229 lines
6.6 KiB
C#
229 lines
6.6 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 EinavPuzzle2
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{
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/**
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*
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* A programming puzzle from Einav.
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*
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* From
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* "A programming puzzle from Einav"
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* http://gcanyon.wordpress.com/2009/10/28/a-programming-puzzle-from-einav/
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* """
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* My friend Einav gave me this programming puzzle to work on. Given
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* this array of positive and negative numbers:
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* 33 30 -10 -6 18 7 -11 -23 6
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* ...
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* -25 4 16 30 33 -23 -4 4 -23
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*
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* You can flip the sign of entire rows and columns, as many of them
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* as you like. The goal is to make all the rows and columns sum to positive
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* numbers (or zero), and then to find the solution (there are more than one)
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* that has the smallest overall sum. So for example, for this array:
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* 33 30 -10
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* -16 19 9
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* -17 -12 -14
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* You could flip the sign for the bottom row to get this array:
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* 33 30 -10
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* -16 19 9
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* 17 12 14
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* Now all the rows and columns have positive sums, and the overall total is
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* 108.
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* But you could instead flip the second and third columns, and the second
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* row, to get this array:
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* 33 -30 10
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* 16 19 9
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* -17 12 14
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* All the rows and columns still total positive, and the overall sum is just
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* 66. So this solution is better (I don't know if it's the best)
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* A pure brute force solution would have to try over 30 billion solutions.
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* I wrote code to solve this in J. I'll post that separately.
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* """
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*
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* Note:
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* This is a port of Larent Perrons's Python version of my own einav_puzzle.py.
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* He removed some of the decision variables and made it more efficient.
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* Thanks!
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*
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* Also see http://www.hakank.org/or-tools/einav_puzzle2.py
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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("EinavPuzzle2");
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//
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// Data
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//
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// Small problem
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// int rows = 3;
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// int cols = 3;
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// int[,] data = {
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// { 33, 30, -10},
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// {-16, 19, 9},
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// {-17, -12, -14}
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// };
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// Full problem
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int rows = 27;
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int cols = 9;
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int[,] data = {
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{33,30,10,-6,18,-7,-11,23,-6},
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{16,-19,9,-26,-8,-19,-8,-21,-14},
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{17,12,-14,31,-30,13,-13,19,16},
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{-6,-11,1,17,-12,-4,-7,14,-21},
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{18,-31,34,-22,17,-19,20,24,6},
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{33,-18,17,-15,31,-5,3,27,-3},
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{-18,-20,-18,31,6,4,-2,-12,24},
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{27,14,4,-29,-3,5,-29,8,-12},
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{-15,-7,-23,23,-9,-8,6,8,-12},
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{33,-23,-19,-4,-8,-7,11,-12,31},
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{-20,19,-15,-30,11,32,7,14,-5},
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{-23,18,-32,-2,-31,-7,8,24,16},
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{32,-4,-10,-14,-6,-1,0,23,23},
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{25,0,-23,22,12,28,-27,15,4},
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{-30,-13,-16,-3,-3,-32,-3,27,-31},
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{22,1,26,4,-2,-13,26,17,14},
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{-9,-18,3,-20,-27,-32,-11,27,13},
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{-17,33,-7,19,-32,13,-31,-2,-24},
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{-31,27,-31,-29,15,2,29,-15,33},
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{-18,-23,15,28,0,30,-4,12,-32},
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{-3,34,27,-25,-18,26,1,34,26},
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{-21,-31,-10,-13,-30,-17,-12,-26,31},
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{23,-31,-19,21,-17,-10,2,-23,23},
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{-3,6,0,-3,-32,0,-10,-25,14},
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{-19,9,14,-27,20,15,-5,-27,18},
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{11,-6,24,7,-17,26,20,-31,-25},
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{-25,4,-16,30,33,23,-4,-4,23}
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};
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IEnumerable<int> ROWS = Enumerable.Range(0, rows);
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IEnumerable<int> COLS = Enumerable.Range(0, cols);
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//
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// Decision variables
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//
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IntVar[,] x = solver.MakeIntVarMatrix(rows, cols, -100, 100, "x");
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IntVar[] x_flat = x.Flatten();
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int[] signs_domain = {-1,1};
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// This don't work at the moment...
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IntVar[] row_signs = solver.MakeIntVarArray(rows, signs_domain, "row_signs");
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IntVar[] col_signs = solver.MakeIntVarArray(cols, signs_domain, "col_signs");
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// To optimize
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IntVar total_sum = x_flat.Sum().VarWithName("total_sum");
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//
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// Constraints
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//
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foreach(int i in ROWS) {
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foreach(int j in COLS) {
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solver.Add(x[i,j] == data[i,j] * row_signs[i] * col_signs[j]);
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}
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}
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// row sums
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IntVar[] row_sums = (from i in ROWS
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select (from j in COLS
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select x[i,j]
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).ToArray().Sum().Var()).ToArray();
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foreach(int i in ROWS) {
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row_sums[i].SetMin(0);
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}
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// col sums
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IntVar[] col_sums = (from j in COLS
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select (from i in ROWS
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select x[i,j]
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).ToArray().Sum().Var()).ToArray();
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foreach(int j in COLS) {
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col_sums[j].SetMin(0);
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}
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//
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// Objective
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//
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OptimizeVar obj = total_sum.Minimize(1);
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//
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// Search
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//
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DecisionBuilder db = solver.MakePhase(col_signs.Concat(row_signs).ToArray(),
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Solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
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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("Sum: {0}",total_sum.Value());
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Console.Write("row_sums: ");
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foreach(int i in ROWS) {
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Console.Write(row_sums[i].Value() + " ");
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}
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Console.Write("\nrow_signs: ");
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foreach(int i in ROWS) {
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Console.Write(row_signs[i].Value() + " ");
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}
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Console.Write("\ncol_sums: ");
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foreach(int j in COLS) {
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Console.Write(col_sums[j].Value() + " ");
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}
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Console.Write("\ncol_signs: ");
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foreach(int j in COLS) {
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Console.Write(col_signs[j].Value() + " ");
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}
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Console.WriteLine("\n");
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foreach(int i in ROWS) {
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foreach(int j in COLS) {
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Console.Write("{0,3} ", x[i,j].Value());
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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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{
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Solve();
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}
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}
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