/**
*
* Discrete tomography
*
* Problem from http://eclipse.crosscoreop.com/examples/tomo.ecl.txt
* """
* This is a little 'tomography' problem, taken from an old issue
* of Scientific American.
*
* A matrix which contains zeroes and ones gets "x-rayed" vertically and
* horizontally, giving the total number of ones in each row and column.
* The problem is to reconstruct the contents of the matrix from this
* information. Sample run:
*
* ?- go.
* 0 0 7 1 6 3 4 5 2 7 0 0
* 0
* 0
* 8 * * * * * * * *
* 2 * *
* 6 * * * * * *
* 4 * * * *
* 5 * * * * *
* 3 * * *
* 7 * * * * * * *
* 0
* 0
*
* Eclipse solution by Joachim Schimpf, IC-Parc
* """
*
* See http://www.hakank.org/or-tools/discrete_tomography.py
*
*/
private static void Solve(int[] rowsums, int[] colsums)
{
Solver solver = new Solver("DiscreteTomography");
//
// Data
//
int r = rowsums.Length;
int c = colsums.Length;
Console.Write("rowsums: ");
for(int i = 0; i < r; i++) {
Console.Write(rowsums[i] + " ");
}
Console.Write("\ncolsums: ");
for(int j = 0; j < c; j++) {
Console.Write(colsums[j] + " ");
}
Console.WriteLine("\n");
//
// Decision variables
//
IntVar[,] x = solver.MakeIntVarMatrix(r, c, 0, 1, "x");
IntVar[] x_flat = x.Flatten();
//
// Constraints
//
// row sums
for(int i = 0; i < r; i++) {
var tmp = from j in Enumerable.Range(0, c) select x[i,j];
solver.Add(tmp.ToArray().Sum() == rowsums[i]);
}
// cols sums
for(int j = 0; j < c; j++) {
var tmp = from i in Enumerable.Range(0, r) select x[i,j];
solver.Add(tmp.ToArray().Sum() == colsums[j]);
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(x_flat,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
for(int i = 0; i < r; i++) {
for(int j = 0; j < c; j++) {
Console.Write("{0} ", x[i,j].Value() == 1 ? "#" : "." );
}
Console.WriteLine();
}
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();
}
private static long Solve(long num_buses_check = 0)
{
SolverParameters sPrm = new SolverParameters();
sPrm.compress_trail = 0;
sPrm.trace_level = 0;
sPrm.profile_level = 0;
Solver solver = new Solver("OrTools",sPrm);
//this works
// IntVar[,] x = solver.MakeIntVarMatrix(2,2, new int[] {-2,0,1,2}, "x");
//this doesn't work
IntVar[,] x = solver.MakeIntVarMatrix(2, 2, new int[] { 0, 1, 2 }, "x");
for (int w = 0; w < 2; w++)
{
IntVar[] b = new IntVar[2];
for (int i = 0; i < 2; i++)
{
b[i] = solver.MakeIsEqualCstVar(x[w, i], 0);
}
solver.Add(solver.MakeSumGreaterOrEqual(b, 2));
}
IntVar[] x_flat = x.Flatten();
DecisionBuilder db = solver.MakePhase(x_flat,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution())
{
Console.WriteLine("x: ");
for (int j = 0; j < 2; j++)
{
Console.Write("worker" + (j + 1).ToString() + ":");
for (int i = 0; i < 2; i++)
{
Console.Write(" {0,2} ", x[j, i].Value());
}
Console.Write("\n");
}
Console.WriteLine("End at---->" + DateTime.Now);
}
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();
return 1;
}
/**
*
* Costas array
*
* From http://mathworld.wolfram.com/CostasArray.html:
* """
* An order-n Costas array is a permutation on {1,...,n} such
* that the distances in each row of the triangular difference
* table are distinct. For example, the permutation {1,3,4,2,5}
* has triangular difference table {2,1,-2,3}, {3,-1,1}, {1,2},
* and {4}. Since each row contains no duplications, the permutation
* is therefore a Costas array.
* """
*
* Also see
* http://en.wikipedia.org/wiki/Costas_array
* http://hakank.org/or-tools/costas_array.py
*
*/
private static void Solve(int n = 6)
{
Solver solver = new Solver("CostasArray");
//
// Data
//
Console.WriteLine("n: {0}", n);
//
// Decision variables
//
IntVar[] costas = solver.MakeIntVarArray(n, 1, n, "costas");
IntVar[,] differences = solver.MakeIntVarMatrix(n, n, -n+1, n-1,
"differences");
//
// Constraints
//
// Fix the values in the lower triangle in the
// difference matrix to -n+1. This removes variants
// of the difference matrix for the the same Costas array.
for(int i = 0; i < n; i++) {
for(int j = 0; j <= i; j++ ) {
solver.Add(differences[i,j] == -n+1);
}
}
// hakank: All the following constraints are from
// Barry O'Sullivans's original model.
//
solver.Add(costas.AllDifferent());
// "How do the positions in the Costas array relate
// to the elements of the distance triangle."
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
if (i < j) {
solver.Add( differences[i,j] - (costas[j] - costas[j-i-1]) == 0);
}
}
}
// "All entries in a particular row of the difference
// triangle must be distint."
for(int i = 0; i < n-2; i++) {
IntVar[] tmp = (
from j in Enumerable.Range(0, n)
where j > i
select differences[i,j]).ToArray();
solver.Add(tmp.AllDifferent());
}
//
// "All the following are redundant - only here to speed up search."
//
// "We can never place a 'token' in the same row as any other."
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
if (i < j) {
solver.Add(differences[i,j] != 0);
solver.Add(differences[i,j] != 0);
}
}
}
for(int k = 2; k < n; k++) {
for(int l = 2; l < n; l++) {
if (k < l) {
solver.Add(
(differences[k-2,l-1] + differences[k,l]) -
(differences[k-1,l-1] + differences[k-1,l]) == 0
);
}
}
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(costas,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.Write("costas: ");
for(int i = 0; i < n; i++) {
Console.Write("{0} ", costas[i].Value());
}
Console.WriteLine("\ndifferences:");
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
long v = differences[i,j].Value();
if (v == -n+1) {
Console.Write(" ");
} else {
Console.Write("{0,2} ", v);
}
}
Console.WriteLine();
}
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();
}
/**
*
* Solves a Sudoku problem.
*
* This is a very simple 4x4 problem instance:
* Problem 26: Shidoku from
* "Taking Sudoku Seriously", page 61
* 4 _ _ _
* 3 1 _ _
*
* _ _ 4 1
* _ _ _ 2
*
*/
private static void Solve()
{
Solver solver = new Solver("Sudoku");
//
// data
//
int block_size = 2;
IEnumerable<int> BLOCK = Enumerable.Range(0, block_size);
int n = block_size * block_size;
IEnumerable<int> RANGE = Enumerable.Range(0, n);
// 0 marks an unknown value
int[,] initial_grid = {{4, 0, 0, 0},
{3, 1, 0, 0},
{0, 0, 4, 1},
{0, 0, 0, 2}};
//
// Decision variables
//
IntVar[,] grid = solver.MakeIntVarMatrix(n, n, 1, n, "grid");
IntVar[] grid_flat = grid.Flatten();
//
// Constraints
//
// init
foreach(int i in RANGE) {
foreach(int j in RANGE) {
if (initial_grid[i,j] > 0) {
solver.Add(grid[i,j] == initial_grid[i,j]);
}
}
}
foreach(int i in RANGE) {
// rows
solver.Add( (from j in RANGE
select grid[i,j]).ToArray().AllDifferent());
// cols
solver.Add( (from j in RANGE
select grid[j,i]).ToArray().AllDifferent());
}
// blocks
foreach(int i in BLOCK) {
foreach(int j in BLOCK) {
solver.Add( (from di in BLOCK
from dj in BLOCK
select grid[i*block_size+di, j*block_size+dj]
).ToArray().AllDifferent());
}
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(grid_flat,
Solver.INT_VAR_SIMPLE,
Solver.INT_VALUE_SIMPLE);
solver.NewSearch(db);
while (solver.NextSolution()) {
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++){
Console.Write("{0} ", grid[i,j].Value());
}
Console.WriteLine();
}
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();
}
/**
*
* Implements the Who killed Agatha problem.
* See http://www.hakank.org/google_or_tools/who_killed_agatha.py
*
*/
private static void Solve()
{
Solver solver = new Solver("WhoKilledAgatha");
int n = 3;
int agatha = 0;
int butler = 1;
int charles = 2;
//
// Decision variables
//
IntVar the_killer = solver.MakeIntVar(0, 2, "the_killer");
IntVar the_victim = solver.MakeIntVar(0, 2, "the_victim");
IntVar[,] hates = solver.MakeIntVarMatrix(n, n, 0, 1, "hates");
IntVar[] hates_flat = hates.Flatten();
IntVar[,] richer = solver.MakeIntVarMatrix(n, n, 0, 1, "richer");
IntVar[] richer_flat = richer.Flatten();
IntVar[] all = new IntVar[2 * n * n]; // for branching
for(int i = 0; i < n*n; i++) {
all[i] = hates_flat[i];
all[(n*n)+i] = richer_flat[i];
}
//
// Constraints
//
// Agatha, the butler, and Charles live in Dreadsbury Mansion, and
// are the only ones to live there.
// A killer always hates, and is no richer than his victim.
// hates[the_killer, the_victim] == 1
// hates_flat[the_killer * n + the_victim] == 1
solver.Add(hates_flat.Element(the_killer * n + the_victim) == 1);
// richer[the_killer, the_victim] == 0
solver.Add(richer_flat.Element(the_killer * n + the_victim) == 0);
// define the concept of richer:
// no one is richer than him-/herself...
for(int i = 0; i < n; i++) {
solver.Add(richer[i,i] == 0);
}
// (contd...) if i is richer than j then j is not richer than i
// if (i != j) =>
// ((richer[i,j] = 1) <=> (richer[j,i] = 0))
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
if (i != j) {
solver.Add((richer[i, j]==1) - (richer[j, i]==0) == 0);
}
}
}
// Charles hates no one that Agatha hates.
// forall i in 0..2:
// (hates[agatha, i] = 1) => (hates[charles, i] = 0)
for(int i = 0; i < n; i++) {
solver.Add((hates[agatha,i]==1) - (hates[charles,i]==0) <= 0);
}
// Agatha hates everybody except the butler.
solver.Add(hates[agatha,charles] == 1);
solver.Add(hates[agatha,agatha] == 1);
solver.Add(hates[agatha,butler] == 0);
// The butler hates everyone not richer than Aunt Agatha.
// forall i in 0..2:
// (richer[i, agatha] = 0) => (hates[butler, i] = 1)
for(int i = 0; i < n; i++) {
solver.Add((richer[i,agatha] == 0)-(hates[butler,i] == 1)<=0);
}
// The butler hates everyone whom Agatha hates.
// forall i : 0..2:
// (hates[agatha, i] = 1) => (hates[butler, i] = 1)
for(int i = 0; i < n; i++) {
solver.Add((hates[agatha,i] == 1)-(hates[butler,i] == 1)<=0);
}
// Noone hates everyone.
// forall i in 0..2:
// (sum j in 0..2: hates[i,j]) <= 2
for(int i = 0; i < n; i++) {
solver.Add((from j in Enumerable.Range(0, n)
select hates[i,j]
).ToArray().Sum() <= 2 );
}
// Who killed Agatha?
solver.Add(the_victim == agatha);
//
// Search
//
DecisionBuilder db = solver.MakePhase(all,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.WriteLine("the_killer: " + the_killer.Value());
}
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();
}
/**
*
* Crew allocation problem in Google CP Solver.
*
* From Gecode example crew
* examples/crew.cc
* """
* Example: Airline crew allocation
*
* Assign 20 flight attendants to 10 flights. Each flight needs a certain
* number of cabin crew, and they have to speak certain languages.
* Every cabin crew member has two flights off after an attended flight.
* """
*
* Also see http://www.hakank.org/or-tools/crew.pl
*
*/
private static void Solve(int sols = 1, int minimize = 0)
{
Solver solver = new Solver("Crew");
//
// Data
//
string[] names = {"Tom",
"David",
"Jeremy",
"Ron",
"Joe",
"Bill",
"Fred",
"Bob",
"Mario",
"Ed",
"Carol",
"Janet",
"Tracy",
"Marilyn",
"Carolyn",
"Cathy",
"Inez",
"Jean",
"Heather",
"Juliet"};
int num_persons = names.Length;
//
// Attributes of the crew
//
int[,] attributes = {
// steward, hostess, french, spanish, german
{1,0,0,0,1}, // Tom = 0
{1,0,0,0,0}, // David = 1
{1,0,0,0,1}, // Jeremy = 2
{1,0,0,0,0}, // Ron = 3
{1,0,0,1,0}, // Joe = 4
{1,0,1,1,0}, // Bill = 5
{1,0,0,1,0}, // Fred = 6
{1,0,0,0,0}, // Bob = 7
{1,0,0,1,1}, // Mario = 8
{1,0,0,0,0}, // Ed = 9
{0,1,0,0,0}, // Carol = 10
{0,1,0,0,0}, // Janet = 11
{0,1,0,0,0}, // Tracy = 12
{0,1,0,1,1}, // Marilyn = 13
{0,1,0,0,0}, // Carolyn = 14
{0,1,0,0,0}, // Cathy = 15
{0,1,1,1,1}, // Inez = 16
{0,1,1,0,0}, // Jean = 17
{0,1,0,1,1}, // Heather = 18
{0,1,1,0,0} // Juliet = 19
};
//
// Required number of crew members.
//
// The columns are in the following order:
// staff : Overall number of cabin crew needed
// stewards : How many stewards are required
// hostesses : How many hostesses are required
// french : How many French speaking employees are required
// spanish : How many Spanish speaking employees are required
// german : How many German speaking employees are required
//
int[,] required_crew = {
{4,1,1,1,1,1}, // Flight 1
{5,1,1,1,1,1}, // Flight 2
{5,1,1,1,1,1}, // ..
{6,2,2,1,1,1},
{7,3,3,1,1,1},
{4,1,1,1,1,1},
{5,1,1,1,1,1},
{6,1,1,1,1,1},
{6,2,2,1,1,1}, // ...
{7,3,3,1,1,1} // Flight 10
};
int num_flights = required_crew.GetLength(0);
//
// Decision variables
//
IntVar[,] crew = solver.MakeIntVarMatrix(num_flights, num_persons,
0, 1, "crew");
IntVar[] crew_flat = crew.Flatten();
// number of working persons
IntVar num_working = solver.MakeIntVar(1, num_persons, "num_working");
//
// Constraints
//
// number of working persons
IntVar[] nw = new IntVar[num_persons];
for(int p = 0; p < num_persons; p++) {
IntVar[] tmp = new IntVar[num_flights];
for(int f = 0; f < num_flights; f++) {
tmp[f] = crew[f,p];
}
nw[p] = tmp.Sum() > 0;
}
solver.Add(nw.Sum() == num_working);
for(int f = 0; f < num_flights; f++) {
// size of crew
IntVar[] tmp = new IntVar[num_persons];
for(int p = 0; p < num_persons; p++) {
tmp[p] = crew[f,p];
}
solver.Add(tmp.Sum() == required_crew[f,0]);
// attributes and requirements
for(int a = 0; a < 5; a++) {
IntVar[] tmp2 = new IntVar[num_persons];
for(int p = 0; p < num_persons; p++) {
tmp2[p] = (crew[f,p]*attributes[p,a]).Var();
}
solver.Add(tmp2.Sum() >= required_crew[f,a+1]);
}
}
// after a flight, break for at least two flights
for(int f = 0; f < num_flights - 2; f++) {
for(int i = 0; i < num_persons; i++) {
solver.Add(crew[f,i] + crew[f+1,i] + crew[f+2,i] <= 1);
}
}
// extra contraint: all must work at least two of the flights
/*
for(int p = 0; p < num_persons; p++) {
IntVar[] tmp = new IntVar[num_flights];
for(int f = 0; f < num_flights; f++) {
tmp[f] = crew[f,p];
}
solver.Add(tmp.Sum() >= 2);
}
*/
//
// Search
//
DecisionBuilder db = solver.MakePhase(crew_flat,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
if (minimize > 0) {
OptimizeVar obj = num_working.Minimize(1);
solver.NewSearch(db, obj);
} else {
solver.NewSearch(db);
}
int num_solutions = 0;
while (solver.NextSolution()) {
num_solutions++;
Console.WriteLine("Solution #{0}", num_solutions);
Console.WriteLine("Number working: {0}", num_working.Value());
for(int f = 0; f < num_flights; f++) {
for(int p = 0; p < num_persons; p++) {
Console.Write(crew[f,p].Value() + " ");
}
Console.WriteLine();
}
Console.WriteLine("\nFlights: ");
for(int f = 0; f < num_flights; f++) {
Console.Write("Flight #{0}: ", f);
for(int p = 0; p < num_persons; p++) {
if (crew[f, p].Value() == 1) {
Console.Write(names[p] + " ");
}
}
Console.WriteLine();
}
Console.WriteLine("\nCrew:");
for(int p = 0; p < num_persons; p++) {
Console.Write("{0,-10}", names[p]);
for(int f = 0; f < num_flights; f++) {
if (crew[f,p].Value() == 1) {
Console.Write(f + " ");
}
}
Console.WriteLine();
}
Console.WriteLine();
if (num_solutions >= sols) {
break;
}
}
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();
}
/**
*
* Nontransitive dice.
*
* From
* http://en.wikipedia.org/wiki/Nontransitive_dice
* """
* A set of nontransitive dice is a set of dice for which the relation
* 'is more likely to roll a higher number' is not transitive. See also
* intransitivity.
*
* This situation is similar to that in the game Rock, Paper, Scissors,
* in which each element has an advantage over one choice and a
* disadvantage to the other.
* """
*
* Also see http://www.hakank.org/or-tools/nontransitive_dice.py
*
*
*/
private static void Solve(int m=3, int n=6, int minimize_val=0)
{
Solver solver = new Solver("Nontransitive_dice");
Console.WriteLine("Number of dice: {0}", m);
Console.WriteLine("Number of sides: {0}", n);
Console.WriteLine("minimize_val: {0}\n", minimize_val);
//
// Decision variables
//
// The dice
IntVar[,] dice = solver.MakeIntVarMatrix(m, n, 1, n*2, "dice");
IntVar[] dice_flat = dice.Flatten();
// For comparison (probability)
IntVar[,] comp = solver.MakeIntVarMatrix(m, 2, 0, n*n, "dice");
IntVar[] comp_flat = comp.Flatten();
// For branching
IntVar[] all = dice_flat.Concat(comp_flat).ToArray();
// The following variables are for summaries or objectives
IntVar[] gap = solver.MakeIntVarArray(m, 0, n*n, "gap");
IntVar gap_sum = gap.Sum().Var();
IntVar max_val = dice_flat.Max().Var();
IntVar max_win = comp_flat.Max().Var();
// number of occurrences of each value of the dice
IntVar[] counts = solver.MakeIntVarArray(n*2+1, 0, n*m, "counts");
//
// Constraints
//
// Number of occurrences for each number
solver.Add(dice_flat.Distribute(counts));
// Order of the number of each die, lowest first
for(int i = 0; i < m; i++) {
for(int j = 0; j < n-1; j++) {
solver.Add(dice[i,j] <= dice[i,j+1]);
}
}
// Nontransitivity
for(int i = 0; i < m; i++) {
solver.Add(comp[i,0] > comp[i,1]);
}
// Probability gap
for(int i = 0; i < m; i++) {
solver.Add(gap[i] == comp[i,0] - comp[i,1]);
solver.Add(gap[i] > 0);
}
// And now we roll...
// comp[] is the number of wins for [A vs B, B vs A]
for(int d = 0; d < m; d++) {
IntVar sum1 = ( from r1 in Enumerable.Range(0, n)
from r2 in Enumerable.Range(0, n)
select (dice[d % m, r1] > dice[(d+1) % m, r2])
).ToArray().Sum().Var();
solver.Add(comp[d%m,0] == sum1);
IntVar sum2 = ( from r1 in Enumerable.Range(0, n)
from r2 in Enumerable.Range(0, n)
select (dice[(d+1) % m, r1] > dice[d % m, r2])
).ToArray().Sum().Var();
solver.Add(comp[d%m,1] == sum2);
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(all,
Solver.INT_VAR_DEFAULT,
Solver.ASSIGN_MIN_VALUE);
if (minimize_val > 0) {
Console.WriteLine("Minimizing max_val");
OptimizeVar obj = max_val.Minimize(1);
// Other experiments:
// OptimizeVar obj = max_win.Maximize(1);
// OptimizeVar obj = gap_sum.Maximize(1);
solver.NewSearch(db, obj);
} else {
solver.NewSearch(db);
}
while (solver.NextSolution()) {
Console.WriteLine("gap_sum: {0}", gap_sum.Value());
Console.WriteLine("gap: {0}", (from i in Enumerable.Range(0, m)
select gap[i].Value().ToString()
).ToArray()
);
Console.WriteLine("max_val: {0}", max_val.Value());
Console.WriteLine("max_win: {0}", max_win.Value());
Console.WriteLine("dice:");
for(int i = 0; i < m; i++) {
for(int j = 0; j < n; j++) {
Console.Write(dice[i,j].Value() + " ");
}
Console.WriteLine();
}
Console.WriteLine("comp:");
for(int i = 0; i < m; i++) {
for(int j = 0; j < 2; j++) {
Console.Write(comp[i,j].Value() + " ");
}
Console.WriteLine();
}
Console.WriteLine("counts:");
for(int i = 1; i < n*2+1; i++) {
int c = (int)counts[i].Value();
if (c > 0) {
Console.Write("{0}({1}) ", i, c);
}
}
Console.WriteLine("\n");
}
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();
}
/**
*
* Word square.
*
* From http://en.wikipedia.org/wiki/Word_square
* """
* A word square is a special case of acrostic. It consists of a set of words,
* all having the same number of letters as the total number of words (the
* 'order' of the square); when the words are written out in a square grid
* horizontally, the same set of words can be read vertically.
* """
*
* See http://www.hakank.org/or-tools/word_square.py
*
*/
private static void Solve(String[] words, int word_len, int num_answers)
{
Solver solver = new Solver("WordSquare");
int num_words = words.Length;
Console.WriteLine("num_words: " + num_words);
int n = word_len;
IEnumerable<int> WORDLEN = Enumerable.Range(0, word_len);
//
// convert a character to integer
//
String alpha = "abcdefghijklmnopqrstuvwxyz";
Hashtable d = new Hashtable();
Hashtable rev = new Hashtable();
int count = 1;
for(int a = 0; a < alpha.Length; a++) {
d[alpha[a]] = count;
rev[count] = a;
count++;
}
int num_letters = alpha.Length;
//
// Decision variables
//
IntVar[,] A = solver.MakeIntVarMatrix(num_words, word_len,
0, num_letters, "A");
IntVar[] A_flat = A.Flatten();
IntVar[] E = solver.MakeIntVarArray(n, 0, num_words, "E");
//
// Constraints
//
solver.Add(E.AllDifferent());
// copy the words to a matrix
for(int i = 0; i < num_words; i++) {
char[] s = words[i].ToArray();
foreach(int j in WORDLEN) {
int t = (int)d[s[j]];
solver.Add(A[i,j] == t);
}
}
foreach(int i in WORDLEN) {
foreach(int j in WORDLEN) {
solver.Add(A_flat.Element(E[i]*word_len+j) ==
A_flat.Element(E[j]*word_len+i));
}
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(E.Concat(A_flat).ToArray(),
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
int num_sols = 0;
while (solver.NextSolution()) {
num_sols++;
for(int i = 0; i < n; i++) {
Console.WriteLine(words[E[i].Value()] + " ");
}
Console.WriteLine();
if (num_answers > 0 && num_sols >= num_answers) {
break;
}
}
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();
}
/**
*
* Solves the Magic Square problem.
* See http://www.hakank.org/or-tools/magic_square.py
*
*/
private static void Solve(int n = 4, int num = 0, int print = 1)
{
Solver solver = new Solver("MagicSquare");
Console.WriteLine("n: {0}", n);
//
// Decision variables
//
IntVar[,] x = solver.MakeIntVarMatrix(n, n, 1, n*n, "x");
// for the branching
IntVar[] x_flat = x.Flatten();
//
// Constraints
//
long s = (n * (n * n + 1)) / 2;
Console.WriteLine("s: " + s);
IntVar[] diag1 = new IntVar[n];
IntVar[] diag2 = new IntVar[n];
for(int i = 0; i < n; i++) {
IntVar[] row = new IntVar[n];
for(int j = 0; j < n; j++) {
row[j] = x[i,j];
}
// sum row to s
solver.Add(row.Sum() == s);
diag1[i] = x[i,i];
diag2[i] = x[i,n - i - 1];
}
// sum diagonals to s
solver.Add(diag1.Sum() == s);
solver.Add(diag2.Sum() == s);
// sum columns to s
for(int j = 0; j < n; j++) {
IntVar[] col = new IntVar[n];
for(int i = 0; i < n; i++) {
col[i] = x[i,j];
}
solver.Add(col.Sum() == s);
}
// all are different
solver.Add(x_flat.AllDifferent());
// symmetry breaking: upper left is 1
// solver.Add(x[0,0] == 1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x_flat,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_CENTER_VALUE);
solver.NewSearch(db);
int c = 0;
while (solver.NextSolution()) {
if (print != 0) {
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
Console.Write(x[i,j].Value() + " ");
}
Console.WriteLine();
}
Console.WriteLine();
}
c++;
if (num > 0 && c >= num) {
break;
}
}
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();
}
/**
*
* 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();
}
/**
*
* Nurse rostering
*
* This is a simple nurse rostering model using a DFA and
* the built-in TransitionConstraint.
*
* The DFA is from MiniZinc Tutorial, Nurse Rostering example:
* - one day off every 4 days
* - no 3 nights in a row.
*
* Also see:
* - http://www.hakank.org/or-tools/nurse_rostering.py
* - http://www.hakank.org/or-tools/nurse_rostering_regular.cs
* which use (a decomposition of) regular constraint
*
*/
private static void Solve(int nurse_multiplier, int week_multiplier)
{
Console.WriteLine("Starting Nurse Rostering");
Console.WriteLine(" - {0} teams of 7 nurses", nurse_multiplier);
Console.WriteLine(" - {0} blocks of 14 days", week_multiplier);
Solver solver = new Solver("NurseRostering");
//
// Data
//
// Note: If you change num_nurses or num_days,
// please also change the constraints
// on nurse_stat and/or day_stat.
int num_nurses = 7 * nurse_multiplier;
int num_days = 14 * week_multiplier;
// Note: I had to add a dummy shift.
int dummy_shift = 0;
int day_shift = 1;
int night_shift = 2;
int off_shift = 3;
int[] shifts = {dummy_shift, day_shift, night_shift, off_shift};
int[] valid_shifts = {day_shift, night_shift, off_shift};
// the DFA (for regular)
int initial_state = 1;
int[] accepting_states = {1,2,3,4,5,6};
/*
// This is the transition function
// used in nurse_rostering_regular.cs
int[,] transition_fn = {
// d,n,o
{2,3,1}, // state 1
{4,4,1}, // state 2
{4,5,1}, // state 3
{6,6,1}, // state 4
{6,0,1}, // state 5
{0,0,1} // state 6
};
*/
// For TransitionConstraint
IntTupleSet transition_tuples = new IntTupleSet(3);
// state, input, next state
transition_tuples.InsertAll(new int[,] { {1,1,2},
{1,2,3},
{1,3,1},
{2,1,4},
{2,2,4},
{2,3,1},
{3,1,4},
{3,2,5},
{3,3,1},
{4,1,6},
{4,2,6},
{4,3,1},
{5,1,6},
{5,3,1},
{6,3,1} });
string[] days = {"d","n","o"}; // for presentation
//
// Decision variables
//
//
// For TransitionConstraint
//
IntVar[,] x =
solver.MakeIntVarMatrix(num_nurses, num_days, valid_shifts, "x");
IntVar[] x_flat = x.Flatten();
//
// summary of the nurses
//
IntVar[] nurse_stat = new IntVar[num_nurses];
//
// summary of the shifts per day
//
int num_shifts = shifts.Length;
IntVar[,] day_stat = new IntVar[num_days, num_shifts];
for(int i = 0; i < num_days; i++) {
for(int j = 0; j < num_shifts; j++) {
day_stat[i,j] = solver.MakeIntVar(0, num_nurses, "day_stat");
}
}
//
// Constraints
//
for(int i = 0; i < num_nurses; i++) {
IntVar[] reg_input = new IntVar[num_days];
for(int j = 0; j < num_days; j++) {
reg_input[j] = x[i,j];
}
solver.Add(reg_input.Transition(transition_tuples,
initial_state,
accepting_states));
}
//
// Statistics and constraints for each nurse
//
for(int nurse = 0; nurse < num_nurses; nurse++) {
// Number of worked days (either day or night shift)
IntVar[] nurse_days = new IntVar[num_days];
for(int day = 0; day < num_days; day++) {
nurse_days[day] =
x[nurse, day].IsMember(new int[] { day_shift, night_shift });
}
nurse_stat[nurse] = nurse_days.Sum().Var();
// Each nurse must work between 7 and 10
// days/nights during this period
solver.Add(nurse_stat[nurse] >= 7 * week_multiplier / nurse_multiplier);
solver.Add(nurse_stat[nurse] <= 10 * week_multiplier / nurse_multiplier);
}
//
// Statistics and constraints for each day
//
for(int day = 0; day < num_days; day++) {
IntVar[] nurses = new IntVar[num_nurses];
for(int nurse = 0; nurse < num_nurses; nurse++) {
nurses[nurse] = x[nurse, day];
}
IntVar[] stats = new IntVar[num_shifts];
for (int shift = 0; shift < num_shifts; ++shift)
{
stats[shift] = day_stat[day, shift];
}
solver.Add(nurses.Distribute(stats));
//
// Some constraints for each day:
//
// Note: We have a strict requirements of
// the number of shifts.
// Using atleast constraints is harder
// in this model.
//
if (day % 7 == 5 || day % 7 == 6) {
// special constraints for the weekends
solver.Add(day_stat[day, day_shift] == 2 * nurse_multiplier);
solver.Add(day_stat[day, night_shift] == nurse_multiplier);
solver.Add(day_stat[day, off_shift] == 4 * nurse_multiplier);
} else {
// for workdays:
// - exactly 3 on day shift
solver.Add(day_stat[day, day_shift] == 3 * nurse_multiplier);
// - exactly 2 on night
solver.Add(day_stat[day, night_shift] == 2 * nurse_multiplier);
// - exactly 2 off duty
solver.Add(day_stat[day, off_shift] == 2 * nurse_multiplier);
}
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(x_flat,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
SearchMonitor log = solver.MakeSearchLog(1000000);
solver.NewSearch(db, log);
int num_solutions = 0;
while (solver.NextSolution()) {
num_solutions++;
for(int i = 0; i < num_nurses; i++) {
Console.Write("Nurse #{0,-2}: ", i);
var occ = new Dictionary<int, int>();
for(int j = 0; j < num_days; j++) {
int v = (int)x[i,j].Value()-1;
if (!occ.ContainsKey(v)) {
occ[v] = 0;
}
occ[v]++;
Console.Write(days[v] + " ");
}
Console.Write(" #workdays: {0,2}", nurse_stat[i].Value());
foreach(int s in valid_shifts) {
int v = 0;
if (occ.ContainsKey(s-1)) {
v = occ[s-1];
}
Console.Write(" {0}:{1}", days[s-1], v);
}
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("Statistics per day:\nDay d n o");
for(int j = 0; j < num_days; j++) {
Console.Write("Day #{0,2}: ", j);
foreach(int t in valid_shifts) {
Console.Write(day_stat[j,t].Value() + " ");
}
Console.WriteLine();
}
Console.WriteLine();
// We just show 2 solutions
if (num_solutions > 1) {
break;
}
}
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();
}
/**
*
* Fill-a-Pix problem
*
* From http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/basiclogic
* """
* Each puzzle consists of a grid containing clues in various places. The
* object is to reveal a hidden picture by painting the squares around each
* clue so that the number of painted squares, including the square with
* the clue, matches the value of the clue.
* """
*
* http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/rules
* """
* Fill-a-Pix is a Minesweeper-like puzzle based on a grid with a pixilated
* picture hidden inside. Using logic alone, the solver determines which
* squares are painted and which should remain empty until the hidden picture
* is completely exposed.
* """
*
* Fill-a-pix History:
* http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/history
*
* Also see http://www.hakank.org/google_or_tools/fill_a_pix.py
*
*
*/
private static void Solve()
{
Solver solver = new Solver("FillAPix");
//
// data
//
int[] S = {-1, 0, 1};
Console.WriteLine("Problem:");
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
if (puzzle[i,j] > X) {
Console.Write(puzzle[i,j] + " ");
} else {
Console.Write("X ");
}
}
Console.WriteLine();
}
Console.WriteLine();
//
// Decision variables
//
IntVar[,] pict = solver.MakeIntVarMatrix(n, n, 0, 1, "pict");
IntVar[] pict_flat = pict.Flatten(); // for branching
//
// Constraints
//
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
if (puzzle[i,j] > X) {
// this cell is the sum of all surrounding cells
var tmp = from a in S from b in S where
i + a >= 0 &&
j + b >= 0 &&
i + a < n &&
j + b < n
select(pict[i+a,j+b]);
solver.Add(tmp.ToArray().Sum() == puzzle[i,j]);
}
}
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(pict_flat,
Solver.INT_VAR_DEFAULT,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db);
int sol = 0;
while (solver.NextSolution()) {
sol++;
Console.WriteLine("Solution #{0} ", sol + " ");
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++){
Console.Write(pict[i,j].Value() == 1 ? "#" : " ");
}
Console.WriteLine();
}
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();
}
/**
*
* Set partition problem.
*
* Problem formulation from
* http://www.koalog.com/resources/samples/PartitionProblem.java.html
* """
* This is a partition problem.
* Given the set S = {1, 2, ..., n},
* it consists in finding two sets A and B such that:
*
* A U B = S,
* |A| = |B|,
* sum(A) = sum(B),
* sum_squares(A) = sum_squares(B)
*
* """
*
* This model uses a binary matrix to represent the sets.
*
*
* Also see http://www.hakank.org/or-tools/set_partition.py
*
*/
private static void Solve(int n=16, int num_sets=2)
{
Solver solver = new Solver("SetPartition");
Console.WriteLine("n: {0}", n);
Console.WriteLine("num_sets: {0}", num_sets);
IEnumerable<int> Sets = Enumerable.Range(0, num_sets);
IEnumerable<int> NRange = Enumerable.Range(0, n);
//
// Decision variables
//
IntVar[,] a = solver.MakeIntVarMatrix(num_sets, n, 0, 1, "a");
IntVar[] a_flat = a.Flatten();
//
// Constraints
//
// partition set
partition_sets(solver, a, num_sets, n);
foreach(int i in Sets) {
foreach(int j in Sets) {
// same cardinality
solver.Add(
(from k in NRange select a[i,k]).ToArray().Sum()
==
(from k in NRange select a[j,k]).ToArray().Sum());
// same sum
solver.Add(
(from k in NRange select (k*a[i,k])).ToArray().Sum()
==
(from k in NRange select (k*a[j,k])).ToArray().Sum());
// same sum squared
solver.Add(
(from k in NRange select (k*a[i,k]*k*a[i,k])).ToArray().Sum()
==
(from k in NRange select (k*a[j,k]*k*a[j,k])).ToArray().Sum());
}
}
// symmetry breaking for num_sets == 2
if (num_sets == 2) {
solver.Add(a[0,0] == 1);
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(a_flat,
Solver.INT_VAR_DEFAULT,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db);
while (solver.NextSolution()) {
int[,] a_val = new int[num_sets, n];
foreach(int i in Sets) {
foreach(int j in NRange) {
a_val[i,j] = (int)a[i,j].Value();
}
}
Console.WriteLine("sums: {0}",
(from j in NRange
select (j+1)*a_val[0,j]).ToArray().Sum());
Console.WriteLine("sums squared: {0}",
(from j in NRange
select (int)Math.Pow((j+1)*a_val[0,j],2)).ToArray().Sum());
// Show the numbers in each set
foreach(int i in Sets) {
if ( (from j in NRange select a_val[i,j]).ToArray().Sum() > 0 ) {
Console.Write(i+1 + ": ");
foreach(int j in NRange) {
if (a_val[i,j] == 1) {
Console.Write((j+1) + " ");
}
}
Console.WriteLine();
}
}
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();
}
/**
*
* Nurse rostering
*
* This is a simple nurse rostering model using a DFA and
* my decomposition of regular constraint.
*
* The DFA is from MiniZinc Tutorial, Nurse Rostering example:
* - one day off every 4 days
* - no 3 nights in a row.
*
* Also see http://www.hakank.org/or-tools/nurse_rostering.py
*
*/
private static void Solve()
{
Solver solver = new Solver("NurseRostering");
//
// Data
//
// Note: If you change num_nurses or num_days,
// please also change the constraints
// on nurse_stat and/or day_stat.
int num_nurses = 7;
int num_days = 14;
// Note: I had to add a dummy shift.
int dummy_shift = 0;
int day_shift = 1;
int night_shift = 2;
int off_shift = 3;
int[] shifts = {dummy_shift, day_shift, night_shift, off_shift};
int[] valid_shifts = {day_shift, night_shift, off_shift};
// the DFA (for regular)
int n_states = 6;
int input_max = 3;
int initial_state = 1; // 0 is for the failing state
int[] accepting_states = {1,2,3,4,5,6};
int[,] transition_fn = {
// d,n,o
{2,3,1}, // state 1
{4,4,1}, // state 2
{4,5,1}, // state 3
{6,6,1}, // state 4
{6,0,1}, // state 5
{0,0,1} // state 6
};
string[] days = {"d","n","o"}; // for presentation
//
// Decision variables
//
// For regular
IntVar[,] x =
solver.MakeIntVarMatrix(num_nurses, num_days, valid_shifts, "x");
IntVar[] x_flat = x.Flatten();
// summary of the nurses
IntVar[] nurse_stat =
solver.MakeIntVarArray(num_nurses, 0, num_days, "nurse_stat");
// summary of the shifts per day
int num_shifts = shifts.Length;
IntVar[,] day_stat = new IntVar[num_days, num_shifts];
for(int i = 0; i < num_days; i++) {
for(int j = 0; j < num_shifts; j++) {
day_stat[i,j] = solver.MakeIntVar(0, num_nurses, "day_stat");
}
}
//
// Constraints
//
for(int i = 0; i < num_nurses; i++) {
IntVar[] reg_input = new IntVar[num_days];
for(int j = 0; j < num_days; j++) {
reg_input[j] = x[i,j];
}
MyRegular(solver, reg_input, n_states, input_max, transition_fn,
initial_state, accepting_states);
}
//
// Statistics and constraints for each nurse
//
for(int i = 0; i < num_nurses; i++) {
// Number of worked days (either day or night shift)
IntVar[] b = new IntVar[num_days];
for(int j = 0; j < num_days; j++) {
b[j] = ((x[i,j] == day_shift) + (x[i,j] == night_shift)).Var();
}
solver.Add(b.Sum() == nurse_stat[i]);
// Each nurse must work between 7 and 10
// days/nights during this period
solver.Add(nurse_stat[i] >= 7);
solver.Add(nurse_stat[i] <= 10);
}
//
// Statistics and constraints for each day
//
for(int j = 0; j < num_days; j++) {
for(int t = 0; t < num_shifts; t++) {
IntVar[] b = new IntVar[num_nurses];
for(int i = 0; i < num_nurses; i++) {
b[i] = x[i,j] == t;
}
solver.Add(b.Sum() == day_stat[j,t]);
}
//
// Some constraints for each day:
//
// Note: We have a strict requirements of
// the number of shifts.
// Using atleast constraints is harder
// in this model.
//
if (j % 7 == 5 || j % 7 == 6) {
// special constraints for the weekends
solver.Add(day_stat[j,day_shift] == 2);
solver.Add(day_stat[j,night_shift] == 1);
solver.Add(day_stat[j,off_shift] == 4 );
} else {
// for workdays:
// - exactly 3 on day shift
solver.Add(day_stat[j,day_shift] == 3);
// - exactly 2 on night
solver.Add(day_stat[j,night_shift] == 2);
// - exactly 2 off duty
solver.Add(day_stat[j,off_shift] == 2 );
}
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(x_flat,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
int num_solutions = 0;
while (solver.NextSolution()) {
num_solutions++;
for(int i = 0; i < num_nurses; i++) {
Console.Write("Nurse #{0,-2}: ", i);
var occ = new Dictionary<int, int>();
for(int j = 0; j < num_days; j++) {
int v = (int)x[i,j].Value()-1;
if (!occ.ContainsKey(v)) {
occ[v] = 0;
}
occ[v]++;
Console.Write(days[v] + " ");
}
Console.Write(" #workdays: {0,2}", nurse_stat[i].Value());
foreach(int s in valid_shifts) {
int v = 0;
if (occ.ContainsKey(s-1)) {
v = occ[s-1];
}
Console.Write(" {0}:{1}", days[s-1], v);
}
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("Statistics per day:\nDay d n o");
for(int j = 0; j < num_days; j++) {
Console.Write("Day #{0,2}: ", j);
foreach(int t in valid_shifts) {
Console.Write(day_stat[j,t].Value() + " ");
}
Console.WriteLine();
}
Console.WriteLine();
// We just show 2 solutions
if (num_solutions > 1) {
break;
}
}
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();
}
/**
*
* Max flow problem.
*
* From Winston 'Operations Research', page 420f, 423f
* Sunco Oil example.
*
*
* Also see http://www.hakank.org/or-tools/max_flow_winston1.py
*
*/
private static void Solve()
{
Solver solver = new Solver("MaxFlowWinston1");
//
// Data
//
int n = 5;
IEnumerable<int> NODES = Enumerable.Range(0, n);
// The arcs
// Note:
// This is 1-based to be compatible with other implementations.
//
int[,] arcs1 = {
{1, 2},
{1, 3},
{2, 3},
{2, 4},
{3, 5},
{4, 5},
{5, 1}
};
// Capacities
int [] cap = {2,3,3,4,2,1,100};
// Convert arcs to 0-based
int num_arcs = arcs1.GetLength(0);
IEnumerable<int> ARCS = Enumerable.Range(0, num_arcs);
int[,] arcs = new int[num_arcs, 2];
foreach(int i in ARCS) {
for(int j = 0; j < 2; j++) {
arcs[i,j] = arcs1[i,j] - 1;
}
}
// Convert arcs to matrix (for sanity checking below)
int[,] mat = new int[num_arcs, num_arcs];
foreach(int i in NODES) {
foreach(int j in NODES) {
int c = 0;
foreach(int k in ARCS) {
if (arcs[k,0] == i && arcs[k,1] == j) {
c = 1;
}
}
mat[i,j] = c;
}
}
//
// Decision variables
//
IntVar[,] flow = solver.MakeIntVarMatrix(n, n, 0, 200, "flow");
IntVar z = flow[n-1, 0].VarWithName("z");
//
// Constraints
//
// capacity of arcs
foreach(int i in ARCS) {
solver.Add(flow[arcs[i,0], arcs[i,1]] <= cap[i]);
}
// inflows == outflows
foreach(int i in NODES) {
var s1 = (from k in ARCS
where arcs[k,1] == i
select flow[arcs[k,0], arcs[k,1]]
).ToArray().Sum();
var s2 = (from k in ARCS
where arcs[k,0] == i
select flow[arcs[k,0], arcs[k,1]]
).ToArray().Sum();
solver.Add(s1 == s2);
}
// Sanity check: just arcs with connections can have a flow.
foreach(int i in NODES) {
foreach(int j in NODES) {
if (mat[i,j] == 0) {
solver.Add(flow[i,j] == 0);
}
}
}
//
// Objective
//
OptimizeVar obj = z.Maximize(1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(flow.Flatten(),
Solver.INT_VAR_DEFAULT,
Solver.ASSIGN_MAX_VALUE);
solver.NewSearch(db, obj);
while (solver.NextSolution()) {
Console.WriteLine("z: {0}",z.Value());
foreach(int i in NODES) {
foreach(int j in NODES) {
Console.Write(flow[i,j].Value() + " ");
}
Console.WriteLine();
}
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();
}
/**
*
* From Programmers Stack Exchange (C#)
* http://programmers.stackexchange.com/questions/153184/partitioning-set-into-subsets-with-respect-to-equality-of-sum-among-subsets
* Partitioning set into subsets with respect to equality of sum among subsets
* """
* let say i have {3, 1, 1, 2, 2, 1,5,2,7} set of numbers, I need to split the
* numbers such that sum of subset1 should be equal to sum of subset2
* {3,2,7} {1,1,2,1,5,2}. First we should identify whether we can split number(one
* way might be dividable by 2 without any remainder) and if we can, we should
* write our algorithm two create s1 and s2 out of s.
*
* How to proceed with this approach? I read partition problem in wiki and even in some
* articles but i am not able to get anything. Can someone help me to find the
* right algorithm and its explanation in simple English?
*
*
* Also see http://www.hakank.org/or-tools/set_partition.cs
*
*
* Model by Hakan Kjellerstrand ([email protected])
* See other or-tools/C# models at http://www.hakank.org/or-tools/#csharp
*
*/
private static void Solve(int n = 10, int max = 10, int num_subsets = 2, int sols_to_show = 0)
{
Solver solver = new Solver("PartitionSets");
Console.WriteLine("n: " + n);
Console.WriteLine("max: " + max);
Console.WriteLine("num_subsets: " + num_subsets);
Console.WriteLine("sols_to_show: " + sols_to_show);
//
// Data
//
// int[] s = {3, 1, 1, 2, 2, 1, 5, 2, 7};
// int n = s.Length;
int seed = (int)DateTime.Now.Ticks;
Random generator = new Random(seed);
int[] s = new int[n];
for(int i = 0; i < n; i++) {
s[i] = 1 + generator.Next(max);
}
while (s.Sum() % num_subsets != 0) {
int ix = generator.Next(n);
Console.WriteLine("The sum of s must be divisible by the number of subsets. Adjusting index " + ix);
s[ix] = 1 + generator.Next(max);
}
Console.WriteLine("\n" + n + " numbers generated\n");
int the_sum = (int)s.Sum() / num_subsets;
Console.WriteLine("The sum: " + the_sum);
IEnumerable<int> NRange = Enumerable.Range(0, n);
IEnumerable<int> Sets = Enumerable.Range(0, num_subsets);
//
// Decision variables
//
// To which subset (s) do x[s, i] belong?
IntVar[,] x = solver.MakeIntVarMatrix(num_subsets, n, 0, 1, "x");
IntVar[] x_flat = x.Flatten();
//
// Constraints
//
// Ensure that a number is in exact one subset
for(int k = 0; k < n; k++) {
solver.Add( (from p in Sets select (x[p,k])).ToArray().Sum() == 1);
}
// Ensure that the sum of all subsets are the same.
// for(int p = 0; p < num_subsets-1; p++) {
// solver.Add(
// (from k in NRange select (s[k]*x[p,k])).ToArray().Sum()
// ==
// (from k in NRange select (s[k]*x[p+1,k])).ToArray().Sum()
// );
// }
for(int p = 0; p < num_subsets; p++) {
solver.Add(
(from k in NRange select (s[k]*x[p,k])).ToArray().Sum() == the_sum
);
}
// symmetry breaking: assign first number to subset 1
solver.Add(x[0,0] == 1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x_flat,
Solver.INT_VAR_DEFAULT,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db);
int sols = 0;
while (solver.NextSolution()) {
sols++;
foreach(int i in Sets) {
Console.Write("subset " + i + ": ");
int sum = 0;
foreach(int j in NRange) {
if ((int)x[i,j].Value() == 1) {
Console.Write(s[j] + " ");
sum += s[j];
}
}
Console.WriteLine(" sum: " + sum);
}
Console.WriteLine();
if (sols_to_show > 0 && sols >= sols_to_show) {
break;
}
}
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();
}
/**
*
* Solves a Strimko problem.
* See http://www.hakank.org/google_or_tools/strimko2.py
*
*/
private static void Solve()
{
Solver solver = new Solver("Strimko2");
//
// data
//
int[,] streams = {{1,1,2,2,2,2,2},
{1,1,2,3,3,3,2},
{1,4,1,3,3,5,5},
{4,4,3,1,3,5,5},
{4,6,6,6,7,7,5},
{6,4,6,4,5,5,7},
{6,6,4,7,7,7,7}};
// Note: This is 1-based
int[,] placed = {{2,1,1},
{2,3,7},
{2,5,6},
{2,7,4},
{3,2,7},
{3,6,1},
{4,1,4},
{4,7,5},
{5,2,2},
{5,6,6}};
int n = streams.GetLength(0);
int num_placed = placed.GetLength(0);
//
// Decision variables
//
IntVar[,] x = solver.MakeIntVarMatrix(n, n, 1, n, "x");
IntVar[] x_flat = x.Flatten();
//
// Constraints
//
// all rows and columns must be unique, i.e. a Latin Square
for(int i = 0; i < n; i++) {
IntVar[] row = new IntVar[n];
IntVar[] col = new IntVar[n];
for(int j = 0; j < n; j++) {
row[j] = x[i,j];
col[j] = x[j,i];
}
solver.Add(row.AllDifferent());
solver.Add(col.AllDifferent());
}
// streams
for(int s = 1; s <= n; s++) {
IntVar[] tmp = (from i in Enumerable.Range(0, n)
from j in Enumerable.Range(0, n)
where streams[i,j] == s
select x[i,j]).ToArray();
solver.Add(tmp.AllDifferent());
}
// placed
for(int i = 0; i < num_placed; i++) {
// note: also adjust to 0-based
solver.Add(x[placed[i,0] - 1,placed[i,1] - 1] == placed[i,2]);
}
//
// 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++) {
Console.Write(x[i,j].Value() + " ");
}
Console.WriteLine();
}
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();
}
/**
*
* Futoshiki problem.
*
* From http://en.wikipedia.org/wiki/Futoshiki
* """
* The puzzle is played on a square grid, such as 5 x 5. The objective
* is to place the numbers 1 to 5 (or whatever the dimensions are)
* such that each row, and column contains each of the digits 1 to 5.
* Some digits may be given at the start. In addition, inequality
* constraints are also initially specifed between some of the squares,
* such that one must be higher or lower than its neighbour. These
* constraints must be honoured as the grid is filled out.
* """
*
* Also see http://www.hakank.org/or-tools/futoshiki.py
*
*/
private static void Solve(int[,] values, int[,] lt)
{
Solver solver = new Solver("Futoshiki");
int size = values.GetLength(0);
IEnumerable<int> RANGE = Enumerable.Range(0, size);
IEnumerable<int> NUMQD = Enumerable.Range(0, lt.GetLength(0));
//
// Decision variables
//
IntVar[,] field = solver.MakeIntVarMatrix(size, size, 1, size, "field");
IntVar[] field_flat = field.Flatten();
//
// Constraints
//
// set initial values
foreach(int row in RANGE) {
foreach(int col in RANGE) {
if (values[row,col] > 0) {
solver.Add(field[row,col] == values[row,col]);
}
}
}
// all rows have to be different
foreach(int row in RANGE) {
solver.Add((from col in RANGE
select field[row,col]).ToArray().AllDifferent());
}
// all columns have to be different
foreach(int col in RANGE) {
solver.Add((from row in RANGE
select field[row,col]).ToArray().AllDifferent());
}
// all < constraints are satisfied
// Also: make 0-based
foreach(int i in NUMQD) {
solver.Add(field[ lt[i,0]-1, lt[i,1]-1 ] <
field[ lt[i,2]-1, lt[i,3]-1 ] );
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(field_flat,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
foreach(int i in RANGE) {
foreach(int j in RANGE) {
Console.Write("{0} ", field[i,j].Value());
}
Console.WriteLine();
}
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();
}
/**
*
* Solving a simple crossword.
* See http://www.hakank.org/or-tools/crossword2.py
*
*
*/
private static void Solve()
{
Solver solver = new Solver("Crossword");
//
// data
//
String[] alpha = {"_","a","b","c","d","e","f",
"g","h","i","j","k","l","m",
"n","o","p","q","r","s","t",
"u","v","w","x","y","z"};
int a=1; int b=2; int c=3; int d=4; int e=5; int f=6;
int g=7; int h=8; int i=9; int j=10; int k=11; int l=12;
int m=13; int n=14; int o=15; int p=16; int q=17; int r=18;
int s=19; int t=20; int u=21; int v=22; int w=23; int x=24;
int y=25; int z=26;
const int num_words = 15;
int word_len = 5;
int[,] AA = {{h, o, s, e, s}, // HOSES
{l, a, s, e, r}, // LASER
{s, a, i, l, s}, // SAILS
{s, h, e, e, t}, // SHEET
{s, t, e, e, r}, // STEER
{h, e, e, l, 0}, // HEEL
{h, i, k, e, 0}, // HIKE
{k, e, e, l, 0}, // KEEL
{k, n, o, t, 0}, // KNOT
{l, i, n, e, 0}, // LINE
{a, f, t, 0, 0}, // AFT
{a, l, e, 0, 0}, // ALE
{e, e, l, 0, 0}, // EEL
{l, e, e, 0, 0}, // LEE
{t, i, e, 0, 0}}; // TIE
int num_overlapping = 12;
int[,] overlapping = {{0, 2, 1, 0}, // s
{0, 4, 2, 0}, // s
{3, 1, 1, 2}, // i
{3, 2, 4, 0}, // k
{3, 3, 2, 2}, // e
{6, 0, 1, 3}, // l
{6, 1, 4, 1}, // e
{6, 2, 2, 3}, // e
{7, 0, 5, 1}, // l
{7, 2, 1, 4}, // s
{7, 3, 4, 2}, // e
{7, 4, 2, 4}}; // r
int N = 8;
//
// Decision variables
//
// for labeling on A and E
IntVar[,] A = solver.MakeIntVarMatrix(num_words, word_len,
0, 26, "A");
IntVar[] A_flat = A.Flatten();
IntVar[] all = new IntVar[(num_words * word_len) + N];
for(int I = 0; I < num_words; I++) {
for(int J = 0; J < word_len; J++) {
all[I * word_len + J] = A[I,J];
}
}
IntVar[] E = solver.MakeIntVarArray(N, 0, num_words, "E");
for(int I = 0; I < N; I++) {
all[num_words * word_len + I] = E[I];
}
//
// Constraints
//
solver.Add(E.AllDifferent());
for(int I = 0; I < num_words; I++) {
for(int J = 0; J < word_len; J++) {
solver.Add(A[I,J] == AA[I,J]);
}
}
// This contraint handles the overlappings.
//
// It's coded in MiniZinc as
//
// forall(i in 1..num_overlapping) (
// A[E[overlapping[i,1]], overlapping[i,2]] =
// A[E[overlapping[i,3]], overlapping[i,4]]
// )
// and in or-tools/Python as
// solver.Add(
// solver.Element(A_flat,E[overlapping[I][0]]*word_len+overlapping[I][1])
// ==
// solver.Element(A_flat,E[overlapping[I][2]]*word_len+overlapping[I][3]))
//
for(int I = 0; I < num_overlapping; I++) {
solver.Add(
A_flat.Element(E[overlapping[I,0]] * word_len + overlapping[I,1]) ==
A_flat.Element(E[overlapping[I,2]] * word_len + overlapping[I,3]));
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(all,
Solver.INT_VAR_DEFAULT,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.WriteLine("E: ");
for(int ee = 0; ee < N; ee++) {
int e_val = (int)E[ee].Value();
Console.Write(ee + ": (" + e_val + ") ");
for(int ii = 0; ii < word_len; ii++) {
Console.Write(alpha[(int)A[ee,ii].Value()]);
}
Console.WriteLine();
}
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();
}
/**
*
* Solves the Quasigroup Completion problem.
* See http://www.hakank.org/or-tools/quasigroup_completion.py
*
*/
private static void Solve()
{
Solver solver = new Solver("QuasigroupCompletion");
//
// data
//
Console.WriteLine("Problem:");
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
Console.Write(problem[i,j] + " ");
}
Console.WriteLine();
}
Console.WriteLine();
//
// Decision variables
//
IntVar[,] x = solver.MakeIntVarMatrix(n, n, 1, n, "x");
IntVar[] x_flat = x.Flatten();
//
// Constraints
//
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
if (problem[i,j] > X) {
solver.Add(x[i,j] == problem[i,j]);
}
}
}
//
// rows and columns must be different
//
// rows
for(int i = 0; i < n; i++) {
IntVar[] row = new IntVar[n];
for(int j = 0; j < n; j++) {
row[j] = x[i,j];
}
solver.Add(row.AllDifferent());
}
// columns
for(int j = 0; j < n; j++) {
IntVar[] col = new IntVar[n];
for(int i = 0; i < n; i++) {
col[i] = x[i,j];
}
solver.Add(col.AllDifferent());
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(x_flat,
Solver.INT_VAR_SIMPLE,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
int sol = 0;
while (solver.NextSolution()) {
sol++;
Console.WriteLine("Solution #{0} ", sol + " ");
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++){
Console.Write("{0} ", x[i,j].Value());
}
Console.WriteLine();
}
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();
}
/**
*
* From Programmers Stack Exchange (C#)
* http://programmers.stackexchange.com/questions/153184/partitioning-set-into-subsets-with-respect-to-equality-of-sum-among-subsets
* Partitioning set into subsets with respect to equality of sum among subsets
* """
* let say i have {3, 1, 1, 2, 2, 1,5,2,7} set of numbers, I need to split the
* numbers such that sum of subset1 should be equal to sum of subset2
* {3,2,7} {1,1,2,1,5,2}. First we should identify whether we can split number(one
* way might be dividable by 2 without any remainder) and if we can, we should
* write our algorithm two create s1 and s2 out of s.
*
* How to proceed with this approach? I read partition problem in wiki and even in some
* articles but i am not able to get anything. Can someone help me to find the
* right algorithm and its explanation in simple English?
*
*
* Also see http://www.hakank.org/or-tools/set_partition.cs
*
* Model by Hakan Kjellerstrand ([email protected])
* See other or-tools/C# models at http://www.hakank.org/or-tools/#csharp
*
*/
private static void Solve()
{
Solver solver = new Solver("PartitionSets");
//
// Data
//
int[] s = {3, 1, 1, 2, 2, 1, 5, 2, 7};
int n = s.Length;
int num_subsets = 2;
IEnumerable<int> NRange = Enumerable.Range(0, n);
IEnumerable<int> Sets = Enumerable.Range(0, num_subsets);
//
// Decision variables
//
// To which subset do x[i] belong?
IntVar[,] x = solver.MakeIntVarMatrix(num_subsets, n, 0, 1, "x");
IntVar[] x_flat = x.Flatten();
//
// Constraints
//
// Ensure that a number is in exact one subset
for(int k = 0; k < n; k++) {
solver.Add( (from p in Sets select (x[p,k])).ToArray().Sum() == 1);
}
// Ensure that the sum of all subsets are the same.
for(int p = 0; p < num_subsets-1; p++) {
solver.Add(
(from k in NRange select (s[k]*x[p,k])).ToArray().Sum()
==
(from k in NRange select (s[k]*x[p+1,k])).ToArray().Sum()
);
}
// symmetry breaking: assign first number to subset 1
solver.Add(x[0,0] == 1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x_flat,
Solver.INT_VAR_DEFAULT,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db);
while (solver.NextSolution()) {
foreach(int i in Sets) {
Console.Write("subset " + i + ": ");
foreach(int j in NRange) {
if ((int)x[i,j].Value() == 1) {
Console.Write(s[j] + " ");
}
}
Console.WriteLine();
}
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();
}
/**
*
* Solves the Minesweeper problems.
*
* See http://www.hakank.org/google_or_tools/minesweeper.py
*
*/
private static void Solve()
{
Solver solver = new Solver("Minesweeper");
//
// data
//
int[] S = {-1, 0, 1};
Console.WriteLine("Problem:");
for(int i = 0; i < r; i++) {
for(int j = 0; j < c; j++) {
if (game[i,j] > X) {
Console.Write(game[i,j] + " ");
} else {
Console.Write("X ");
}
}
Console.WriteLine();
}
Console.WriteLine();
//
// Decision variables
//
IntVar[,] mines = solver.MakeIntVarMatrix(r, c, 0, 1, "mines");
// for branching
IntVar[] mines_flat = mines.Flatten();
//
// Constraints
//
for(int i = 0; i < r; i++) {
for(int j = 0; j < c; j++) {
if (game[i,j] >= 0) {
solver.Add( mines[i,j] == 0);
// this cell is the sum of all its neighbours
var tmp = from a in S from b in S where
i + a >= 0 &&
j + b >= 0 &&
i + a < r &&
j + b < c
select(mines[i+a,j+b]);
solver.Add(tmp.ToArray().Sum() == game[i,j]);
}
if (game[i,j] > X) {
// This cell cannot be a mine since it
// has some value assigned to it
solver.Add(mines[i,j] == 0);
}
}
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(mines_flat,
Solver.CHOOSE_PATH,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
int sol = 0;
while (solver.NextSolution()) {
sol++;
Console.WriteLine("Solution #{0} ", sol + " ");
for(int i = 0; i < r; i++) {
for(int j = 0; j < c; j++){
Console.Write("{0} ", mines[i,j].Value());
}
Console.WriteLine();
}
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();
}
/**
*
* P-median problem.
*
* Model and data from the OPL Manual, which describes the problem:
* """
* The P-Median problem is a well known problem in Operations Research.
* The problem can be stated very simply, like this: given a set of customers
* with known amounts of demand, a set of candidate locations for warehouses,
* and the distance between each pair of customer-warehouse, choose P
* warehouses to open that minimize the demand-weighted distance of serving
* all customers from those P warehouses.
* """
*
* Also see http://www.hakank.org/or-tools/p_median.py
*
*/
private static void Solve()
{
Solver solver = new Solver("PMedian");
//
// Data
//
int p = 2;
int num_customers = 4;
IEnumerable<int> CUSTOMERS = Enumerable.Range(0, num_customers);
int num_warehouses = 3;
IEnumerable<int> WAREHOUSES = Enumerable.Range(0, num_warehouses);
int[] demand = {100,80,80,70};
int [,] distance = {
{ 2, 10, 50},
{ 2, 10, 52},
{50, 60, 3},
{40, 60, 1}
};
//
// Decision variables
//
IntVar[] open = solver.MakeIntVarArray(num_warehouses, 0, num_warehouses, "open");
IntVar[,] ship = solver.MakeIntVarMatrix(num_customers, num_warehouses,
0, 1, "ship");
IntVar z = solver.MakeIntVar(0, 1000, "z");
//
// Constraints
//
solver.Add((from c in CUSTOMERS
from w in WAREHOUSES
select (demand[c]*distance[c,w]*ship[c,w])
).ToArray().Sum() == z);
solver.Add(open.Sum() == p);
foreach(int c in CUSTOMERS) {
foreach(int w in WAREHOUSES) {
solver.Add(ship[c,w] <= open[w]);
}
solver.Add((from w in WAREHOUSES select ship[c,w]).ToArray().Sum() == 1);
}
//
// Objective
//
OptimizeVar obj = z.Minimize(1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(open.Concat(ship.Flatten()).ToArray(),
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db, obj);
while (solver.NextSolution()) {
Console.WriteLine("z: {0}",z.Value());
Console.Write("open:");
foreach(int w in WAREHOUSES) {
Console.Write(open[w].Value() + " ");
}
Console.WriteLine();
foreach(int c in CUSTOMERS) {
foreach(int w in WAREHOUSES) {
Console.Write(ship[c,w].Value()+ " ");
}
Console.WriteLine();
}
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();
}
/**
*
* Magic squares and cards problem.
*
* Martin Gardner (July 1971)
* """
* Allowing duplicates values, what is the largest constant sum for an order-3
* magic square that can be formed with nine cards from the deck.
* """
*
*
* Also see http://www.hakank.org/or-tools/magic_square_and_cards.py
*
*/
private static void Solve(int n=3)
{
Solver solver = new Solver("MagicSquareAndCards");
IEnumerable<int> RANGE = Enumerable.Range(0, n);
//
// Decision variables
//
IntVar[,] x = solver.MakeIntVarMatrix(n, n, 1, 13, "x");
IntVar[] x_flat = x.Flatten();
IntVar s = solver.MakeIntVar(1, 13*4, "s");
IntVar[] counts = solver.MakeIntVarArray(14, 0, 4, "counts");
//
// Constraints
//
solver.Add(x_flat.Distribute(counts));
// the standard magic square constraints (sans all_different)
foreach(int i in RANGE) {
// rows
solver.Add( (from j in RANGE select x[i,j]).ToArray().Sum() == s);
// columns
solver.Add( (from j in RANGE select x[j,i]).ToArray().Sum() == s);
}
// diagonals
solver.Add( (from i in RANGE select x[i,i]).ToArray().Sum() == s);
solver.Add( (from i in RANGE select x[i,n-i-1]).ToArray().Sum() == s);
// redundant constraint
solver.Add(counts.Sum() == n*n);
//
// Objective
//
OptimizeVar obj = s.Maximize(1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x_flat,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MAX_VALUE);
solver.NewSearch(db, obj);
while (solver.NextSolution()) {
Console.WriteLine("s: {0}", s.Value());
Console.Write("counts:");
for(int i = 0; i < 14; i++) {
Console.Write(counts[i].Value() + " ");
}
Console.WriteLine();
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
Console.Write(x[i,j].Value() + " ");
}
Console.WriteLine();
}
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();
}
/**
*
* A programming puzzle from Einav.
*
* From
* "A programming puzzle from Einav"
* http://gcanyon.wordpress.com/2009/10/28/a-programming-puzzle-from-einav/
* """
* My friend Einav gave me this programming puzzle to work on. Given
* this array of positive and negative numbers:
* 33 30 -10 -6 18 7 -11 -23 6
* ...
* -25 4 16 30 33 -23 -4 4 -23
*
* You can flip the sign of entire rows and columns, as many of them
* as you like. The goal is to make all the rows and columns sum to positive
* numbers (or zero), and then to find the solution (there are more than one)
* that has the smallest overall sum. So for example, for this array:
* 33 30 -10
* -16 19 9
* -17 -12 -14
* You could flip the sign for the bottom row to get this array:
* 33 30 -10
* -16 19 9
* 17 12 14
* Now all the rows and columns have positive sums, and the overall total is
* 108.
* But you could instead flip the second and third columns, and the second
* row, to get this array:
* 33 -30 10
* 16 19 9
* -17 12 14
* All the rows and columns still total positive, and the overall sum is just
* 66. So this solution is better (I don't know if it's the best)
* A pure brute force solution would have to try over 30 billion solutions.
* I wrote code to solve this in J. I'll post that separately.
* """
*
* Note:
* This is a port of Larent Perrons's Python version of my own einav_puzzle.py.
* He removed some of the decision variables and made it more efficient.
* Thanks!
*
* Also see http://www.hakank.org/or-tools/einav_puzzle2.py
*
*/
private static void Solve()
{
Solver solver = new Solver("EinavPuzzle2");
//
// Data
//
// Small problem
// int rows = 3;
// int cols = 3;
// int[,] data = {
// { 33, 30, -10},
// {-16, 19, 9},
// {-17, -12, -14}
// };
// Full problem
int rows = 27;
int cols = 9;
int[,] data = {
{33,30,10,-6,18,-7,-11,23,-6},
{16,-19,9,-26,-8,-19,-8,-21,-14},
{17,12,-14,31,-30,13,-13,19,16},
{-6,-11,1,17,-12,-4,-7,14,-21},
{18,-31,34,-22,17,-19,20,24,6},
{33,-18,17,-15,31,-5,3,27,-3},
{-18,-20,-18,31,6,4,-2,-12,24},
{27,14,4,-29,-3,5,-29,8,-12},
{-15,-7,-23,23,-9,-8,6,8,-12},
{33,-23,-19,-4,-8,-7,11,-12,31},
{-20,19,-15,-30,11,32,7,14,-5},
{-23,18,-32,-2,-31,-7,8,24,16},
{32,-4,-10,-14,-6,-1,0,23,23},
{25,0,-23,22,12,28,-27,15,4},
{-30,-13,-16,-3,-3,-32,-3,27,-31},
{22,1,26,4,-2,-13,26,17,14},
{-9,-18,3,-20,-27,-32,-11,27,13},
{-17,33,-7,19,-32,13,-31,-2,-24},
{-31,27,-31,-29,15,2,29,-15,33},
{-18,-23,15,28,0,30,-4,12,-32},
{-3,34,27,-25,-18,26,1,34,26},
{-21,-31,-10,-13,-30,-17,-12,-26,31},
{23,-31,-19,21,-17,-10,2,-23,23},
{-3,6,0,-3,-32,0,-10,-25,14},
{-19,9,14,-27,20,15,-5,-27,18},
{11,-6,24,7,-17,26,20,-31,-25},
{-25,4,-16,30,33,23,-4,-4,23}
};
IEnumerable<int> ROWS = Enumerable.Range(0, rows);
IEnumerable<int> COLS = Enumerable.Range(0, cols);
//
// Decision variables
//
IntVar[,] x = solver.MakeIntVarMatrix(rows, cols, -100, 100, "x");
IntVar[] x_flat = x.Flatten();
int[] signs_domain = {-1,1};
// This don't work at the moment...
IntVar[] row_signs = solver.MakeIntVarArray(rows, signs_domain, "row_signs");
IntVar[] col_signs = solver.MakeIntVarArray(cols, signs_domain, "col_signs");
// To optimize
IntVar total_sum = x_flat.Sum().VarWithName("total_sum");
//
// Constraints
//
foreach(int i in ROWS) {
foreach(int j in COLS) {
solver.Add(x[i,j] == data[i,j] * row_signs[i] * col_signs[j]);
}
}
// row sums
IntVar[] row_sums = (from i in ROWS
select (from j in COLS
select x[i,j]
).ToArray().Sum().Var()).ToArray();
foreach(int i in ROWS) {
row_sums[i].SetMin(0);
}
// col sums
IntVar[] col_sums = (from j in COLS
select (from i in ROWS
select x[i,j]
).ToArray().Sum().Var()).ToArray();
foreach(int j in COLS) {
col_sums[j].SetMin(0);
}
//
// Objective
//
OptimizeVar obj = total_sum.Minimize(1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(col_signs.Concat(row_signs).ToArray(),
Solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
Solver.ASSIGN_MAX_VALUE);
solver.NewSearch(db, obj);
while (solver.NextSolution()) {
Console.WriteLine("Sum: {0}",total_sum.Value());
Console.Write("row_sums: ");
foreach(int i in ROWS) {
Console.Write(row_sums[i].Value() + " ");
}
Console.Write("\nrow_signs: ");
foreach(int i in ROWS) {
Console.Write(row_signs[i].Value() + " ");
}
Console.Write("\ncol_sums: ");
foreach(int j in COLS) {
Console.Write(col_sums[j].Value() + " ");
}
Console.Write("\ncol_signs: ");
foreach(int j in COLS) {
Console.Write(col_signs[j].Value() + " ");
}
Console.WriteLine("\n");
foreach(int i in ROWS) {
foreach(int j in COLS) {
Console.Write("{0,3} ", x[i,j].Value());
}
Console.WriteLine();
}
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();
}
/**
*
* Kakuru puzzle.
*
* http://en.wikipedia.org/wiki/Kakuro
* """
* The object of the puzzle is to insert a digit from 1 to 9 inclusive
* into each white cell such that the sum of the numbers in each entry
* matches the clue associated with it and that no digit is duplicated in
* any entry. It is that lack of duplication that makes creating Kakuro
* puzzles with unique solutions possible, and which means solving a Kakuro
* puzzle involves investigating combinations more, compared to Sudoku in
* which the focus is on permutations. There is an unwritten rule for
* making Kakuro puzzles that each clue must have at least two numbers
* that add up to it. This is because including one number is mathematically
* trivial when solving Kakuro puzzles; one can simply disregard the
* number entirely and subtract it from the clue it indicates.
* """
*
* This model solves the problem at the Wikipedia page.
* For a larger picture, see
* http://en.wikipedia.org/wiki/File:Kakuro_black_box.svg
*
* The solution:
* 9 7 0 0 8 7 9
* 8 9 0 8 9 5 7
* 6 8 5 9 7 0 0
* 0 6 1 0 2 6 0
* 0 0 4 6 1 3 2
* 8 9 3 1 0 1 4
* 3 1 2 0 0 2 1
*
* Also see http://www.hakank.org/or-tools/kakuro.py
* though this C# model has another representation of
* the problem instance.
*
*/
private static void Solve()
{
Solver solver = new Solver("Kakuro");
// size of matrix
int n = 7;
// segments:
// sum, the segments
// Note: this is 1-based
int[][] problem =
{
new int[] {16, 1,1, 1,2},
new int[] {24, 1,5, 1,6, 1,7},
new int[] {17, 2,1, 2,2},
new int[] {29, 2,4, 2,5, 2,6, 2,7},
new int[] {35, 3,1, 3,2, 3,3, 3,4, 3,5},
new int[] { 7, 4,2, 4,3},
new int[] { 8, 4,5, 4,6},
new int[] {16, 5,3, 5,4, 5,5, 5,6, 5,7},
new int[] {21, 6,1, 6,2, 6,3, 6,4},
new int[] { 5, 6,6, 6,7},
new int[] { 6, 7,1, 7,2, 7,3},
new int[] { 3, 7,6, 7,7},
new int[] {23, 1,1, 2,1, 3,1},
new int[] {30, 1,2, 2,2, 3,2, 4,2},
new int[] {27, 1,5, 2,5, 3,5, 4,5, 5,5},
new int[] {12, 1,6, 2,6},
new int[] {16, 1,7, 2,7},
new int[] {17, 2,4, 3,4},
new int[] {15, 3,3, 4,3, 5,3, 6,3, 7,3},
new int[] {12, 4,6, 5,6, 6,6, 7,6},
new int[] { 7, 5,4, 6,4},
new int[] { 7, 5,7, 6,7, 7,7},
new int[] {11, 6,1, 7,1},
new int[] {10, 6,2, 7,2}
};
int num_p = 24; // Number of segments
// The blanks
// Note: 1-based
int[,] blanks = {
{1,3}, {1,4},
{2,3},
{3,6}, {3,7},
{4,1}, {4,4}, {4,7},
{5,1}, {5,2},
{6,5},
{7,4}, {7,5}
};
int num_blanks = blanks.GetLength(0);
//
// Decision variables
//
IntVar[,] x = solver.MakeIntVarMatrix(n, n, 0, 9, "x");
IntVar[] x_flat = x.Flatten();
//
// Constraints
//
// fill the blanks with 0
for(int i = 0; i < num_blanks; i++) {
solver.Add(x[blanks[i,0]-1,blanks[i,1]-1]==0);
}
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.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
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();
}
/**
*
* KenKen puzzle.
*
* http://en.wikipedia.org/wiki/KenKen
* """
* KenKen or KEN-KEN is a style of arithmetic and logical puzzle sharing
* several characteristics with sudoku. The name comes from Japanese and
* is translated as 'square wisdom' or 'cleverness squared'.
* ...
* The objective is to fill the grid in with the digits 1 through 6 such that:
*
* * Each row contains exactly one of each digit
* * Each column contains exactly one of each digit
* * Each bold-outlined group of cells is a cage containing digits which
* achieve the specified result using the specified mathematical operation:
* addition (+),
* subtraction (-),
* multiplication (x),
* and division (/).
* (Unlike in Killer sudoku, digits may repeat within a group.)
*
* ...
* More complex KenKen problems are formed using the principles described
* above but omitting the symbols +, -, x and /, thus leaving them as
* yet another unknown to be determined.
* """
*
* The solution is:
*
* 5 6 3 4 1 2
* 6 1 4 5 2 3
* 4 5 2 3 6 1
* 3 4 1 2 5 6
* 2 3 6 1 4 5
* 1 2 5 6 3 4
*
*
* Also see http://www.hakank.org/or-tools/kenken2.py
* though this C# model has another representation of
* the problem instance.
*
*/
private static void Solve()
{
Solver solver = new Solver("KenKen2");
// size of matrix
int n = 6;
IEnumerable<int> RANGE = Enumerable.Range(0, n);
// For a better view of the problem, see
// http://en.wikipedia.org/wiki/File:KenKenProblem.svg
// hints
// sum, the hints
// Note: this is 1-based
int[][] problem =
{
new int[] { 11, 1,1, 2,1},
new int[] { 2, 1,2, 1,3},
new int[] { 20, 1,4, 2,4},
new int[] { 6, 1,5, 1,6, 2,6, 3,6},
new int[] { 3, 2,2, 2,3},
new int[] { 3, 2,5, 3,5},
new int[] {240, 3,1, 3,2, 4,1, 4,2},
new int[] { 6, 3,3, 3,4},
new int[] { 6, 4,3, 5,3},
new int[] { 7, 4,4, 5,4, 5,5},
new int[] { 30, 4,5, 4,6},
new int[] { 6, 5,1, 5,2},
new int[] { 9, 5,6, 6,6},
new int[] { 8, 6,1, 6,2, 6,3},
new int[] { 2, 6,4, 6,5}
};
int num_p = problem.GetLength(0); // Number of segments
//
// Decision variables
//
IntVar[,] x = solver.MakeIntVarMatrix(n, n, 1, n, "x");
IntVar[] x_flat = x.Flatten();
//
// Constraints
//
//
// 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());
}
// Calculate the segments
for(int i = 0; i < num_p; i++) {
int[] segment = problem[i];
// Remove the sum from the segment
int len = segment.Length-1;
int[] s2 = new int[len];
Array.Copy(segment, 1, s2, 0, len);
// sum this segment
calc(solver, s2, x, segment[0]);
}
//
// 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++) {
Console.Write(x[i,j].Value() + " ");
}
Console.WriteLine();
}
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();
}
/**
*
* Solves the Seseman convent problem.
* See http://www.hakank.org/google_or_tools/seseman.py
*
*/
private static void Solve(int n = 3)
{
Solver solver = new Solver("Seseman");
//
// data
//
int border_sum = n * n;
//
// Decision variables
//
IntVar[,] x = solver.MakeIntVarMatrix(n, n, 0, n*n, "x");
IntVar[] x_flat = x.Flatten();
IntVar total_sum = x_flat.Sum().Var();
//
// Constraints
//
// zero in all middle cells
for(int i = 1; i < n-1; i++) {
for(int j = 1; j < n-1; j++) {
solver.Add(x[i,j] == 0);
}
}
// all borders must be >= 1
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
if (i == 0 || j == 0 || i == n - 1 || j == n - 1) {
solver.Add(x[i,j] >= 1);
}
}
}
// sum the four borders
IntVar[] border1 = new IntVar[n];
IntVar[] border2 = new IntVar[n];
IntVar[] border3 = new IntVar[n];
IntVar[] border4 = new IntVar[n];
for(int i = 0; i < n; i++) {
border1[i] = x[i,0];
border2[i] = x[i,n-1];
border3[i] = x[0,i];
border4[i] = x[n-1,i];
}
solver.Add(border1.Sum() == border_sum);
solver.Add(border2.Sum() == border_sum);
solver.Add(border3.Sum() == border_sum);
solver.Add(border4.Sum() == border_sum);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x_flat,
Solver.CHOOSE_PATH,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.WriteLine("total_sum: {0} ", total_sum.Value());
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++){
Console.Write("{0} ", x[i,j].Value());
}
Console.WriteLine();
}
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();
}
/**
*
* Implements Young tableaux and partitions.
* See http://www.hakank.org/or-tools/young_tableuax.py
*
*/
private static void Solve(int n)
{
Solver solver = new Solver("YoungTableaux");
//
// data
//
Console.WriteLine("n: {0}\n", n);
//
// Decision variables
//
IntVar[,] x = solver.MakeIntVarMatrix(n, n, 1, n + 1, "x");
IntVar[] x_flat = x.Flatten();
// partition structure
IntVar[] p = solver.MakeIntVarArray(n, 0, n + 1, "p");
//
// Constraints
//
// 1..n is used exactly once
for(int i = 1; i <= n; i++) {
solver.Add(x_flat.Count(i, 1));
}
solver.Add(x[0,0] == 1);
// row wise
for(int i = 0; i < n; i++) {
for(int j = 1; j < n; j++) {
solver.Add(x[i,j] >= x[i,j - 1]);
}
}
// column wise
for(int j = 0; j < n; j++) {
for(int i = 1; i < n; i++) {
solver.Add(x[i,j] >= x[i - 1, j]);
}
}
// calculate the structure (i.e. the partition)
for(int i = 0; i < n; i++) {
IntVar[] b = new IntVar[n];
for(int j = 0; j < n; j++) {
b[j] = x[i, j] <= n;
}
solver.Add(p[i] == b.Sum());
}
solver.Add(p.Sum() == n);
for(int i = 1; i < n; i++) {
solver.Add(p[i - 1] >= p[i]);
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(x_flat,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.Write("p: ");
for(int i = 0; i < n; i++) {
Console.Write(p[i].Value() + " ");
}
Console.WriteLine("\nx:");
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
long val = x[i,j].Value();
if (val <= n) {
Console.Write(val + " ");
}
}
if (p[i].Value() > 0) {
Console.WriteLine();
}
}
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();
}
/**
*
* Solves the Coins Grid problm.
* See http://www.hakank.org/google_or_tools/coins_grid.py
*
*/
private static void Solve(int n = 31, int c = 14)
{
Solver solver = new Solver("CoinsGrid");
//
// Decision variables
//
IntVar[,] x = solver.MakeIntVarMatrix(n, n, 0, 1 , "x");
IntVar[] x_flat = x.Flatten();
//
// Constraints
//
// sum row/columns == c
for(int i = 0; i < n; i++) {
IntVar[] row = new IntVar[n];
IntVar[] col = new IntVar[n];
for(int j = 0; j < n; j++) {
row[j] = x[i,j];
col[j] = x[j,i];
}
solver.Add(row.Sum() == c);
solver.Add(col.Sum() == c);
}
// quadratic horizonal distance
IntVar[] obj_tmp = new IntVar[n * n];
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
obj_tmp[i * n + j] = (x[i,j] * (i - j) * (i - j)).Var();
}
}
IntVar obj_var = obj_tmp.Sum().Var();
//
// Objective
//
OptimizeVar obj = obj_var.Minimize(1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x_flat,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MAX_VALUE);
solver.NewSearch(db, obj);
while (solver.NextSolution()) {
Console.WriteLine("obj: " + obj_var.Value());
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
Console.Write(x[i,j].Value() + " ");
}
Console.WriteLine();
}
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();
}
