/**
*
* Traffic lights problem.
*
* CSPLib problem 16
* http://www.cs.st-andrews.ac.uk/~ianm/CSPLib/prob/prob016/index.html
* """
* Specification:
* Consider a four way traffic junction with eight traffic lights. Four of the traffic
* lights are for the vehicles and can be represented by the variables V1 to V4 with domains
* {r,ry,g,y} (for red, red-yellow, green and yellow). The other four traffic lights are
* for the pedestrians and can be represented by the variables P1 to P4 with domains {r,g}.
*
* The constraints on these variables can be modelled by quaternary constraints on
* (Vi, Pi, Vj, Pj ) for 1<=i<=4, j=(1+i)mod 4 which allow just the tuples
* {(r,r,g,g), (ry,r,y,r), (g,g,r,r), (y,r,ry,r)}.
*
* It would be interesting to consider other types of junction (e.g. five roads
* intersecting) as well as modelling the evolution over time of the traffic light sequence.
* ...
*
* Results
* Only 2^2 out of the 2^12 possible assignments are solutions.
*
* (V1,P1,V2,P2,V3,P3,V4,P4) =
* {(r,r,g,g,r,r,g,g), (ry,r,y,r,ry,r,y,r), (g,g,r,r,g,g,r,r), (y,r,ry,r,y,r,ry,r)}
* [(1,1,3,3,1,1,3,3), ( 2,1,4,1, 2,1,4,1), (3,3,1,1,3,3,1,1), (4,1, 2,1,4,1, 2,1)}
* The problem has relative few constraints, but each is very
* tight. Local propagation appears to be rather ineffective on this
* problem.
*
* """
* Note: In this model we use only the constraint
* solver.AllowedAssignments().
*
*
* See http://www.hakank.org/or-tools/traffic_lights.py
*
*/
private static void Solve()
{
Solver solver = new Solver("TrafficLights");
//
// data
//
int n = 4;
int r = 0;
int ry = 1;
int g = 2;
int y = 3;
string[] lights = { "r", "ry", "g", "y" };
// The allowed combinations
IntTupleSet allowed = new IntTupleSet(4);
allowed.InsertAll(new int[, ] {
{ r, r, g, g },
{ ry, r, y, r },
{ g, g, r, r },
{ y, r, ry, r }
});
//
// Decision variables
//
IntVar[] V = solver.MakeIntVarArray(n, 0, n - 1, "V");
IntVar[] P = solver.MakeIntVarArray(n, 0, n - 1, "P");
// for search
IntVar[] VP = new IntVar[2 * n];
for (int i = 0; i < n; i++)
{
VP[i] = V[i];
VP[i + n] = P[i];
}
//
// Constraints
//
for (int i = 0; i < n; i++)
{
int j = (1 + i) % n;
IntVar[] tmp = new IntVar[] { V[i], P[i], V[j], P[j] };
solver.Add(tmp.AllowedAssignments(allowed));
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(VP,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution())
{
for (int i = 0; i < n; i++)
{
Console.Write("{0,2} {1,2} ",
lights[V[i].Value()],
lights[P[i].Value()]);
}
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();
}
/**
*
* Hidato puzzle in Google CP Solver.
*
* http://www.hidato.com/
* """
* Puzzles start semi-filled with numbered tiles.
* The first and last numbers are circled.
* Connect the numbers together to win. Consecutive
* number must touch horizontally, vertically, or
* diagonally.
* """
*
* This is a port of the Python model hidato_table.py
* made by Laurent Perron (using AllowedAssignments),
* based on my (much slower) model hidato.py.
*
*/
private static void Solve(int model = 1)
{
Solver solver = new Solver("HidatoTable");
//
// models, a 0 indicates an open cell which number is not yet known.
//
int[,] puzzle = null;
if (model == 1)
{
// Simple problem
// Solution 1:
// 6 7 9
// 5 2 8
// 1 4 3
int[,] puzzle1 = { { 6, 0, 9 }, { 0, 2, 8 }, { 1, 0, 0 } };
puzzle = puzzle1;
}
else if (model == 2)
{
int[,] puzzle2 = { { 0, 44, 41, 0, 0, 0, 0 }, { 0, 43, 0, 28, 29, 0, 0 }, { 0, 1, 0, 0, 0, 33, 0 },
{ 0, 2, 25, 4, 34, 0, 36 }, { 49, 16, 0, 23, 0, 0, 0 }, { 0, 19, 0, 0, 12, 7, 0 },
{ 0, 0, 0, 14, 0, 0, 0 } };
puzzle = puzzle2;
}
else if (model == 3)
{
// Problems from the book:
// Gyora Bededek: "Hidato: 2000 Pure Logic Puzzles"
// Problem 1 (Practice)
int[,] puzzle3 =
{
{ 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 }
};
puzzle = puzzle3;
}
else if (model == 4)
{
// problem 2 (Practice)
int[,] puzzle4 =
{
{ 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 }
};
puzzle = puzzle4;
}
else if (model == 5)
{
// problem 3 (Beginner)
int[,] puzzle5 = { { 0, 26, 0, 0, 0, 18 }, { 0, 0, 27, 0, 0, 19 }, { 31, 23, 0, 0, 14, 0 },
{ 0, 33, 8, 0, 15, 1 }, { 0, 0, 0, 5, 0, 0 }, { 35, 36, 0, 10, 0, 0 } };
puzzle = puzzle5;
}
else if (model == 6)
{
// Problem 15 (Intermediate)
int[,] puzzle6 = { { 64, 0, 0, 0, 0, 0, 0, 0 }, { 1, 63, 0, 59, 15, 57, 53, 0 },
{ 0, 4, 0, 14, 0, 0, 0, 0 }, { 3, 0, 11, 0, 20, 19, 0, 50 },
{ 0, 0, 0, 0, 22, 0, 48, 40 }, { 9, 0, 0, 32, 23, 0, 0, 41 },
{ 27, 0, 0, 0, 36, 0, 46, 0 }, { 28, 30, 0, 35, 0, 0, 0, 0 } };
puzzle = puzzle6;
}
int r = puzzle.GetLength(0);
int c = puzzle.GetLength(1);
Console.WriteLine();
Console.WriteLine("----- Solving problem {0} -----", model);
Console.WriteLine();
PrintMatrix(puzzle);
//
// Decision variables
//
IntVar[] positions = solver.MakeIntVarArray(r * c, 0, r * c - 1, "p");
//
// Constraints
//
solver.Add(positions.AllDifferent());
//
// Fill in the clues
//
for (int i = 0; i < r; i++)
{
for (int j = 0; j < c; j++)
{
if (puzzle[i, j] > 0)
{
solver.Add(positions[puzzle[i, j] - 1] == i * c + j);
}
}
}
// Consecutive numbers much touch each other in the grid.
// We use an allowed assignment constraint to model it.
IntTupleSet close_tuples = BuildPairs(r, c);
for (int k = 1; k < r * c - 1; k++)
{
IntVar[] tmp = new IntVar[] { positions[k], positions[k + 1] };
solver.Add(tmp.AllowedAssignments(close_tuples));
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(positions, Solver.CHOOSE_MIN_SIZE_LOWEST_MIN, Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
int num_solution = 0;
while (solver.NextSolution())
{
num_solution++;
PrintOneSolution(positions, r, c, num_solution);
}
Console.WriteLine("\nSolutions: " + solver.Solutions());
Console.WriteLine("WallTime: " + solver.WallTime() + "ms ");
Console.WriteLine("Failures: " + solver.Failures());
Console.WriteLine("Branches: " + solver.Branches());
solver.EndSearch();
}
/**
*
* Hidato puzzle in Google CP Solver.
*
* http://www.hidato.com/
* """
* Puzzles start semi-filled with numbered tiles.
* The first and last numbers are circled.
* Connect the numbers together to win. Consecutive
* number must touch horizontally, vertically, or
* diagonally.
* """
*
* This is a port of the Python model hidato_table.py
* made by Laurent Perron (using AllowedAssignments),
* based on my (much slower) model hidato.py.
*
*/
private static void Solve(int model = 1)
{
Solver solver = new Solver("HidatoTable");
//
// models, a 0 indicates an open cell which number is not yet known.
//
int[,] puzzle = null;
if (model == 1) {
// Simple problem
// Solution 1:
// 6 7 9
// 5 2 8
// 1 4 3
int[,] puzzle1 = {{6, 0, 9},
{0, 2, 8},
{1, 0, 0}};
puzzle = puzzle1;
} else if (model == 2) {
int[,] puzzle2 = {{0, 44, 41, 0, 0, 0, 0},
{0, 43, 0, 28, 29, 0, 0},
{0, 1, 0, 0, 0, 33, 0},
{0, 2, 25, 4, 34, 0, 36},
{49, 16, 0, 23, 0, 0, 0},
{0, 19, 0, 0, 12, 7, 0},
{0, 0, 0, 14, 0, 0, 0}};
puzzle = puzzle2;
} else if (model == 3) {
// Problems from the book:
// Gyora Bededek: "Hidato: 2000 Pure Logic Puzzles"
// Problem 1 (Practice)
int[,] puzzle3 = {{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}};
puzzle = puzzle3;
} else if (model == 4) {
// problem 2 (Practice)
int[,] puzzle4 = {{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}};
puzzle = puzzle4;
} else if (model == 5) {
// problem 3 (Beginner)
int[,] puzzle5 = {{0, 26, 0, 0, 0, 18},
{0, 0, 27, 0, 0, 19},
{31, 23, 0, 0, 14, 0},
{0, 33, 8, 0, 15, 1},
{0, 0, 0, 5, 0, 0},
{35, 36, 0, 10, 0, 0}};
puzzle = puzzle5;
} else if (model == 6) {
// Problem 15 (Intermediate)
int[,] puzzle6 = {{64, 0, 0, 0, 0, 0, 0, 0},
{1, 63, 0, 59, 15, 57, 53, 0},
{0, 4, 0, 14, 0, 0, 0, 0},
{3, 0, 11, 0, 20, 19, 0, 50},
{0, 0, 0, 0, 22, 0, 48, 40},
{9, 0, 0, 32, 23, 0, 0, 41},
{27, 0, 0, 0, 36, 0, 46, 0},
{28, 30, 0, 35, 0, 0, 0, 0}};
puzzle = puzzle6;
}
int r = puzzle.GetLength(0);
int c = puzzle.GetLength(1);
Console.WriteLine();
Console.WriteLine("----- Solving problem {0} -----", model);
Console.WriteLine();
PrintMatrix(puzzle);
//
// Decision variables
//
IntVar[] positions = solver.MakeIntVarArray(r*c, 0, r * c - 1, "p");
//
// Constraints
//
solver.Add(positions.AllDifferent());
//
// Fill in the clues
//
for(int i = 0; i < r; i++) {
for(int j = 0; j < c; j++) {
if (puzzle[i,j] > 0) {
solver.Add(positions[puzzle[i,j] - 1] == i * c + j);
}
}
}
// Consecutive numbers much touch each other in the grid.
// We use an allowed assignment constraint to model it.
IntTupleSet close_tuples = BuildPairs(r, c);
for(int k = 1; k < r * c - 1; k++) {
IntVar[] tmp = new IntVar[] {positions[k], positions[k + 1]};
solver.Add(tmp.AllowedAssignments(close_tuples));
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(positions,
Solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
int num_solution = 0;
while (solver.NextSolution()) {
num_solution++;
PrintOneSolution(positions, r, c, num_solution);
}
Console.WriteLine("\nSolutions: " + solver.Solutions());
Console.WriteLine("WallTime: " + solver.WallTime() + "ms ");
Console.WriteLine("Failures: " + solver.Failures());
Console.WriteLine("Branches: " + solver.Branches());
solver.EndSearch();
}
/**
*
* Traffic lights problem.
*
* CSPLib problem 16
* http://www.csplib.org/Problems/prob016
* """
* Specification:
* Consider a four way traffic junction with eight traffic lights. Four of the traffic
* lights are for the vehicles and can be represented by the variables V1 to V4 with domains
* {r,ry,g,y} (for red, red-yellow, green and yellow). The other four traffic lights are
* for the pedestrians and can be represented by the variables P1 to P4 with domains {r,g}.
*
* The constraints on these variables can be modelled by quaternary constraints on
* (Vi, Pi, Vj, Pj ) for 1<=i<=4, j=(1+i)mod 4 which allow just the tuples
* {(r,r,g,g), (ry,r,y,r), (g,g,r,r), (y,r,ry,r)}.
*
* It would be interesting to consider other types of junction (e.g. five roads
* intersecting) as well as modelling the evolution over time of the traffic light sequence.
* ...
*
* Results
* Only 2^2 out of the 2^12 possible assignments are solutions.
*
* (V1,P1,V2,P2,V3,P3,V4,P4) =
* {(r,r,g,g,r,r,g,g), (ry,r,y,r,ry,r,y,r), (g,g,r,r,g,g,r,r), (y,r,ry,r,y,r,ry,r)}
* [(1,1,3,3,1,1,3,3), ( 2,1,4,1, 2,1,4,1), (3,3,1,1,3,3,1,1), (4,1, 2,1,4,1, 2,1)}
* The problem has relative few constraints, but each is very
* tight. Local propagation appears to be rather ineffective on this
* problem.
*
* """
* Note: In this model we use only the constraint
* solver.AllowedAssignments().
*
*
* See http://www.hakank.org/or-tools/traffic_lights.py
*
*/
private static void Solve()
{
Solver solver = new Solver("TrafficLights");
//
// data
//
int n = 4;
int r = 0;
int ry = 1;
int g = 2;
int y = 3;
string[] lights = {"r", "ry", "g", "y"};
// The allowed combinations
IntTupleSet allowed = new IntTupleSet(4);
allowed.InsertAll(new int[,] {{r,r,g,g},
{ry,r,y,r},
{g,g,r,r},
{y,r,ry,r}});
//
// Decision variables
//
IntVar[] V = solver.MakeIntVarArray(n, 0, n-1, "V");
IntVar[] P = solver.MakeIntVarArray(n, 0, n-1, "P");
// for search
IntVar[] VP = new IntVar[2 * n];
for(int i = 0; i < n; i++) {
VP[i] = V[i];
VP[i+n] = P[i];
}
//
// Constraints
//
for(int i = 0; i < n; i++) {
int j = (1+i) % n;
IntVar[] tmp = new IntVar[] {V[i],P[i],V[j],P[j]};
solver.Add(tmp.AllowedAssignments(allowed));
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(VP,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
for(int i = 0; i < n; i++) {
Console.Write("{0,2} {1,2} ",
lights[V[i].Value()],
lights[P[i].Value()]);
}
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();
}