269 lines
7.9 KiB
C#
269 lines
7.9 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.Linq;
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using Google.OrTools.ConstraintSolver;
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public class HidatoTable
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{
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/*
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* Build closeness pairs for consecutive numbers.
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*
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* Build set of allowed pairs such that two consecutive numbers touch
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* each other in the grid.
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*
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* Returns:
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* A list of pairs for allowed consecutive position of numbers.
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*
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* Args:
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* rows: the number of rows in the grid
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* cols: the number of columns in the grid
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*/
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public static IntTupleSet BuildPairs(int rows, int cols)
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{
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int[] ix = { -1, 0, 1 };
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var result_tmp =
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(from x in Enumerable.Range(0, rows) from y in Enumerable.Range(0, cols)
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from dx in ix from dy in ix where x +
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dx >=
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0 &&
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x + dx < rows && y + dy >= 0 && y + dy < cols &&
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(dx != 0 || dy != 0)
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select new int[]{x * cols + y, (x + dx) * cols + (y + dy)})
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.ToArray();
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// Convert to len x 2 matrix
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int len = result_tmp.Length;
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IntTupleSet result = new IntTupleSet(2);
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foreach (int[] r in result_tmp)
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{
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result.Insert(r);
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}
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return result;
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}
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/**
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*
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* Hidato puzzle in Google CP Solver.
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*
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* http://www.hidato.com/
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* """
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* Puzzles start semi-filled with numbered tiles.
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* The first and last numbers are circled.
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* Connect the numbers together to win. Consecutive
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* number must touch horizontally, vertically, or
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* diagonally.
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* """
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*
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* This is a port of the Python model hidato_table.py
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* made by Laurent Perron (using AllowedAssignments),
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* based on my (much slower) model hidato.py.
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*
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*/
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private static void Solve(int model = 1)
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{
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Solver solver = new Solver("HidatoTable");
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//
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// models, a 0 indicates an open cell which number is not yet known.
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//
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int[,] puzzle = null;
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if (model == 1)
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{
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// Simple problem
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// Solution 1:
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// 6 7 9
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// 5 2 8
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// 1 4 3
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int[,] puzzle1 = { { 6, 0, 9 }, { 0, 2, 8 }, { 1, 0, 0 } };
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puzzle = puzzle1;
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}
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else if (model == 2)
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{
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int[,] puzzle2 = { { 0, 44, 41, 0, 0, 0, 0 }, { 0, 43, 0, 28, 29, 0, 0 }, { 0, 1, 0, 0, 0, 33, 0 },
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{ 0, 2, 25, 4, 34, 0, 36 }, { 49, 16, 0, 23, 0, 0, 0 }, { 0, 19, 0, 0, 12, 7, 0 },
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{ 0, 0, 0, 14, 0, 0, 0 } };
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puzzle = puzzle2;
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}
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else if (model == 3)
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{
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// Problems from the book:
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// Gyora Bededek: "Hidato: 2000 Pure Logic Puzzles"
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// Problem 1 (Practice)
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int[,] puzzle3 = {
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{ 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 }
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};
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puzzle = puzzle3;
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}
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else if (model == 4)
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{
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// problem 2 (Practice)
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int[,] puzzle4 = {
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{ 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 }
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};
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puzzle = puzzle4;
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}
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else if (model == 5)
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{
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// problem 3 (Beginner)
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int[,] puzzle5 = { { 0, 26, 0, 0, 0, 18 }, { 0, 0, 27, 0, 0, 19 }, { 31, 23, 0, 0, 14, 0 },
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{ 0, 33, 8, 0, 15, 1 }, { 0, 0, 0, 5, 0, 0 }, { 35, 36, 0, 10, 0, 0 } };
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puzzle = puzzle5;
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}
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else if (model == 6)
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{
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// Problem 15 (Intermediate)
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int[,] puzzle6 = { { 64, 0, 0, 0, 0, 0, 0, 0 }, { 1, 63, 0, 59, 15, 57, 53, 0 },
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{ 0, 4, 0, 14, 0, 0, 0, 0 }, { 3, 0, 11, 0, 20, 19, 0, 50 },
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{ 0, 0, 0, 0, 22, 0, 48, 40 }, { 9, 0, 0, 32, 23, 0, 0, 41 },
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{ 27, 0, 0, 0, 36, 0, 46, 0 }, { 28, 30, 0, 35, 0, 0, 0, 0 } };
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puzzle = puzzle6;
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}
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int r = puzzle.GetLength(0);
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int c = puzzle.GetLength(1);
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Console.WriteLine();
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Console.WriteLine("----- Solving problem {0} -----", model);
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Console.WriteLine();
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PrintMatrix(puzzle);
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//
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// Decision variables
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//
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IntVar[] positions = solver.MakeIntVarArray(r * c, 0, r * c - 1, "p");
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//
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// Constraints
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//
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solver.Add(positions.AllDifferent());
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//
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// Fill in the clues
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//
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for (int i = 0; i < r; i++)
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{
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for (int j = 0; j < c; j++)
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{
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if (puzzle[i, j] > 0)
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{
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solver.Add(positions[puzzle[i, j] - 1] == i * c + j);
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}
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}
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}
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// Consecutive numbers much touch each other in the grid.
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// We use an allowed assignment constraint to model it.
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IntTupleSet close_tuples = BuildPairs(r, c);
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for (int k = 1; k < r * c - 1; k++)
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{
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IntVar[] tmp = new IntVar[] { positions[k], positions[k + 1] };
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solver.Add(tmp.AllowedAssignments(close_tuples));
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}
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//
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// Search
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//
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DecisionBuilder db = solver.MakePhase(positions, Solver.CHOOSE_MIN_SIZE_LOWEST_MIN, Solver.ASSIGN_MIN_VALUE);
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solver.NewSearch(db);
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int num_solution = 0;
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while (solver.NextSolution())
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{
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num_solution++;
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PrintOneSolution(positions, r, c, num_solution);
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}
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Console.WriteLine("\nSolutions: " + solver.Solutions());
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Console.WriteLine("WallTime: " + solver.WallTime() + "ms ");
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Console.WriteLine("Failures: " + solver.Failures());
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Console.WriteLine("Branches: " + solver.Branches());
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solver.EndSearch();
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}
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// Print the current solution
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public static void PrintOneSolution(IntVar[] positions, int rows, int cols, int num_solution)
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{
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Console.WriteLine("Solution {0}", num_solution);
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// Create empty board
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int[,] board = new int[rows, cols];
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for (int i = 0; i < rows; i++)
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{
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for (int j = 0; j < cols; j++)
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{
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board[i, j] = 0;
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}
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}
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// Fill board with solution value
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for (int k = 0; k < rows * cols; k++)
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{
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int position = (int)positions[k].Value();
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board[position / cols, position % cols] = k + 1;
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}
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PrintMatrix(board);
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}
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// Pretty print of the matrix
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public static void PrintMatrix(int[,] game)
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{
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int rows = game.GetLength(0);
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int cols = game.GetLength(1);
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for (int i = 0; i < rows; i++)
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{
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for (int j = 0; j < cols; j++)
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{
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if (game[i, j] == 0)
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{
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Console.Write(" .");
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}
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else
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{
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Console.Write(" {0,2}", game[i, j]);
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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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public static void Main(String[] args)
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{
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int model = 1;
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if (args.Length > 1)
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{
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model = Convert.ToInt32(args[1]);
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Solve(model);
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}
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else
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{
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for (int m = 1; m <= 6; m++)
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{
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Solve(m);
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}
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}
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}
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}
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