Download
//
// 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();
}
}