examples/notebook/contrib/coins_grid.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Coins grid problem in Google CP Solver.
Problem from Tony Hurlimann: "A coin puzzle - SVOR-contest 2007" http://www.svor.ch/competitions/competition2007/AsroContestSolution.pdf ''' In a quadratic grid (or a larger chessboard) with 31x31 cells, one should place coins in such a way that the following conditions are fulfilled: 1. In each row exactly 14 coins must be placed. 2. In each column exactly 14 coins must be placed. 3. The sum of the quadratic horizontal distance from the main diagonal of all cells containing a coin must be as small as possible. 4. In each cell at most one coin can be placed. The description says to place 14x31 = 434 coins on the chessboard each row containing 14 coins and each column also containing 14 coins. '''
Cf the LPL model: http://diuflx71.unifr.ch/lpl/GetModel?name=/puzzles/coin
Note: Laurent Perron helped me to improve this model.
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/
import sys
from ortools.constraint_solver import pywrapcp
def main(n, c):
# Create the solver.
solver = pywrapcp.Solver("Coins grid")
# data
print("n: ", n)
print("c: ", c)
# declare variables
x = {}
for i in range(n):
for j in range(n):
x[(i, j)] = solver.BoolVar("x %i %i" % (i, j))
#
# constraints
#
# sum rows/columns == c
for i in range(n):
solver.Add(solver.SumEquality([x[(i, j)] for j in range(n)], c)) # sum rows
solver.Add(solver.SumEquality([x[(j, i)] for j in range(n)], c)) # sum cols
# quadratic horizonal distance var
objective_var = solver.Sum(
[x[(i, j)] * (i - j) * (i - j) for i in range(n) for j in range(n)])
# objective
objective = solver.Minimize(objective_var, 1)
#
# solution and search
#
solution = solver.Assignment()
solution.Add([x[(i, j)] for i in range(n) for j in range(n)])
solution.AddObjective(objective_var)
# last solutions
collector = solver.LastSolutionCollector(solution)
search_log = solver.SearchLog(1000000, objective_var)
restart = solver.ConstantRestart(300)
solver.Solve(
solver.Phase([x[(i, j)] for i in range(n) for j in range(n)],
solver.CHOOSE_RANDOM, solver.ASSIGN_MAX_VALUE),
[collector, search_log, objective])
print("objective:", collector.ObjectiveValue(0))
for i in range(n):
for j in range(n):
print(collector.Value(0, x[(i, j)]), end=" ")
print()
print()
print("failures:", solver.Failures())
print("branches:", solver.Branches())
print("WallTime:", solver.WallTime())
# data
n = 5 # the grid size
c = 2 # number of coins per row/column
if len(sys.argv) > 1:
n = int(sys.argv[1])
if len(sys.argv) > 2:
c = int(sys.argv[2])
main(n, c)