_sum
a + d + f = border_sum
c + e + h = border_sum
f + g + h = border_sum
a + b + c + d + e + f = total_sum
Compare with 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(unused_argv):
# Create the solver.
solver = pywrapcp.Solver("Seseman Convent problem")
# data
n = 3
border_sum = n * n
# declare variables
total_sum = solver.IntVar(1, n * n * n * n, "total_sum")
# x[0..n-1,0..n-1]
x = {}
for i in range(n):
for j in range(n):
x[(i, j)] = solver.IntVar(0, n * n, "x %i %i" % (i, j))
#
# constraints
#
# zero all middle cells
for i in range(1, n - 1):
for j in range(1, n - 1):
solver.Add(x[(i, j)] == 0)
# all borders must be >= 1
for i in range(n):
for j in range(n):
if i == 0 or j == 0 or i == n - 1 or j == n - 1:
solver.Add(x[(i, j)] >= 1)
# sum the borders (border_sum)
solver.Add(solver.Sum([x[(i, 0)] for i in range(n)]) == border_sum)
solver.Add(solver.Sum([x[(i, n - 1)] for i in range(n)]) == border_sum)
solver.Add(solver.Sum([x[(0, i)] for i in range(n)]) == border_sum)
solver.Add(solver.Sum([x[(n - 1, i)] for i in range(n)]) == border_sum)
# total
solver.Add(
solver.Sum([x[(i, j)] for i in range(n) for j in range(n)]) == total_sum)
#
# solution and search
#
solution = solver.Assignment()
solution.Add([x[(i, j)] for i in range(n) for j in range(n)])
solution.Add(total_sum)
# all solutions
collector = solver.AllSolutionCollector(solution)
# search_log = solver.SearchLog(100, total_sum)
solver.Solve(
solver.Phase([x[(i, j)] for i in range(n) for j in range(n)],
solver.CHOOSE_PATH, solver.ASSIGN_MIN_VALUE), [collector])
#[collector, search_log])
num_solutions = collector.SolutionCount()
# print "x:", x
print("num_solutions:", num_solutions)
print()
for s in range(num_solutions):
# print [collector.Value(s, x[(i,j)])
# for i in range(n) for j in range(n)]
print("total_sum:", collector.Value(s, total_sum))
for i in range(n):
for j in range(n):
print(collector.Value(s, x[(i, j)]), end=" ")
print()
print()
print("failures:", solver.Failures())
print("branches:", solver.Branches())
print("WallTime:", solver.WallTime())
print("num_solutions:", num_solutions)
main("cp sample")