144 lines
4.1 KiB
C#
144 lines
4.1 KiB
C#
//
|
|
// Copyright 2012 Hakan Kjellerstrand
|
|
//
|
|
// Licensed under the Apache License, Version 2.0 (the "License");
|
|
// you may not use this file except in compliance with the License.
|
|
// You may obtain a copy of the License at
|
|
//
|
|
// http://www.apache.org/licenses/LICENSE-2.0
|
|
//
|
|
// Unless required by applicable law or agreed to in writing, software
|
|
// distributed under the License is distributed on an "AS IS" BASIS,
|
|
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
// See the License for the specific language governing permissions and
|
|
// limitations under the License.
|
|
|
|
using System;
|
|
using System.Collections;
|
|
using System.Collections.Generic;
|
|
using System.Linq;
|
|
using Google.OrTools.ConstraintSolver;
|
|
|
|
public class SichermanDice
|
|
{
|
|
/**
|
|
*
|
|
* Sicherman Dice.
|
|
*
|
|
* From http://en.wikipedia.org/wiki/Sicherman_dice
|
|
* ""
|
|
* Sicherman dice are the only pair of 6-sided dice which are not normal dice,
|
|
* bear only positive integers, and have the same probability distribution for
|
|
* the sum as normal dice.
|
|
*
|
|
* The faces on the dice are numbered 1, 2, 2, 3, 3, 4 and 1, 3, 4, 5, 6, 8.
|
|
* ""
|
|
*
|
|
* I read about this problem in a book/column by Martin Gardner long
|
|
* time ago, and got inspired to model it now by the WolframBlog post
|
|
* "Sicherman Dice": http://blog.wolfram.com/2010/07/13/sicherman-dice/
|
|
*
|
|
* This model gets the two different ways, first the standard way and
|
|
* then the Sicherman dice:
|
|
*
|
|
* x1 = [1, 2, 3, 4, 5, 6]
|
|
* x2 = [1, 2, 3, 4, 5, 6]
|
|
* ----------
|
|
* x1 = [1, 2, 2, 3, 3, 4]
|
|
* x2 = [1, 3, 4, 5, 6, 8]
|
|
*
|
|
*
|
|
* Extra: If we also allow 0 (zero) as a valid value then the
|
|
* following two solutions are also valid:
|
|
*
|
|
* x1 = [0, 1, 1, 2, 2, 3]
|
|
* x2 = [2, 4, 5, 6, 7, 9]
|
|
* ----------
|
|
* x1 = [0, 1, 2, 3, 4, 5]
|
|
* x2 = [2, 3, 4, 5, 6, 7]
|
|
*
|
|
* These two extra cases are mentioned here:
|
|
* http://mathworld.wolfram.com/SichermanDice.html
|
|
*
|
|
*
|
|
* Also see http://www.hakank.org/or-tools/sicherman_dice.py
|
|
*
|
|
*/
|
|
private static void Solve()
|
|
{
|
|
Solver solver = new Solver("SichermanDice");
|
|
|
|
//
|
|
// Data
|
|
//
|
|
int n = 6;
|
|
int m = 10;
|
|
int lowest_value = 0;
|
|
|
|
// standard distribution
|
|
int[] standard_dist = { 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1 };
|
|
|
|
IEnumerable<int> RANGE = Enumerable.Range(0, n);
|
|
IEnumerable<int> RANGE1 = Enumerable.Range(0, n - 1);
|
|
|
|
//
|
|
// Decision variables
|
|
//
|
|
|
|
IntVar[] x1 = solver.MakeIntVarArray(n, lowest_value, m, "x1");
|
|
IntVar[] x2 = solver.MakeIntVarArray(n, lowest_value, m, "x2");
|
|
|
|
//
|
|
// Constraints
|
|
//
|
|
for (int k = 0; k < standard_dist.Length; k++)
|
|
{
|
|
solver.Add((from i in RANGE from j in RANGE select x1[i] + x2[j] == k + 2).ToArray().Sum() ==
|
|
standard_dist[k]);
|
|
}
|
|
|
|
// symmetry breaking
|
|
foreach (int i in RANGE1)
|
|
{
|
|
solver.Add(x1[i] <= x1[i + 1]);
|
|
solver.Add(x2[i] <= x2[i + 1]);
|
|
solver.Add(x1[i] <= x2[i]);
|
|
}
|
|
|
|
//
|
|
// Search
|
|
//
|
|
DecisionBuilder db =
|
|
solver.MakePhase(x1.Concat(x2).ToArray(), Solver.INT_VAR_DEFAULT, Solver.INT_VALUE_DEFAULT);
|
|
|
|
solver.NewSearch(db);
|
|
|
|
while (solver.NextSolution())
|
|
{
|
|
Console.Write("x1: ");
|
|
foreach (int i in RANGE)
|
|
{
|
|
Console.Write(x1[i].Value() + " ");
|
|
}
|
|
Console.Write("\nx2: ");
|
|
foreach (int i in RANGE)
|
|
{
|
|
Console.Write(x2[i].Value() + " ");
|
|
}
|
|
Console.WriteLine("\n");
|
|
}
|
|
|
|
Console.WriteLine("\nSolutions: {0}", solver.Solutions());
|
|
Console.WriteLine("WallTime: {0}ms", solver.WallTime());
|
|
Console.WriteLine("Failures: {0}", solver.Failures());
|
|
Console.WriteLine("Branches: {0} ", solver.Branches());
|
|
|
|
solver.EndSearch();
|
|
}
|
|
|
|
public static void Main(String[] args)
|
|
{
|
|
Solve();
|
|
}
|
|
}
|