/**
*
* Implements the all interval problem.
* See http://www.hakank.org/google_or_tools/all_interval.py
*
*/
private static void Solve(int n=12)
{
Solver solver = new Solver("AllInterval");
//
// Decision variables
//
IntVar[] x = solver.MakeIntVarArray(n, 0, n-1, "x");
IntVar[] diffs = solver.MakeIntVarArray(n-1, 1, n-1, "diffs");
//
// Constraints
//
solver.Add(x.AllDifferent());
solver.Add(diffs.AllDifferent());
for(int k = 0; k < n - 1; k++) {
// solver.Add(diffs[k] == (x[k + 1] - x[k]).Abs());
solver.Add(diffs[k] == (x[k + 1] - x[k].Abs()));
}
// symmetry breaking
solver.Add(x[0] < x[n - 1]);
solver.Add(diffs[0] < diffs[1]);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.Write("x: ");
for(int i = 0; i < n; i++) {
Console.Write("{0} ", x[i].Value());
}
Console.Write(" diffs: ");
for(int i = 0; i < n-1; i++) {
Console.Write("{0} ", diffs[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();
}
/**
*
* Implements a (decomposition) of the global constraint circuit
* and extracting the path.
*
* One circuit for n = 5 is 3 0 4 2 1
* Thus the extracted path is 0 -> 3 -> 2 -> 4 -> 1 -> 0
*
*/
private static void Solve(int n = 5)
{
Solver solver = new Solver("CircuitTest2");
//
// Decision variables
//
IntVar[] x = solver.MakeIntVarArray(n, 0, n-1, "x");
IntVar[] path = solver.MakeIntVarArray(n, 0, n-1, "path");
//
// Constraints
//
circuit(solver, x, path);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x,
Solver.INT_VAR_DEFAULT,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.Write("x : ");
for(int i = 0; i < n; i++) {
Console.Write("{0} ", x[i].Value());
}
Console.Write("\npath: ");
for(int i = 0; i < n; i++) {
Console.Write("{0} ", path[i].Value());
}
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();
}
/**
*
* Secret Santa problem in Google CP Solver.
*
* From Ruby Quiz Secret Santa
* http://www.rubyquiz.com/quiz2.html
* """
* Honoring a long standing tradition started by my wife's dad, my friends
* all play a Secret Santa game around Christmas time. We draw names and
* spend a week sneaking that person gifts and clues to our identity. On the
* last night of the game, we get together, have dinner, share stories, and,
* most importantly, try to guess who our Secret Santa was. It's a crazily
* fun way to enjoy each other's company during the holidays.
*
* To choose Santas, we use to draw names out of a hat. This system was
* tedious, prone to many 'Wait, I got myself...' problems. This year, we
* made a change to the rules that further complicated picking and we knew
* the hat draw would not stand up to the challenge. Naturally, to solve
* this problem, I scripted the process. Since that turned out to be more
* interesting than I had expected, I decided to share.
*
* This weeks Ruby Quiz is to implement a Secret Santa selection script.
* * Your script will be fed a list of names on STDIN.
* ...
* Your script should then choose a Secret Santa for every name in the list.
* Obviously, a person cannot be their own Secret Santa. In addition, my friends
* no longer allow people in the same family to be Santas for each other and your
* script should take this into account.
* """
*
* Comment: This model skips the file input and mail parts. We
* assume that the friends are identified with a number from 1..n,
* and the families is identified with a number 1..num_families.
*
* Also see http://www.hakank.org/or-tools/secret_santa.py
* Also see http://www.hakank.org/or-tools/secret_santa2.cs
*
*/
private static void Solve()
{
Solver solver = new Solver("SecretSanta");
int[] family = {1,1,1,1, 2, 3,3,3,3,3, 4,4};
int n = family.Length;
Console.WriteLine("n = {0}", n);
IEnumerable<int> RANGE = Enumerable.Range(0, n);
//
// Decision variables
//
IntVar[] x = solver.MakeIntVarArray(n, 0, n-1, "x");
//
// Constraints
//
solver.Add(x.AllDifferent());
// Can't be one own"s Secret Santa
// (i.e. ensure that there are no fix-point in the array.)
foreach(int i in RANGE) {
solver.Add(x[i] != i);
}
// No Secret Santa to a person in the same family
foreach(int i in RANGE) {
solver.Add(solver.MakeIntConst(family[i]) != family.Element(x[i]));
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(x,
Solver.INT_VAR_SIMPLE,
Solver.INT_VALUE_SIMPLE);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.Write("x: ");
foreach(int i in RANGE) {
Console.Write(x[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();
}
public static IntVar[] subset_sum(Solver solver,
int[] values,
int total) {
int n = values.Length;
IntVar[] x = solver.MakeIntVarArray(n, 0, n, "x");
solver.Add(x.ScalProd(values) == total);
return x;
}
/**
*
* Scheduling speakers problem
*
* From Rina Dechter, Constraint Processing, page 72
* Scheduling of 6 speakers in 6 slots.
*
* See http://www.hakank.org/google_or_tools/scheduling_speakers.py
*
*/
private static void Solve()
{
Solver solver = new Solver("SchedulingSpeakers");
// number of speakers
int n = 6;
// slots available to speak
int[][] available = {
// Reasoning:
new int[] {3,4,5,6}, // 2) the only one with 6 after speaker F -> 1
new int[] {3,4}, // 5) 3 or 4
new int[] {2,3,4,5}, // 3) only with 5 after F -> 1 and A -> 6
new int[] {2,3,4}, // 4) only with 2 after C -> 5 and F -> 1
new int[] {3,4}, // 5) 3 or 4
new int[] {1,2,3,4,5,6} // 1) the only with 1
};
//
// Decision variables
//
IntVar[] x = solver.MakeIntVarArray(n, 1, n, "x");
//
// Constraints
//
solver.Add(x.AllDifferent());
for(int i = 0; i < n; i++) {
solver.Add(x[i].Member(available[i]));
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(x,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.WriteLine(string.Join(",", (from i in x select i.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();
}
/**
*
* Dudeney numbers
* From Pierre Schaus blog post
* Dudeney number
* http://cp-is-fun.blogspot.com/2010/09/test-python.html
* """
* I discovered yesterday Dudeney Numbers
* A Dudeney Numbers is a positive integer that is a perfect cube such that the sum
* of its decimal digits is equal to the cube root of the number. There are only six
* Dudeney Numbers and those are very easy to find with CP.
* I made my first experience with google cp solver so find these numbers (model below)
* and must say that I found it very convenient to build CP models in python!
* When you take a close look at the line:
* solver.Add(sum([10**(n-i-1)*x[i] for i in range(n)]) == nb)
* It is difficult to argue that it is very far from dedicated
* optimization languages!
* """
*
* Also see: http://en.wikipedia.org/wiki/Dudeney_number
*
*/
private static void Solve()
{
Solver solver = new Solver("DudeneyNumbers");
//
// data
//
int n = 6;
//
// Decision variables
//
IntVar[] x = solver.MakeIntVarArray(n, 0, 9, "x");
IntVar nb = solver.MakeIntVar(3, (int)Math.Pow(10,n), "nb");
IntVar s = solver.MakeIntVar(1,9*n+1,"s");
//
// Constraints
//
solver.Add(nb == s*s*s);
solver.Add(x.Sum() == s);
// solver.Add(ToNum(x, nb, 10));
// alternative
solver.Add((from i in Enumerable.Range(0, n)
select (x[i]*(int)Math.Pow(10,n-i-1)).Var()).
ToArray().Sum() == nb);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x,
Solver.INT_VAR_DEFAULT,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.WriteLine(nb.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();
}
/**
*
* Decomposition of alldifferent_except_0
*
* See http://www.hakank.org/google_or_tools/map.py
*
*
*/
private static void Solve()
{
Solver solver = new Solver("AllDifferentExcept0");
//
// data
//
int n = 6;
//
// Decision variables
//
IntVar[] x = solver.MakeIntVarArray(n, 0, n - 1 , "x");
//
// Constraints
//
AllDifferentExcept0(solver, x);
// we also require at least 2 0's
IntVar[] z_tmp = new IntVar[n];
for(int i = 0; i < n; i++) {
z_tmp[i] = x[i] == 0;
}
IntVar z = z_tmp.Sum().VarWithName("z");
solver.Add(z == 2);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.Write("z: {0} x: ", z.Value());
for(int i = 0; i < n; i++) {
Console.Write("{0} ", x[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();
}
/*
* Global constraint regular
*
* This is a translation of MiniZinc's regular constraint (defined in
* lib/zinc/globals.mzn), via the Comet code refered above.
* All comments are from the MiniZinc code.
* """
* The sequence of values in array 'x' (which must all be in the range 1..S)
* is accepted by the DFA of 'Q' states with input 1..S and transition
* function 'd' (which maps (1..Q, 1..S) -> 0..Q)) and initial state 'q0'
* (which must be in 1..Q) and accepting states 'F' (which all must be in
* 1..Q). We reserve state 0 to be an always failing state.
* """
*
* x : IntVar array
* Q : number of states
* S : input_max
* d : transition matrix
* q0: initial state
* F : accepting states
*
*/
static void MyRegular(Solver solver,
IntVar[] x,
int Q,
int S,
int[,] d,
int q0,
int[] F) {
// d2 is the same as d, except we add one extra transition for
// each possible input; each extra transition is from state zero
// to state zero. This allows us to continue even if we hit a
// non-accepted input.
int[][] d2 = new int[Q+1][];
for(int i = 0; i <= Q; i++) {
int[] row = new int[S];
for(int j = 0; j < S; j++) {
if (i == 0) {
row[j] = 0;
} else {
row[j] = d[i-1,j];
}
}
d2[i] = row;
}
int[] d2_flatten = (from i in Enumerable.Range(0, Q+1)
from j in Enumerable.Range(0, S)
select d2[i][j]).ToArray();
// If x has index set m..n, then a[m-1] holds the initial state
// (q0), and a[i+1] holds the state we're in after processing
// x[i]. If a[n] is in F, then we succeed (ie. accept the
// string).
int m = 0;
int n = x.Length;
IntVar[] a = solver.MakeIntVarArray(n+1-m, 0,Q+1, "a");
// Check that the final state is in F
solver.Add(a[a.Length-1].Member(F));
// First state is q0
solver.Add(a[m] == q0);
for(int i = 0; i < n; i++) {
solver.Add(x[i] >= 1);
solver.Add(x[i] <= S);
// Determine a[i+1]: a[i+1] == d2[a[i], x[i]]
solver.Add(a[i+1] == d2_flatten.Element(((a[i]*S)+(x[i]-1))));
}
}
/**
*
* Magic sequence problem.
*
* This is a port of the Python model
* https://code.google.com/p/or-tools/source/browse/trunk/python/magic_sequence_distribute.py
* """
* This models aims at building a sequence of numbers such that the number of
* occurrences of i in this sequence is equal to the value of the ith number.
* It uses an aggregated formulation of the count expression called
* distribute().
* """
*
*/
private static void Solve(int size)
{
Solver solver = new Solver("MagicSequence");
Console.WriteLine("\nSize: {0}", size);
//
// data
//
int[] all_values = new int[size];
for (int i = 0; i < size; i++) {
all_values[i] = i;
}
//
// Decision variables
//
IntVar[] all_vars = solver.MakeIntVarArray(size, 0, size - 1, "vars");
//
// Constraints
//
solver.Add(all_vars.Distribute(all_values, all_vars));
solver.Add(all_vars.Sum() == size);
//
// Search
//
DecisionBuilder db = solver.MakePhase(all_vars,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
for(int i = 0; i < size; i++) {
Console.Write(all_vars[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();
}
/**
*
* Implements toNum: channeling between a number and an array.
* See http://www.hakank.org/or-tools/toNum.py
*
*/
private static void Solve()
{
Solver solver = new Solver("ToNum");
int n = 5;
int bbase = 10;
//
// Decision variables
//
IntVar[] x = solver.MakeIntVarArray(n, 0, bbase - 1, "x");
IntVar num = solver.MakeIntVar(0, (int)Math.Pow(bbase, n) - 1, "num");
//
// Constraints
//
solver.Add(x.AllDifferent());
solver.Add(ToNum(x, num, bbase));
// extra constraint (just for fun)
// second digit should be 7
// solver.Add(x[1] == 7);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.Write("\n" + num.Value() + ": ");
for(int i = 0; i < n; i++) {
Console.Write(x[i].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();
}
/**
*
* Global constraint contiguity using Transition
*
* This version use the built-in TransitionConstraint.
*
* From Global Constraint Catalogue
* http://www.emn.fr/x-info/sdemasse/gccat/Cglobal_contiguity.html
* """
* Enforce all variables of the VARIABLES collection to be assigned to 0 or 1.
* In addition, all variables assigned to value 1 appear contiguously.
*
* Example:
* (<0, 1, 1, 0>)
*
* The global_contiguity constraint holds since the sequence 0 1 1 0 contains
* no more than one group of contiguous 1.
* """
*
* Also see http://www.hakank.org/or-tools/contiguity_regular.py
*
*/
private static void Solve()
{
Solver solver = new Solver("ContiguityRegular");
//
// Data
//
int n = 7; // length of the array
//
// Decision variables
//
IntVar[] reg_input = solver.MakeIntVarArray(n, 0, 1, "reg_input");
//
// Constraints
//
MyContiguity(solver, reg_input);
//
// Search
//
DecisionBuilder db = solver.MakePhase(reg_input,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
for(int i = 0; i < n; i++) {
Console.Write((reg_input[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();
}
/**
*
* Grocery problem.
*
* From Christian Schulte, Gert Smolka, Finite Domain
* http://www.mozart-oz.org/documentation/fdt/
* Constraint Programming in Oz. A Tutorial. 2001.
* """
* A kid goes into a grocery store and buys four items. The cashier
* charges $7.11, the kid pays and is about to leave when the cashier
* calls the kid back, and says 'Hold on, I multiplied the four items
* instead of adding them; I'll try again; Hah, with adding them the
* price still comes to $7.11'. What were the prices of the four items?
* """
*
*/
private static void Solve()
{
Solver solver = new Solver("Grocery");
int n = 4;
int c = 711;
//
// Decision variables
//
IntVar[] item = solver.MakeIntVarArray(n, 0, c / 2, "item");
//
// Constraints
//
solver.Add(item.Sum() == c);
// solver.Add(item[0] * item[1] * item[2] * item[3] == c * 100*100*100);
// solver.Add(item.Prod() == c * 100*100*100);
solver.Add(MyProd(item, c * 100*100*100));
// Symmetry breaking
Decreasing(solver, item);
//
// Search
//
DecisionBuilder db = solver.MakePhase(item,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
for(int i = 0; i < n; i++) {
Console.Write(item[i].Value() + " ");
}
Console.WriteLine();
}
Console.WriteLine("\nWallTime: " + solver.WallTime() + "ms ");
Console.WriteLine("Failures: " + solver.Failures());
Console.WriteLine("Branches: " + solver.Branches());
solver.EndSearch();
}
/**
*
* Solve the xkcd problem
* See http://www.hakank.org/google_or_tools/xkcd.py
*
*/
private static void Solve()
{
Solver solver = new Solver("Xkcd");
//
// Constants, inits
//
int n = 6;
// for price and total: multiplied by 100 to be able to use integers
int[] price = {215, 275, 335, 355, 420, 580};
int total = 1505;
//
// Decision variables
//
IntVar[] x = solver.MakeIntVarArray(n, 0, 10, "x");
//
// Constraints
//
solver.Add(x.ScalProd(price) == total);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
for(int i = 0; i < n; i++) {
Console.Write(x[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();
}
/**
* circuit(solver, x)
*
* A decomposition of the global constraint circuit, based
* on some observation of the orbits in an array.
*
* Note: The domain of x must be 0..n-1 (not 1..n)
* since C# is 0-based.
*/
public static void circuit(Solver solver, IntVar[] x) {
int n = x.Length;
IntVar[] z = solver.MakeIntVarArray(n, 0, n - 1, "z");
solver.Add(x.AllDifferent());
solver.Add(z.AllDifferent());
// put the orbit of x[0] in z[0..n-1]
solver.Add(z[0] == x[0]);
for(int i = 1; i < n-1; i++) {
solver.Add(z[i] == x.Element(z[i-1]));
}
// z may not be 0 for i < n-1
for(int i = 1; i < n - 1; i++) {
solver.Add(z[i] != 0);
}
// when i = n-1 it must be 0
solver.Add(z[n - 1] == 0);
}
/**
*
* Crypto problem.
*
* This is the standard benchmark "crypto" problem.
*
* From GLPK:s model cryto.mod.
*
* """
* This problem comes from the newsgroup rec.puzzle.
* The numbers from 1 to 26 are assigned to the letters of the alphabet.
* The numbers beside each word are the total of the values assigned to
* the letters in the word (e.g. for LYRE: L, Y, R, E might be to equal
* 5, 9, 20 and 13, or any other combination that add up to 47).
* Find the value of each letter under the equations:
*
* BALLET 45 GLEE 66 POLKA 59 SONG 61
* CELLO 43 JAZZ 58 QUARTET 50 SOPRANO 82
* CONCERT 74 LYRE 47 SAXOPHONE 134 THEME 72
* FLUTE 30 OBOE 53 SCALE 51 VIOLIN 100
* FUGUE 50 OPERA 65 SOLO 37 WALTZ 34
*
* Solution:
* 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
* 5,13,9,16,20,4,24,21,25,17,23,2,8,12,10,19,7,11,15,3,1,26,6,22,14,18
*
* Reference:
* Koalog Constraint Solver <http://www.koalog.com/php/jcs.php>,
* Simple problems, the crypto-arithmetic puzzle ALPHACIPHER.
* """
*
* Also see http://hakank.org/or-tools/crypto.py
*
*/
private static void Solve()
{
Solver solver = new Solver("Crypto");
int num_letters = 26;
int BALLET = 45;
int CELLO = 43;
int CONCERT = 74;
int FLUTE = 30;
int FUGUE = 50;
int GLEE = 66;
int JAZZ = 58;
int LYRE = 47;
int OBOE = 53;
int OPERA = 65;
int POLKA = 59;
int QUARTET = 50;
int SAXOPHONE = 134;
int SCALE = 51;
int SOLO = 37;
int SONG = 61;
int SOPRANO = 82;
int THEME = 72;
int VIOLIN = 100;
int WALTZ = 34;
//
// Decision variables
//
IntVar[] LD = solver.MakeIntVarArray(num_letters, 1, num_letters, "LD");
// Note D is not used in the constraints below
IntVar A = LD[0]; IntVar B = LD[1]; IntVar C = LD[2]; // IntVar D = LD[3];
IntVar E = LD[4]; IntVar F = LD[5]; IntVar G = LD[6]; IntVar H = LD[7];
IntVar I = LD[8]; IntVar J = LD[9]; IntVar K = LD[10]; IntVar L = LD[11];
IntVar M = LD[12]; IntVar N = LD[13]; IntVar O = LD[14]; IntVar P = LD[15];
IntVar Q = LD[16]; IntVar R = LD[17]; IntVar S = LD[18]; IntVar T = LD[19];
IntVar U = LD[20]; IntVar V = LD[21]; IntVar W = LD[22]; IntVar X = LD[23];
IntVar Y = LD[24]; IntVar Z = LD[25];
//
// Constraints
//
solver.Add(LD.AllDifferent());
solver.Add( B + A + L + L + E + T == BALLET);
solver.Add( C + E + L + L + O == CELLO);
solver.Add( C + O + N + C + E + R + T == CONCERT);
solver.Add( F + L + U + T + E == FLUTE);
solver.Add( F + U + G + U + E == FUGUE);
solver.Add( G + L + E + E == GLEE);
solver.Add( J + A + Z + Z == JAZZ);
solver.Add( L + Y + R + E == LYRE);
solver.Add( O + B + O + E == OBOE);
solver.Add( O + P + E + R + A == OPERA);
solver.Add( P + O + L + K + A == POLKA);
solver.Add( Q + U + A + R + T + E + T == QUARTET);
solver.Add(S + A + X + O + P + H + O + N + E == SAXOPHONE);
solver.Add( S + C + A + L + E == SCALE);
solver.Add( S + O + L + O == SOLO);
solver.Add( S + O + N + G == SONG);
solver.Add( S + O + P + R + A + N + O == SOPRANO);
solver.Add( T + H + E + M + E == THEME);
solver.Add( V + I + O + L + I + N == VIOLIN);
solver.Add( W + A + L + T + Z == WALTZ);
//
// Search
//
DecisionBuilder db = solver.MakePhase(LD,
Solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
Solver.ASSIGN_CENTER_VALUE);
solver.NewSearch(db);
String str = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
while (solver.NextSolution()) {
for(int i = 0; i < num_letters; i++) {
Console.WriteLine("{0}: {1,2}", str[i], LD[i].Value());
}
Console.WriteLine();
}
Console.WriteLine("\nWallTime: " + solver.WallTime() + "ms ");
Console.WriteLine("Failures: " + solver.Failures());
Console.WriteLine("Branches: " + solver.Branches());
solver.EndSearch();
}
/**
*
* Lectures problem in Google CP Solver.
*
* Biggs: Discrete Mathematics (2nd ed), page 187.
* """
* Suppose we wish to schedule six one-hour lectures, v1, v2, v3, v4, v5, v6.
* Among the the potential audience there are people who wish to hear both
*
* - v1 and v2
* - v1 and v4
* - v3 and v5
* - v2 and v6
* - v4 and v5
* - v5 and v6
* - v1 and v6
*
* How many hours are necessary in order that the lectures can be given
* without clashes?
* """
*
* Note: This can be seen as a coloring problem.
*
* Also see http://www.hakank.org/or-tools/lectures.py
*
*/
private static void Solve()
{
Solver solver = new Solver("Lectures");
//
// The schedule requirements:
// lecture a cannot be held at the same time as b
// Note: 1-based (compensated in the constraints).
int[,] g =
{
{1, 2},
{1, 4},
{3, 5},
{2, 6},
{4, 5},
{5, 6},
{1, 6}
};
// number of nodes
int n = 6;
// number of edges
int edges = g.GetLength(0);
//
// Decision variables
//
//
// declare variables
//
IntVar[] v = solver.MakeIntVarArray(n, 0, n-1,"v");
// Maximum color (hour) to minimize.
// Note: since C# is 0-based, the
// number of colors is max_c+1.
IntVar max_c = v.Max().VarWithName("max_c");
//
// Constraints
//
// Ensure that there are no clashes
// also, adjust to 0-base.
for(int i = 0; i < edges; i++) {
solver.Add(v[g[i,0]-1] != v[g[i,1]-1]);
}
// Symmetry breaking:
// - v0 has the color 0,
// - v1 has either color 0 or 1
solver.Add(v[0] == 0);
solver.Add(v[1] <= 1);
//
// Objective
//
OptimizeVar obj = max_c.Minimize(1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(v,
Solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db, obj);
while (solver.NextSolution()) {
Console.WriteLine("\nmax hours: {0}", max_c.Value()+1);
Console.WriteLine("v: " +
String.Join(" ", (from i in Enumerable.Range(0, n)
select v[i].Value()).ToArray()));
for(int i = 0; i < n; i++) {
Console.WriteLine("Lecture {0} at {1}h", i, v[i].Value());
}
Console.WriteLine("\n");
}
Console.WriteLine("\nSolutions: " + solver.Solutions());
Console.WriteLine("WallTime: " + solver.WallTime() + "ms ");
Console.WriteLine("Failures: " + solver.Failures());
Console.WriteLine("Branches: " + 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();
}
/**
*
* 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();
}
/**
*
*
* Organizing a day.
*
* Simple scheduling problem.
*
* Problem formulation from ECLiPSe:
* Slides on (Finite Domain) Constraint Logic Programming, page 38f
* http://eclipse-clp.org/reports/eclipse.ppt
*
*
* Also see http://www.hakank.org/google_or_tools/organize_day.py
*
*/
private static void Solve()
{
Solver solver = new Solver("OrganizeDay");
int n = 4;
int work = 0;
int mail = 1;
int shop = 2;
int bank = 3;
int[] tasks = {work, mail, shop, bank};
int[] durations = {4,1,2,1};
// task [i,0] must be finished before task [i,1]
int[,] before_tasks = {
{bank, shop},
{mail, work}
};
// the valid times of the day
int begin = 9;
int end = 17;
//
// Decision variables
//
IntVar[] begins = solver.MakeIntVarArray(n, begin, end, "begins");
IntVar[] ends = solver.MakeIntVarArray(n, begin, end, "ends");
//
// Constraints
//
foreach(int t in tasks) {
solver.Add(ends[t] == begins[t] + durations[t]);
}
foreach(int i in tasks) {
foreach(int j in tasks) {
if (i < j) {
NoOverlap(solver,
begins[i], durations[i],
begins[j], durations[j]);
}
}
}
// specific constraints
for(int t = 0; t < before_tasks.GetLength(0); t++) {
solver.Add(ends[before_tasks[t,0]] <= begins[before_tasks[t,1]]);
}
solver.Add(begins[work] >= 11);
//
// Search
//
DecisionBuilder db = solver.MakePhase(begins,
Solver.INT_VAR_DEFAULT,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db);
while (solver.NextSolution()) {
foreach(int t in tasks) {
Console.WriteLine("Task {0}: {1,2} .. ({2}) .. {3,2}",
t,
begins[t].Value(),
durations[t],
ends[t].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();
}
/**
*
* 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();
}
/**
*
* Olympic puzzle.
*
* Benchmark for Prolog (BProlog)
* """
* File : olympic.pl
* Author : Neng-Fa ZHOU
* Date : 1993
*
* Purpose: solve a puzzle taken from Olympic Arithmetic Contest
*
* Given ten variables with the following configuration:
*
* X7 X8 X9 X10
*
* X4 X5 X6
*
* X2 X3
*
* X1
*
* We already know that X1 is equal to 3 and want to assign each variable
* with a different integer from {1,2,...,10} such that for any three
* variables
* Xi Xj
*
* Xk
*
* the following constraint is satisfied:
*
* |Xi-Xj| = Xk
* """
*
* Also see http://www.hakank.org/or-tools/olympic.py
*
*/
private static void Solve()
{
Solver solver = new Solver("Olympic");
//
// Data
//
int n = 10;
//
// Decision variables
//
IntVar[] x = solver.MakeIntVarArray(n, 1, n, "x");
IntVar X1 = x[0];
IntVar X2 = x[1];
IntVar X3 = x[2];
IntVar X4 = x[3];
IntVar X5 = x[4];
IntVar X6 = x[5];
IntVar X7 = x[6];
IntVar X8 = x[7];
IntVar X9 = x[8];
IntVar X10 = x[9];
//
// Constraints
//
solver.Add(x.AllDifferent());
solver.Add(X1 == 3);
minus(solver, X2, X3, X1);
minus(solver, X4, X5, X2);
minus(solver, X5, X6, X3);
minus(solver, X7, X8, X4);
minus(solver, X8, X9, X5);
minus(solver, X9, X10, X6);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x,
Solver.INT_VAR_SIMPLE,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db);
while (solver.NextSolution()) {
for(int i = 0; i < n; i++) {
Console.Write("{0,2} ", x[i].Value());
}
Console.WriteLine();
}
Console.WriteLine("\nSolutions: " + solver.Solutions());
Console.WriteLine("WallTime: " + solver.WallTime() + "ms ");
Console.WriteLine("Failures: " + solver.Failures());
Console.WriteLine("Branches: " + solver.Branches());
solver.EndSearch();
}
/**
*
* Labeled dice problem.
*
* From Jim Orlin 'Colored letters, labeled dice: a logic puzzle'
* http://jimorlin.wordpress.com/2009/02/17/colored-letters-labeled-dice-a-logic-puzzle/
* """
* My daughter Jenn bough a puzzle book, and showed me a cute puzzle. There
* are 13 words as follows: BUOY, CAVE, CELT, FLUB, FORK, HEMP, JUDY,
* JUNK, LIMN, QUIP, SWAG, VISA, WISH.
*
* There are 24 different letters that appear in the 13 words. The question
* is: can one assign the 24 letters to 4 different cubes so that the
* four letters of each word appears on different cubes. (There is one
* letter from each word on each cube.) It might be fun for you to try
* it. I'll give a small hint at the end of this post. The puzzle was
* created by Humphrey Dudley.
* """
*
* Jim Orlin's followup 'Update on Logic Puzzle':
* http://jimorlin.wordpress.com/2009/02/21/update-on-logic-puzzle/
*
*
* Also see http://www.hakank.org/or-tools/labeled_dice.py
*
*/
private static void Solve()
{
Solver solver = new Solver("LabeledDice");
//
// Data
//
int n = 4;
int m = 24;
int A = 0;
int B = 1;
int C = 2;
int D = 3;
int E = 4;
int F = 5;
int G = 6;
int H = 7;
int I = 8;
int J = 9;
int K = 10;
int L = 11;
int M = 12;
int N = 13;
int O = 14;
int P = 15;
int Q = 16;
int R = 17;
int S = 18;
int T = 19;
int U = 20;
int V = 21;
int W = 22;
int Y = 23;
String[] letters_str = {"A","B","C","D","E","F","G","H","I","J","K","L","M",
"N","O","P","Q","R","S","T","U","V","W","Y"};
int num_words = 13;
int[,] words =
{
{B,U,O,Y},
{C,A,V,E},
{C,E,L,T},
{F,L,U,B},
{F,O,R,K},
{H,E,M,P},
{J,U,D,Y},
{J,U,N,K},
{L,I,M,N},
{Q,U,I,P},
{S,W,A,G},
{V,I,S,A},
{W,I,S,H}
};
//
// Decision variables
//
IntVar[] dice = solver.MakeIntVarArray(m, 0, n-1, "dice");
IntVar[] gcc = solver.MakeIntVarArray(n, 6, 6, "gcc");
//
// Constraints
//
// the letters in a word must be on a different die
for(int i = 0; i < num_words; i++) {
solver.Add( (from j in Enumerable.Range(0, n)
select dice[words[i,j]]
).ToArray().AllDifferent());
}
// there must be exactly 6 letters of each die
/*
for(int i = 0; i < n; i++) {
solver.Add( ( from j in Enumerable.Range(0, m)
select (dice[j] == i)
).ToArray().Sum() == 6 );
}
*/
// Use Distribute (Global Cardinality Count) instead.
solver.Add(dice.Distribute(gcc));
//
// Search
//
DecisionBuilder db = solver.MakePhase(dice,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
for(int d = 0; d < n; d++) {
Console.Write("die {0}: ", d);
for(int i = 0; i < m; i++) {
if (dice[i].Value() == d) {
Console.Write(letters_str[i]);
}
}
Console.WriteLine();
}
Console.WriteLine("The words with the cube label:");
for(int i = 0; i < num_words; i++) {
for(int j = 0; j < n; j++) {
Console.Write("{0} ({1})", letters_str[words[i,j]], dice[words[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();
}
/**
*
* Just forgotten puzzle (Enigma 1517) in Google CP Solver.
*
* From http://www.f1compiler.com/samples/Enigma 201517.f1.html
* """
* Enigma 1517 Bob Walker, New Scientist magazine, October 25, 2008.
*
* Joe was furious when he forgot one of his bank account numbers.
* He remembered that it had all the digits 0 to 9 in some order,
* so he tried the following four sets without success:
*
* 9 4 6 2 1 5 7 8 3 0
* 8 6 0 4 3 9 1 2 5 7
* 1 6 4 0 2 9 7 8 5 3
* 6 8 2 4 3 1 9 0 7 5
*
* When Joe finally remembered his account number, he realised that
* in each set just four of the digits were in their correct position
* and that, if one knew that, it was possible to work out his
* account number. What was it?
* """
*
* Also see http://www.hakank.org/google_or_tools/just_forgotten.py
*
*/
private static void Solve()
{
Solver solver = new Solver("JustForgotten");
int rows = 4;
int cols = 10;
// The four tries
int[,] a = {{9,4,6,2,1,5,7,8,3,0},
{8,6,0,4,3,9,1,2,5,7},
{1,6,4,0,2,9,7,8,5,3},
{6,8,2,4,3,1,9,0,7,5}};
//
// Decision variables
//
IntVar[] x = solver.MakeIntVarArray(cols, 0, 9, "x");
//
// Constraints
//
solver.Add(x.AllDifferent());
for(int r = 0; r < rows; r++) {
solver.Add( (from c in Enumerable.Range(0, cols)
select x[c] == a[r,c]).ToArray().Sum() == 4);
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(x,
Solver.INT_VAR_DEFAULT,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.WriteLine("Account number:");
for(int j = 0; j < cols; j++) {
Console.Write(x[j].Value() + " ");
}
Console.WriteLine("\n");
Console.WriteLine("The four tries, where '!' represents a correct digit:");
for(int i = 0; i < rows; i++) {
for(int j = 0; j < cols; j++) {
String c = " ";
if (a[i,j] == x[j].Value()) {
c = "!";
}
Console.Write("{0}{1} ", a[i,j], c);
}
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 some stable marriage problems.
*
* This version randomize the problem instances.
*
* Also, see http://www.hakank.org/or-tools/stable_marriage.cs
*
*
*/
private static void Solve(int n = 10, int sols_to_show = 0)
{
Solver solver = new Solver("StableMarriage");
//
// data
//
int seed = (int)DateTime.Now.Ticks;
Random generator = new Random(seed);
int[][] rankMen = new int[n][];
int[][] rankWomen = new int[n][];
for (int i = 0; i < n; i++) {
int[] m = shuffle(n, generator);
int[] w = shuffle(n, generator);
rankMen[i] = new int[n];
rankWomen[i] = new int[n];
for (int j = 0; j < n; j++) {
rankMen[i][j] = m[j];
rankWomen[i][j] = w[j];
}
}
Console.WriteLine("after generating...");
if (n <= 20) {
Console.Write("rankMen: ");
printRank("rankMen", rankMen);
printRank("rankWomen", rankWomen);
}
//
// Decision variables
//
IntVar[] wife = solver.MakeIntVarArray(n, 0, n - 1, "wife");
IntVar[] husband = solver.MakeIntVarArray(n, 0, n - 1, "husband");
//
// Constraints
//
// (The comments below are the Comet code)
//
// forall(m in Men)
// cp.post(husband[wife[m]] == m);
for(int m = 0; m < n; m++) {
solver.Add(husband.Element(wife[m]) == m);
}
// forall(w in Women)
// cp.post(wife[husband[w]] == w);
for(int w = 0; w < n; w++) {
solver.Add(wife.Element(husband[w]) == w);
}
// forall(m in Men, o in Women)
// cp.post(rankMen[m,o] < rankMen[m, wife[m]] =>
// rankWomen[o,husband[o]] < rankWomen[o,m]);
for(int m = 0; m < n; m++) {
for(int o = 0; o < n; o++) {
IntVar b1 = rankMen[m].Element(wife[m]) > rankMen[m][o];
IntVar b2 = rankWomen[o].Element(husband[o]) < rankWomen[o][m];
solver.Add(b1 <= b2);
}
}
// forall(w in Women, o in Men)
// cp.post(rankWomen[w,o] < rankWomen[w,husband[w]] =>
// rankMen[o,wife[o]] < rankMen[o,w]);
for(int w = 0; w < n; w++) {
for(int o = 0; o < n; o++) {
IntVar b1 = rankWomen[w].Element(husband[w]) > rankWomen[w][o];
IntVar b2 = rankMen[o].Element(wife[o]) < rankMen[o][w];
solver.Add(b1 <= b2);
}
}
//
// Search
//
DecisionBuilder db = solver.MakePhase(wife,
// Solver.INT_VAR_DEFAULT,
// Solver.INT_VAR_SIMPLE,
Solver.CHOOSE_FIRST_UNBOUND,
// Solver.CHOOSE_RANDOM,
// Solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
// Solver.CHOOSE_MIN_SIZE_HIGHEST_MIN,
// Solver.CHOOSE_MIN_SIZE_LOWEST_MAX,
// Solver.CHOOSE_MIN_SIZE_HIGHEST_MAX,
// Solver.CHOOSE_PATH,
// Solver.CHOOSE_MIN_SIZE,
// Solver.CHOOSE_MAX_SIZE,
// Solver.CHOOSE_MAX_REGRET,
// Solver.INT_VALUE_DEFAULT
// Solver.INT_VALUE_SIMPLE
Solver.ASSIGN_MIN_VALUE
// Solver.ASSIGN_MAX_VALUE
// Solver.ASSIGN_RANDOM_VALUE
// Solver.ASSIGN_CENTER_VALUE
// Solver.SPLIT_LOWER_HALF
// Solver.SPLIT_UPPER_HALF
);
solver.NewSearch(db);
int sols = 0;
while (solver.NextSolution()) {
sols += 1;
Console.Write("wife : ");
for(int i = 0; i < n; i++) {
Console.Write(wife[i].Value() + " ");
}
Console.Write("\nhusband: ");
for(int i = 0; i < n; i++) {
Console.Write(husband[i].Value() + " ");
}
Console.WriteLine("\n");
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();
}
/**
*
* Moving furnitures (scheduling) problem in Google CP Solver.
*
* Marriott & Stukey: 'Programming with constraints', page 112f
*
* The model implements an decomposition of the global constraint
* cumulative (see above).
*
* Also see http://www.hakank.org/or-tools/furniture_moving.py
*
*/
private static void Solve()
{
Solver solver = new Solver("FurnitureMoving");
int n = 4;
int[] duration = {30,10,15,15};
int[] demand = { 3, 1, 3, 2};
int upper_limit = 160;
//
// Decision variables
//
IntVar[] start_times = solver.MakeIntVarArray(n, 0, upper_limit, "start_times");
IntVar[] end_times = solver.MakeIntVarArray(n, 0, upper_limit * 2, "end_times");
IntVar end_time = solver.MakeIntVar(0, upper_limit * 2, "end_time");
// number of needed resources, to be minimized or constrained
IntVar num_resources = solver.MakeIntVar(0, 10, "num_resources");
//
// Constraints
//
for(int i = 0; i < n; i++) {
solver.Add(end_times[i] == start_times[i] + duration[i]);
}
solver.Add(end_time == end_times.Max());
MyCumulative(solver, start_times, duration, demand, num_resources);
//
// Some extra constraints to play with
//
// all tasks must end within an hour
// solver.Add(end_time <= 60);
// All tasks should start at time 0
// for(int i = 0; i < n; i++) {
// solver.Add(start_times[i] == 0);
// }
// limitation of the number of people
// solver.Add(num_resources <= 3);
solver.Add(num_resources <= 4);
//
// Objective
//
// OptimizeVar obj = num_resources.Minimize(1);
OptimizeVar obj = end_time.Minimize(1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(start_times,
Solver.CHOOSE_FIRST_UNBOUND,
Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db, obj);
while (solver.NextSolution()) {
Console.WriteLine("num_resources: {0} end_time: {1}",
num_resources.Value(), end_time.Value());
for(int i = 0; i < n; i++) {
Console.WriteLine("Task {0,1}: {1,2} -> {2,2} -> {3,2} (demand: {4})",
i,
start_times[i].Value(),
duration[i],
end_times[i].Value(),
demand[i]);
}
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();
}
/**
*
* Solves a set covering problem.
* See See http://www.hakank.org/or-tools/set_covering4.py
*
*/
private static void Solve(int set_partition)
{
Solver solver = new Solver("SetCovering4");
//
// data
//
// Set partition and set covering problem from
// Example from the Swedish book
// Lundgren, Roennqvist, Vaebrand
// 'Optimeringslaera' (translation: 'Optimization theory'),
// page 408.
int num_alternatives = 10;
int num_objects = 8;
// costs for the alternatives
int[] costs = {19, 16, 18, 13, 15, 19, 15, 17, 16, 15};
// the alternatives, and their objects
int[,] a = {
// 1 2 3 4 5 6 7 8 the objects
{1,0,0,0,0,1,0,0}, // alternative 1
{0,1,0,0,0,1,0,1}, // alternative 2
{1,0,0,1,0,0,1,0}, // alternative 3
{0,1,1,0,1,0,0,0}, // alternative 4
{0,1,0,0,1,0,0,0}, // alternative 5
{0,1,1,0,0,0,0,0}, // alternative 6
{0,1,1,1,0,0,0,0}, // alternative 7
{0,0,0,1,1,0,0,1}, // alternative 8
{0,0,1,0,0,1,0,1}, // alternative 9
{1,0,0,0,0,1,1,0}}; // alternative 10
//
// Decision variables
//
IntVar[] x = solver.MakeIntVarArray(num_alternatives, 0, 1, "x");
// number of assigned senators, to be minimized
IntVar z = x.ScalProd(costs).VarWithName("z");
//
// Constraints
//
for(int j = 0; j < num_objects; j++) {
IntVar[] b = new IntVar[num_alternatives];
for(int i = 0; i < num_alternatives; i++) {
b[i] = (x[i] * a[i,j]).Var();
}
if (set_partition == 1) {
solver.Add(b.Sum() >= 1);
} else {
solver.Add(b.Sum() == 1);
}
}
//
// objective
//
OptimizeVar objective = z.Minimize(1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x,
Solver.INT_VAR_DEFAULT,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db, objective);
while (solver.NextSolution()) {
Console.WriteLine("z: " + z.Value());
Console.Write("Selected alternatives: ");
for(int i = 0; i < num_alternatives; i++) {
if (x[i].Value() == 1) {
Console.Write((i+1) + " ");
}
}
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();
}
/**
*
* Solves a set covering problem.
* See See http://www.hakank.org/or-tools/set_covering2.py
*
*/
private static void Solve()
{
Solver solver = new Solver("SetCovering2");
//
// data
//
// Example 9.1-2 from
// Taha "Operations Research - An Introduction",
// page 354ff.
// Minimize the number of security telephones in street
// corners on a campus.
int n = 8; // maximum number of corners
int num_streets = 11; // number of connected streets
// corners of each street
// Note: 1-based (handled below)
int[,] corner = {{1,2},
{2,3},
{4,5},
{7,8},
{6,7},
{2,6},
{1,6},
{4,7},
{2,4},
{5,8},
{3,5}};
//
// Decision variables
//
IntVar[] x = solver.MakeIntVarArray(n, 0, 1, "x");
// number of telephones, to be minimized
IntVar z = x.Sum().Var();
//
// Constraints
//
// ensure that all streets are covered
for(int i = 0; i < num_streets; i++) {
solver.Add(x[corner[i,0] - 1] + x[corner[i,1] - 1] >= 1);
}
//
// objective
//
OptimizeVar objective = z.Minimize(1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x,
Solver.INT_VAR_DEFAULT,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db, objective);
while (solver.NextSolution()) {
Console.WriteLine("z: {0}", z.Value());
Console.Write("x: ");
for(int i = 0; i < n; i++) {
Console.Write(x[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();
}
/**
*
* Rogo puzzle solver.
*
* From http://www.rogopuzzle.co.nz/
* """
* The object is to collect the biggest score possible using a given
* number of steps in a loop around a grid. The best possible score
* for a puzzle is given with it, so you can easily check that you have
* solved the puzzle. Rogo puzzles can also include forbidden squares,
* which must be avoided in your loop.
* """
*
* Also see Mike Trick:
* "Operations Research, Sudoko, Rogo, and Puzzles"
* http://mat.tepper.cmu.edu/blog/?p=1302
*
*
* Also see, http://www.hakank.org/or-tools/rogo2.py
* though this model differs in a couple of central points
* which makes it much faster:
*
* - it use a table (
AllowedAssignments) with the valid connections
* - instead of two coordinates arrays, it use a single path array
*
*/
private static void Solve()
{
Solver solver = new Solver("Rogo2");
Console.WriteLine("\n");
Console.WriteLine("**********************************************");
Console.WriteLine(" {0}", problem_name);
Console.WriteLine("**********************************************\n");
//
// Data
//
int B = -1;
Console.WriteLine("Rows: {0} Cols: {1} Max Steps: {2}", rows, cols, max_steps);
int[] problem_flatten = problem.Cast<int>().ToArray();
int max_point = problem_flatten.Max();
int max_sum = problem_flatten.Sum();
Console.WriteLine("max_point: {0} max_sum: {1} best: {2}", max_point, max_sum, best);
IEnumerable<int> STEPS = Enumerable.Range(0, max_steps);
IEnumerable<int> STEPS1 = Enumerable.Range(0, max_steps-1);
// the valid connections, to be used with AllowedAssignments
IntTupleSet valid_connections = ValidConnections(rows, cols);
//
// Decision variables
//
IntVar[] path = solver.MakeIntVarArray(max_steps, 0, rows*cols-1, "path");
IntVar[] points = solver.MakeIntVarArray(max_steps, 0, best, "points");
IntVar sum_points = points.Sum().VarWithName("sum_points");
//
// Constraints
//
foreach(int s in STEPS) {
// calculate the points (to maximize)
solver.Add(points[s] == problem_flatten.Element(path[s]));
// ensure that there are no black cells in
// the path
solver.Add(problem_flatten.Element(path[s]) != B);
}
solver.Add(path.AllDifferent());
// valid connections
foreach(int s in STEPS1) {
solver.Add(new IntVar[] {path[s], path[s+1]}.
AllowedAssignments(valid_connections));
}
// around the corner
solver.Add(new IntVar[] {path[max_steps-1], path[0]}.
AllowedAssignments(valid_connections));
// Symmetry breaking
for(int s = 1; s < max_steps; s++) {
solver.Add(path[0] < path[s]);
}
//
// Objective
//
OptimizeVar obj = sum_points.Maximize(1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(path,
Solver.INT_VAR_DEFAULT,
Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db, obj);
while (solver.NextSolution()) {
Console.WriteLine("sum_points: {0}", sum_points.Value());
Console.Write("path: ");
foreach(int s in STEPS) {
Console.Write("{0} ", path[s].Value());
}
Console.WriteLine();
Console.WriteLine("(Adding 1 to coords...)");
int[,] sol = new int[rows, cols];
foreach(int s in STEPS) {
int p = (int) path[s].Value();
int x = (int) (p / cols);
int y = (int) (p % cols);
Console.WriteLine("{0,2},{1,2} ({2} points)", x+1, y+1, points[s].Value());
sol[x, y] = 1;
}
Console.WriteLine("\nThe path is marked by 'X's:");
for(int i = 0; i < rows; i++) {
for(int j = 0; j < cols; j++) {
String p = sol[i,j] == 1 ? "X" : " ";
String q = problem[i,j] == B ? "B" :
problem[i,j] == 0 ? "." : problem[i,j].ToString();
Console.Write("{0,2}{1} ", q, p);
}
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 simple map coloring problem.
*
* Alternative version, using a matrix to represent
* the neighbours.
*
* See http://www.hakank.org/google_or_tools/map.py
*
*
*/
private static void Solve()
{
Solver solver = new Solver("Map2");
//
// data
//
int Belgium = 0;
int Denmark = 1;
int France = 2;
int Germany = 3;
int Netherlands = 4;
int Luxembourg = 5;
int n = 6;
int max_num_colors = 4;
int[,] neighbours = {{France, Belgium},
{France, Luxembourg},
{France, Germany},
{Luxembourg, Germany},
{Luxembourg, Belgium},
{Belgium, Netherlands},
{Belgium, Germany},
{Germany, Netherlands},
{Germany, Denmark}};
//
// Decision variables
//
IntVar[] color = solver.MakeIntVarArray(n, 1, max_num_colors, "color");
//
// Constraints
//
for(int i = 0; i < neighbours.GetLength(0); i++) {
solver.Add(color[neighbours[i,0]] != color[neighbours[i,1]]);
}
// Symmetry breaking
solver.Add(color[Belgium] == 1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(color,
Solver.CHOOSE_MIN_SIZE_LOWEST_MAX,
Solver.ASSIGN_CENTER_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
Console.Write("colors: ");
for(int i = 0; i < n; i++) {
Console.Write("{0} ", color[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();
}
