124 lines
3.3 KiB
C#
124 lines
3.3 KiB
C#
//
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// Copyright 2012 Hakan Kjellerstrand
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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using System;
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using System.Collections;
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using System.Collections.Generic;
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using System.Linq;
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using Google.OrTools.ConstraintSolver;
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public class MagicSquareAndCards {
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/**
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*
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* Magic squares and cards problem.
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*
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* Martin Gardner (July 1971)
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* """
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* Allowing duplicates values, what is the largest constant sum for an order-3
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* magic square that can be formed with nine cards from the deck.
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* """
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*
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*
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* Also see http://www.hakank.org/or-tools/magic_square_and_cards.py
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*
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*/
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private static void Solve(int n = 3) {
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Solver solver = new Solver("MagicSquareAndCards");
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IEnumerable<int> RANGE = Enumerable.Range(0, n);
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//
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// Decision variables
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//
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IntVar[, ] x = solver.MakeIntVarMatrix(n, n, 1, 13, "x");
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IntVar[] x_flat = x.Flatten();
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IntVar s = solver.MakeIntVar(1, 13 * 4, "s");
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IntVar[] counts = solver.MakeIntVarArray(14, 0, 4, "counts");
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//
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// Constraints
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//
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solver.Add(x_flat.Distribute(counts));
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// the standard magic square constraints (sans all_different)
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foreach (int i in RANGE) {
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// rows
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solver.Add((from j in RANGE select x[i, j]).ToArray().Sum() == s);
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// columns
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solver.Add((from j in RANGE select x[j, i]).ToArray().Sum() == s);
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}
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// diagonals
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solver.Add((from i in RANGE select x[i, i]).ToArray().Sum() == s);
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solver.Add((from i in RANGE select x[i, n - i - 1]).ToArray().Sum() == s);
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// redundant constraint
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solver.Add(counts.Sum() == n * n);
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//
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// Objective
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//
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OptimizeVar obj = s.Maximize(1);
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//
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// Search
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//
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DecisionBuilder db = solver.MakePhase(x_flat, Solver.CHOOSE_FIRST_UNBOUND,
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Solver.ASSIGN_MAX_VALUE);
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solver.NewSearch(db, obj);
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while (solver.NextSolution()) {
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Console.WriteLine("s: {0}", s.Value());
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Console.Write("counts:");
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for (int i = 0; i < 14; i++) {
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Console.Write(counts [i]
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.Value() +
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" ");
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}
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Console.WriteLine();
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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Console.Write(x [i, j]
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.Value() +
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" ");
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}
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Console.WriteLine();
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}
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Console.WriteLine();
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}
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Console.WriteLine("\nSolutions: {0}", solver.Solutions());
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Console.WriteLine("WallTime: {0}ms", solver.WallTime());
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Console.WriteLine("Failures: {0}", solver.Failures());
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Console.WriteLine("Branches: {0} ", solver.Branches());
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solver.EndSearch();
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}
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public static void Main(String[] args) {
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int n = 3;
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if (args.Length > 0) {
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n = Convert.ToInt32(args[0]);
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}
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Solve(n);
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}
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}
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