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//
// 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 KillerSudoku
{
/**
* Ensure that the sum of the segments
* in cc == res
*
*/
public static void calc(Solver solver,
int[] cc,
IntVar[,] x,
int res)
{
// sum the numbers
int len = cc.Length / 2;
solver.Add( (from i in Enumerable.Range(0, len)
select x[cc[i*2]-1,cc[i*2+1]-1]).ToArray().Sum() == res);
}
/**
*
* Killer Sudoku.
*
* http://en.wikipedia.org/wiki/Killer_Sudoku
* """
* Killer sudoku (also killer su doku, sumdoku, sum doku, addoku, or
* samunamupure) is a puzzle that combines elements of sudoku and kakuro.
* Despite the name, the simpler killer sudokus can be easier to solve
* than regular sudokus, depending on the solver's skill at mental arithmetic;
* the hardest ones, however, can take hours to crack.
*
* ...
*
* The objective is to fill the grid with numbers from 1 to 9 in a way that
* the following conditions are met:
*
* - Each row, column, and nonet contains each number exactly once.
* - The sum of all numbers in a cage must match the small number printed
* in its corner.
* - No number appears more than once in a cage. (This is the standard rule
* for killer sudokus, and implies that no cage can include more
* than 9 cells.)
*
* In 'Killer X', an additional rule is that each of the long diagonals
* contains each number once.
* """
*
* Here we solve the problem from the Wikipedia page, also shown here
* http://en.wikipedia.org/wiki/File:Killersudoku_color.svg
*
* The output is:
* 2 1 5 6 4 7 3 9 8
* 3 6 8 9 5 2 1 7 4
* 7 9 4 3 8 1 6 5 2
* 5 8 6 2 7 4 9 3 1
* 1 4 2 5 9 3 8 6 7
* 9 7 3 8 1 6 4 2 5
* 8 2 1 7 3 9 5 4 6
* 6 5 9 4 2 8 7 1 3
* 4 3 7 1 6 5 2 8 9
*
* Also see http://www.hakank.org/or-tools/killer_sudoku.py
* though this C# model has another representation of
* the problem instance.
*
*/
private static void Solve()
{
Solver solver = new Solver("KillerSudoku");
// size of matrix
int cell_size = 3;
IEnumerable<int> CELL = Enumerable.Range(0, cell_size);
int n = cell_size*cell_size;
IEnumerable<int> RANGE = Enumerable.Range(0, n);
// For a better view of the problem, see
// http://en.wikipedia.org/wiki/File:Killersudoku_color.svg
// hints
// sum, the hints
// Note: this is 1-based
int[][] problem =
{
new int[] { 3, 1,1, 1,2},
new int[] {15, 1,3, 1,4, 1,5},
new int[] {22, 1,6, 2,5, 2,6, 3,5},
new int[] {4, 1,7, 2,7},
new int[] {16, 1,8, 2,8},
new int[] {15, 1,9, 2,9, 3,9, 4,9},
new int[] {25, 2,1, 2,2, 3,1, 3,2},
new int[] {17, 2,3, 2,4},
new int[] { 9, 3,3, 3,4, 4,4},
new int[] { 8, 3,6, 4,6, 5,6},
new int[] {20, 3,7, 3,8, 4,7},
new int[] { 6, 4,1, 5,1},
new int[] {14, 4,2, 4,3},
new int[] {17, 4,5, 5,5, 6,5},
new int[] {17, 4,8, 5,7, 5,8},
new int[] {13, 5,2, 5,3, 6,2},
new int[] {20, 5,4, 6,4, 7,4},
new int[] {12, 5,9, 6,9},
new int[] {27, 6,1, 7,1, 8,1, 9,1},
new int[] { 6, 6,3, 7,2, 7,3},
new int[] {20, 6,6, 7,6, 7,7},
new int[] { 6, 6,7, 6,8},
new int[] {10, 7,5, 8,4, 8,5, 9,4},
new int[] {14, 7,8, 7,9, 8,8, 8,9},
new int[] { 8, 8,2, 9,2},
new int[] {16, 8,3, 9,3},
new int[] {15, 8,6, 8,7},
new int[] {13, 9,5, 9,6, 9,7},
new int[] {17, 9,8, 9,9}
};
int num_p = 29; // Number of segments
//
// Decision variables
//
IntVar[,] x = solver.MakeIntVarMatrix(n, n, 0, 9, "x");
IntVar[] x_flat = x.Flatten();
//
// Constraints
//
//
// The first three constraints is the same as for sudokus.cs
//
// alldifferent rows and columns
foreach(int i in RANGE) {
// rows
solver.Add( (from j in RANGE
select x[i,j]).ToArray().AllDifferent());
// cols
solver.Add( (from j in RANGE
select x[j,i]).ToArray().AllDifferent());
}
// cells
foreach(int i in CELL) {
foreach(int j in CELL) {
solver.Add( (from di in CELL
from dj in CELL
select x[i*cell_size+di, j*cell_size+dj]
).ToArray().AllDifferent());
}
}
// Sum the segments and ensure alldifferent
for(int i = 0; i < num_p; i++) {
int[] segment = problem[i];
// Remove the sum from the segment
int[] s2 = new int[segment.Length-1];
for(int j = 1; j < segment.Length; j++) {
s2[j-1] = segment[j];
}
// sum this segment
calc(solver, s2, x, segment[0]);
// all numbers in this segment must be distinct
int len = segment.Length / 2;
solver.Add( (from j in Enumerable.Range(0, len)
select x[s2[j*2]-1, s2[j*2+1]-1])
.ToArray().AllDifferent());
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(x_flat,
Solver.INT_VAR_DEFAULT,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db);
while (solver.NextSolution()) {
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
int v = (int)x[i,j].Value();
if (v > 0) {
Console.Write(v + " ");
} else {
Console.Write(" ");
}
}
Console.WriteLine();
}
}
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();
}
}
This work is licensed under a Creative Commons Attribution 4.0 International License.