230 lines
7.8 KiB
C#
230 lines
7.8 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 KillerSudoku
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{
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/**
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* Ensure that the sum of the segments
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* in cc == res
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*
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*/
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public static void calc(Solver solver, int[] cc, IntVar[,] x, int res)
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{
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// sum the numbers
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int len = cc.Length / 2;
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solver.Add((from i in Enumerable.Range(0, len) select x[cc[i * 2] - 1, cc[i * 2 + 1] - 1]).ToArray().Sum() ==
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res);
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}
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/**
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*
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* Killer Sudoku.
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*
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* http://en.wikipedia.org/wiki/Killer_Sudoku
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* """
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* Killer sudoku (also killer su doku, sumdoku, sum doku, addoku, or
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* samunamupure) is a puzzle that combines elements of sudoku and kakuro.
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* Despite the name, the simpler killer sudokus can be easier to solve
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* than regular sudokus, depending on the solver's skill at mental arithmetic;
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* the hardest ones, however, can take hours to crack.
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*
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* ...
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*
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* The objective is to fill the grid with numbers from 1 to 9 in a way that
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* the following conditions are met:
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*
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* - Each row, column, and nonet contains each number exactly once.
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* - The sum of all numbers in a cage must match the small number printed
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* in its corner.
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* - No number appears more than once in a cage. (This is the standard rule
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* for killer sudokus, and implies that no cage can include more
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* than 9 cells.)
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*
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* In 'Killer X', an additional rule is that each of the long diagonals
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* contains each number once.
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* """
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*
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* Here we solve the problem from the Wikipedia page, also shown here
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* http://en.wikipedia.org/wiki/File:Killersudoku_color.svg
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*
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* The output is:
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* 2 1 5 6 4 7 3 9 8
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* 3 6 8 9 5 2 1 7 4
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* 7 9 4 3 8 1 6 5 2
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* 5 8 6 2 7 4 9 3 1
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* 1 4 2 5 9 3 8 6 7
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* 9 7 3 8 1 6 4 2 5
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* 8 2 1 7 3 9 5 4 6
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* 6 5 9 4 2 8 7 1 3
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* 4 3 7 1 6 5 2 8 9
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*
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* Also see http://www.hakank.org/or-tools/killer_sudoku.py
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* though this C# model has another representation of
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* the problem instance.
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*
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*/
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private static void Solve()
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{
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Solver solver = new Solver("KillerSudoku");
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// size of matrix
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int cell_size = 3;
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IEnumerable<int> CELL = Enumerable.Range(0, cell_size);
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int n = cell_size * cell_size;
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IEnumerable<int> RANGE = Enumerable.Range(0, n);
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// For a better view of the problem, see
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// http://en.wikipedia.org/wiki/File:Killersudoku_color.svg
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// hints
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// sum, the hints
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// Note: this is 1-based
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int[][] problem = { new int[] { 3, 1, 1, 1, 2 },
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new int[] { 15, 1, 3, 1, 4, 1, 5 },
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new int[] { 22, 1, 6, 2, 5, 2, 6, 3, 5 },
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new int[] { 4, 1, 7, 2, 7 },
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new int[] { 16, 1, 8, 2, 8 },
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new int[] { 15, 1, 9, 2, 9, 3, 9, 4, 9 },
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new int[] { 25, 2, 1, 2, 2, 3, 1, 3, 2 },
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new int[] { 17, 2, 3, 2, 4 },
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new int[] { 9, 3, 3, 3, 4, 4, 4 },
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new int[] { 8, 3, 6, 4, 6, 5, 6 },
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new int[] { 20, 3, 7, 3, 8, 4, 7 },
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new int[] { 6, 4, 1, 5, 1 },
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new int[] { 14, 4, 2, 4, 3 },
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new int[] { 17, 4, 5, 5, 5, 6, 5 },
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new int[] { 17, 4, 8, 5, 7, 5, 8 },
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new int[] { 13, 5, 2, 5, 3, 6, 2 },
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new int[] { 20, 5, 4, 6, 4, 7, 4 },
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new int[] { 12, 5, 9, 6, 9 },
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new int[] { 27, 6, 1, 7, 1, 8, 1, 9, 1 },
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new int[] { 6, 6, 3, 7, 2, 7, 3 },
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new int[] { 20, 6, 6, 7, 6, 7, 7 },
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new int[] { 6, 6, 7, 6, 8 },
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new int[] { 10, 7, 5, 8, 4, 8, 5, 9, 4 },
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new int[] { 14, 7, 8, 7, 9, 8, 8, 8, 9 },
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new int[] { 8, 8, 2, 9, 2 },
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new int[] { 16, 8, 3, 9, 3 },
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new int[] { 15, 8, 6, 8, 7 },
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new int[] { 13, 9, 5, 9, 6, 9, 7 },
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new int[] { 17, 9, 8, 9, 9 }
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};
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int num_p = 29; // Number of segments
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//
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// Decision variables
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//
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IntVar[,] x = solver.MakeIntVarMatrix(n, n, 0, 9, "x");
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IntVar[] x_flat = x.Flatten();
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//
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// Constraints
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//
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//
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// The first three constraints is the same as for sudokus.cs
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//
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// alldifferent rows and columns
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foreach (int i in RANGE)
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{
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// rows
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solver.Add((from j in RANGE select x[i, j]).ToArray().AllDifferent());
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// cols
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solver.Add((from j in RANGE select x[j, i]).ToArray().AllDifferent());
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}
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// cells
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foreach (int i in CELL)
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{
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foreach (int j in CELL)
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{
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solver.Add((from di in CELL from dj in CELL select x[i * cell_size + di, j * cell_size + dj])
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.ToArray()
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.AllDifferent());
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}
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}
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// Sum the segments and ensure alldifferent
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for (int i = 0; i < num_p; i++)
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{
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int[] segment = problem[i];
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// Remove the sum from the segment
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int[] s2 = new int[segment.Length - 1];
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for (int j = 1; j < segment.Length; j++)
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{
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s2[j - 1] = segment[j];
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}
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// sum this segment
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calc(solver, s2, x, segment[0]);
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// all numbers in this segment must be distinct
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int len = segment.Length / 2;
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solver.Add((from j in Enumerable.Range(0, len) select x[s2[j * 2] - 1, s2[j * 2 + 1] - 1])
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.ToArray()
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.AllDifferent());
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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(x_flat, Solver.INT_VAR_DEFAULT, Solver.INT_VALUE_DEFAULT);
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solver.NewSearch(db);
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while (solver.NextSolution())
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{
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for (int i = 0; i < n; i++)
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{
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for (int j = 0; j < n; j++)
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{
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int v = (int)x[i, j].Value();
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if (v > 0)
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{
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Console.Write(v + " ");
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}
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else
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{
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Console.Write(" ");
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}
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}
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Console.WriteLine();
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}
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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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{
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Solve();
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}
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}
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