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/*
* This file is part of choco-solver, http://choco-solver.org/
*
* Copyright (c) 2022, IMT Atlantique. All rights reserved.
*
* Licensed under the BSD 4-clause license.
*
* See LICENSE file in the project root for full license information.
*/
package org.chocosolver.solver.constraints;
import gnu.trove.list.array.TIntArrayList;
import gnu.trove.set.TIntSet;
import gnu.trove.set.hash.TIntHashSet;
import org.chocosolver.solver.ISelf;
import org.chocosolver.solver.Model;
import org.chocosolver.solver.constraints.binary.*;
import org.chocosolver.solver.constraints.binary.element.ElementFactory;
import org.chocosolver.solver.constraints.extension.Tuples;
import org.chocosolver.solver.constraints.extension.TuplesFactory;
import org.chocosolver.solver.constraints.extension.binary.*;
import org.chocosolver.solver.constraints.extension.nary.*;
import org.chocosolver.solver.constraints.nary.PropDiffN;
import org.chocosolver.solver.constraints.nary.PropIntValuePrecedeChain;
import org.chocosolver.solver.constraints.nary.PropKLoops;
import org.chocosolver.solver.constraints.nary.PropKnapsack;
import org.chocosolver.solver.constraints.nary.alldifferent.AllDifferent;
import org.chocosolver.solver.constraints.nary.alldifferent.conditions.Condition;
import org.chocosolver.solver.constraints.nary.alldifferent.conditions.PropCondAllDiffInst;
import org.chocosolver.solver.constraints.nary.alldifferent.conditions.PropCondAllDiff_AC;
import org.chocosolver.solver.constraints.nary.alldifferentprec.PropAllDiffPrec;
import org.chocosolver.solver.constraints.nary.among.PropAmongGAC;
import org.chocosolver.solver.constraints.nary.automata.CostRegular;
import org.chocosolver.solver.constraints.nary.automata.FA.IAutomaton;
import org.chocosolver.solver.constraints.nary.automata.FA.ICostAutomaton;
import org.chocosolver.solver.constraints.nary.automata.PropMultiCostRegular;
import org.chocosolver.solver.constraints.nary.automata.PropRegular;
import org.chocosolver.solver.constraints.nary.binPacking.PropBinPacking;
import org.chocosolver.solver.constraints.nary.channeling.PropClauseChanneling;
import org.chocosolver.solver.constraints.nary.channeling.PropEnumDomainChanneling;
import org.chocosolver.solver.constraints.nary.channeling.PropInverseChannelAC;
import org.chocosolver.solver.constraints.nary.channeling.PropInverseChannelBC;
import org.chocosolver.solver.constraints.nary.circuit.*;
import org.chocosolver.solver.constraints.nary.count.PropCountVar;
import org.chocosolver.solver.constraints.nary.count.PropCount_AC;
import org.chocosolver.solver.constraints.nary.cumulative.CumulFilter;
import org.chocosolver.solver.constraints.nary.cumulative.Cumulative;
import org.chocosolver.solver.constraints.nary.element.PropElementV_fast;
import org.chocosolver.solver.constraints.nary.globalcardinality.GlobalCardinality;
import org.chocosolver.solver.constraints.nary.lex.PropLex;
import org.chocosolver.solver.constraints.nary.lex.PropLexChain;
import org.chocosolver.solver.constraints.nary.min_max.*;
import org.chocosolver.solver.constraints.nary.nvalue.*;
import org.chocosolver.solver.constraints.nary.nvalue.amnv.graph.Gci;
import org.chocosolver.solver.constraints.nary.nvalue.amnv.mis.MDRk;
import org.chocosolver.solver.constraints.nary.nvalue.amnv.rules.R;
import org.chocosolver.solver.constraints.nary.nvalue.amnv.rules.R1;
import org.chocosolver.solver.constraints.nary.nvalue.amnv.rules.R3;
import org.chocosolver.solver.constraints.nary.sort.PropKeysorting;
import org.chocosolver.solver.constraints.nary.sum.IntLinCombFactory;
import org.chocosolver.solver.constraints.nary.tree.PropAntiArborescences;
import org.chocosolver.solver.constraints.ternary.*;
import org.chocosolver.solver.constraints.unary.Member;
import org.chocosolver.solver.constraints.unary.NotMember;
import org.chocosolver.solver.exception.SolverException;
import org.chocosolver.solver.variables.BoolVar;
import org.chocosolver.solver.variables.IntVar;
import org.chocosolver.solver.variables.Task;
import org.chocosolver.solver.variables.Variable;
import org.chocosolver.util.iterators.DisposableRangeIterator;
import org.chocosolver.util.objects.graphs.MultivaluedDecisionDiagram;
import org.chocosolver.util.objects.setDataStructures.iterable.IntIterableRangeSet;
import org.chocosolver.util.tools.ArrayUtils;
import org.chocosolver.util.tools.MathUtils;
import org.chocosolver.util.tools.VariableUtils;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.List;
import java.util.stream.IntStream;
import java.util.stream.Stream;
/**
* Interface to make constraints over BoolVar and IntVar
*
* A kind of factory relying on interface default implementation to allow (multiple) inheritance
*
* @author Jean-Guillaume FAGES
* @author Charles Prud'homme
* @since 4.0.0
*/
public interface IIntConstraintFactory extends ISelf {
//##################################################################################################################
// UNARIES #########################################################################################################
//##################################################################################################################
/**
* Creates an arithmetic constraint : var op cste,
* where op in {"=", "!=", ">","<",">=","<="}
*
* @param var a variable
* @param op an operator
* @param cste a constant
*/
default Constraint arithm(IntVar var, String op, int cste) {
return new Arithmetic(var, Operator.get(op), cste);
}
/**
* Creates a member constraint.
* Ensures var takes its values in table
*
* @param var an integer variable
* @param table an array of values
*/
default Constraint member(IntVar var, int[] table) {
return new Member(var, new IntIterableRangeSet(table));
}
/**
* Creates a member constraint.
* Ensures var takes its values in [LB, UB]
*
* @param var an integer variable
* @param lb the lower bound of the interval
* @param ub the upper bound of the interval
*/
default Constraint member(IntVar var, int lb, int ub) {
return new Member(var, lb, ub);
}
/**
* Creates a modulo constraint.
* Ensures X % a = b
*
* @param X an integer variable
* @param mod the value of the modulo operand
* @param res the result of the modulo operation
*/
default Constraint mod(IntVar X, int mod, int res) {
if (mod == 0) {
throw new SolverException("a should not be 0 for " + X.getName() + " MOD a = b");
}
TIntArrayList list = new TIntArrayList();
for (int v = X.getLB(); v <= X.getUB(); v = X.nextValue(v)) {
if (v % mod == res) {
list.add(v);
}
}
return member(X, list.toArray());
}
/**
* Gets the opposite of a given constraint
* Works for any constraint, including globals, but the associated performances might be weak
*
* @param cstr a constraint
* @return the opposite constraint of cstr
*/
default Constraint not(Constraint cstr) {
return cstr.getOpposite();
}
/**
* Creates a notMember constraint.
* Ensures var does not take its values in table
*
* @param var an integer variable
* @param table an array of values
*/
default Constraint notMember(IntVar var, int[] table) {
return new NotMember(var, new IntIterableRangeSet(table));
}
/**
* Creates a member constraint.
* Ensures var takes its values in set
*
* @param var an integer variable
* @param set a set of values
*/
default Constraint member(IntVar var, IntIterableRangeSet set) {
return new Member(var, set);
}
/**
* Creates a notMember constraint.
* Ensures var does not take its values in [lb, UB]
*
* @param var an integer variable
* @param lb the lower bound of the interval
* @param ub the upper bound of the interval
*/
default Constraint notMember(IntVar var, int lb, int ub) {
return new NotMember(var, lb, ub);
}
/**
* Creates a notMember constraint.
* Ensures var does not take its values in set
*
* @param var an integer variable
* @param set a set of values
*/
default Constraint notMember(IntVar var, IntIterableRangeSet set) {
return new NotMember(var, set);
}
//##################################################################################################################
//BINARIES #########################################################################################################
//##################################################################################################################
/**
* Creates an absolute value constraint: var1 = |var2|
*/
default Constraint absolute(IntVar var1, IntVar var2) {
assert var1.getModel() == var2.getModel();
return new Constraint(ConstraintsName.ABSOLUTE, new PropAbsolute(var1, var2));
}
/**
* Creates an arithmetic constraint: var1 op var2,
* where op in {"=", "!=", ">","<",">=","<="}
*
* @param var1 first variable
* @param op an operator
* @param var2 second variable
*/
default Constraint arithm(IntVar var1, String op, IntVar var2) {
if (var2.isInstantiated()) {
return arithm(var1, op, var2.getValue());
}
if (var1.isInstantiated()) {
return arithm(var2, Operator.getFlip(op), var1.getValue());
}
return new Arithmetic(var1, Operator.get(op), var2);
}
/**
* Creates an arithmetic constraint : var1 op var2,
* where op in {"=", "!=", ">","<",">=","<="} or {"+", "-", "*", "/"}
*
* @param var1 first variable
* @param op1 an operator
* @param var2 second variable
* @param op2 another operator
* @param cste an operator
*/
@SuppressWarnings("Duplicates")
default Constraint arithm(IntVar var1, String op1, IntVar var2, String op2, int cste) {
if (op1.equals("*") || op1.equals("/") || op2.equals("*") || op2.equals("/")) {
switch (op1) {
case "*": // v1 * v2 OP cste
if (Operator.EQ.name().equals(op2)) {
return times(var1, var2, cste);
} else {
int[] bounds = VariableUtils.boundsForMultiplication(var1, var2);
IntVar var4 = ref().intVar(bounds[0], bounds[1]);
ref().times(var1, var2, var4).post();
return arithm(var4, op2, cste);
}
case "/":
// v1 / v2 OP cste
if (Operator.EQ.name().equals(op2)) {
return div(var1, var2, ref().intVar(cste));
} else {
int[] bounds = VariableUtils.boundsForDivision(var1, var2);
IntVar var4 = ref().intVar(bounds[0], bounds[1]);
ref().div(var1, var2, var4).post();
return arithm(var4, op2, cste);
}
default:
switch (op2) {
default:
throw new SolverException("Unknown operators for arithm constraint");
case "*": // v1 OP v2 * cste
if (Operator.EQ.name().equals(op1)) {
return times(var2, cste, var1);
} else {
int[] bounds = VariableUtils.boundsForMultiplication(var2, ref().intVar(cste));
IntVar var4 = ref().intVar(bounds[0], bounds[1]);
ref().times(var2, cste, var4).post();
return arithm(var1, op1, var4);
}
case "/":
// v1 OP v2 / cste
if (Operator.EQ.name().equals(op1)) {
return div(var2, ref().intVar(cste), var1);
} else {
// v1 OP v2 / v3
int[] bounds = VariableUtils.boundsForDivision(var2, ref().intVar(cste));
IntVar var4 = ref().intVar(bounds[0], bounds[1]);
ref().div(var2, ref().intVar(cste), var4).post();
return arithm(var1, op1, var4);
}
}
}
} else {
if (var2.isInstantiated()) {
if ("+".equals(op1)) {
return arithm(var1, op2, cste - var2.getValue());
} else if ("-".equals(op1)) {
return arithm(var1, op2, cste + var2.getValue());
}
}
if (var1.isInstantiated()) {
if ("+".equals(op1)) {
return arithm(var2, op2, cste - var1.getValue());
} else if ("-".equals(op1)) {
return arithm(var2, Operator.getFlip(op2), var1.getValue() - cste);
}
}
return new Arithmetic(var1, Operator.get(op1), var2, Operator.get(op2), cste);
}
}
/**
* Creates a distance constraint : |var1-var2| op cste
*
* where op can take its value among {"=", ">", "<", "!="}
*/
default Constraint distance(IntVar var1, IntVar var2, String op, int cste) {
assert var1.getModel() == var2.getModel();
Operator operator = Operator.get(op);
if (operator != Operator.EQ && operator != Operator.GT && operator != Operator.LT && operator != Operator.NQ) {
throw new SolverException("Unexpected operator for distance");
}
return new Constraint(ConstraintsName.DISTANCE, new PropDistanceXYC(ArrayUtils.toArray(var1, var2), operator, cste));
}
/**
* Creates an element constraint: value = table[index-offset]
*
* @param value an integer variable taking its value in table
* @param table an array of integer values
* @param index an integer variable representing the value of value in table
* @param offset offset matching index.lb and table[0] (Generally 0)
*/
default Constraint element(IntVar value, int[] table, IntVar index, int offset) {
return ElementFactory.detect(value, table, index, offset);
}
/**
* Creates an element constraint: value = table[index]
*
* @param value an integer variable taking its value in table
* @param table an array of integer values
* @param index an integer variable representing the value of value in table
*/
default Constraint element(IntVar value, int[] table, IntVar index) {
return element(value, table, index, 0);
}
/**
* Creates a modulo constraint: X % a = Y
*
* @param X first integer variable
* @param mod the value of the modulo operand
* @param Y second integer variable (result of the modulo operation)
*/
default Constraint mod(IntVar X, int mod, IntVar Y) {
if (mod == 0) {
throw new SolverException("a should not be 0 for " + X.getName() + " MOD a = " + Y.getName());
}
if (Y.isInstantiated()) {
return mod(X, mod, Y.getValue());
} else if (TuplesFactory.canBeTupled(X, Y)) {
return table(X, Y, TuplesFactory.modulo(X, mod, Y));
} else {
return new Constraint((X.getName() + " MOD " + mod + " = " + Y.getName()), new PropModXY(X, mod, Y));
}
}
/**
* Creates a square constraint: var1 = var2^2
* @param var1 a variable
* @param var2 a variable
* @return a square constraint
*/
default Constraint square(IntVar var1, IntVar var2) {
assert var2.getModel() == var1.getModel();
if (var2.isInstantiated()) {
int v1 = var2.getValue();
if (var1.isInstantiated()) {
int v2 = var1.getValue();
if(v1 * v1 == v2){
return ref().trueConstraint();
}else{
return ref().falseConstraint();
}
} else {
return ref().arithm(var1, "=", v1*v1);
}
} else {
if (var1.isInstantiated()) {
int v2 = var1.getValue();
if (v2 == 0) {
return ref().arithm(var2, "=", 0);
} else {
if (v2 > 0 && MathUtils.isPerfectSquare(v2)) {
int sqt = (int)Math.sqrt(v2);
return ref().member(var2, new int[]{-sqt, sqt});
} else {
return ref().falseConstraint();
}
}
} else {
return new Constraint(ConstraintsName.SQUARE, new PropSquare(var1, var2));
}
}
}
/**
* Create a table constraint over a couple of variables var1 and var2
*
* Uses AC3rm algorithm by default, except if one variable has a bounded domain.
* In that case, "CT+" is chosen.
*
* @param var1 first variable
* @param var2 second variable
*/
default Constraint table(IntVar var1, IntVar var2, Tuples tuples) {
if (!var1.hasEnumeratedDomain() || !var2.hasEnumeratedDomain()) {
return table(var1, var2, tuples, "CT+");
} else {
return table(var1, var2, tuples, "AC3bit+rm");
}
}
/**
* Creates a table constraint over a couple of variables var1 and var2:
* - AC2001: table constraint which applies the AC2001 algorithm,
* - AC3: table constraint which applies the AC3 algorithm,
* - AC3rm: table constraint which applies the AC3 rm algorithm,
* - AC3bit+rm (default): table constraint which applies the AC3 bit+rm algorithm,
* - FC: table constraint which applies forward checking algorithm.
*
* @param var1 first variable
* @param var2 second variable
* @param tuples the relation between the two variables, among {"AC3", "AC3rm", "AC3bit+rm", "AC2001", "CT+", "FC"}
*/
default Constraint table(IntVar var1, IntVar var2, Tuples tuples, String algo) {
Propagator p;
if (tuples.allowUniversalValue()) {
p = new PropCompactTableStar(new IntVar[]{var1, var2}, tuples);
} else {
switch (algo) {
case "CT+":
p = new PropCompactTable(new IntVar[]{var1, var2}, tuples);
break;
case "AC2001":
p = new PropBinAC2001(var1, var2, tuples);
break;
case "FC":
p = new PropBinFC(var1, var2, tuples);
break;
case "AC3":
p = new PropBinAC3(var1, var2, tuples);
break;
case "AC3rm":
p = new PropBinAC3rm(var1, var2, tuples);
break;
case "AC3bit+rm":
p = new PropBinAC3bitrm(var1, var2, tuples);
break;
default:
throw new SolverException("Table algorithm " + algo + " is unkown");
}
}
return new Constraint(ConstraintsName.TABLE, p);
}
/**
* Creates a multiplication constraint: X * Y = Z
*
* @param X first variable
* @param Y a constant
* @param Z result variable
*/
default Constraint times(IntVar X, int Y, IntVar Z) {
if (Y == 0) {
return arithm(Z, "=", 0);
} else if (Y == 1) {
return arithm(X, "=", Z);
} else if (Y < 0) {
return times(X.getModel().intMinusView(X), -Y, Z);
} else {
return new Constraint(ConstraintsName.TIMES, new PropScale(X, Y, Z));
}
}
/**
* Creates a multiplication constraint: X * Y = Z
*
* @param X first variable
* @param Y second variable
* @param Z a constant (result)
*/
default Constraint times(IntVar X, IntVar Y, int Z) {
return times(X, Y, X.getModel().intVar(Z));
}
//##################################################################################################################
//TERNARIES ########################################################################################################
//##################################################################################################################
/**
* Creates an arithmetic constraint: var1 op1 var2 op2 var3,
* where op1 and op2 in {"=", "!=", ">","<",">=","<="} or {"+", "-", "*", "/"}
*
* @param var1 first variable
* @param op1 an operator
* @param var2 second variable
* @param op2 another operator
* @param var3 third variable
*/
@SuppressWarnings("Duplicates")
default Constraint arithm(IntVar var1, String op1, IntVar var2, String op2, IntVar var3) {
switch (op1) {
case "+":
return scalar(new IntVar[]{var1, var2}, new int[]{1, 1}, op2, var3);
case "-":
return scalar(new IntVar[]{var1, var2}, new int[]{1, -1}, op2, var3);
case "*":
// v1 * v2 = v3
if (Operator.EQ.name().equals(op2)) {
return times(var1, var2, var3);
} else {
// v1 * v2 OP v3
int[] bounds = VariableUtils.boundsForMultiplication(var1, var2);
IntVar var4 = ref().intVar(bounds[0], bounds[1]);
ref().times(var1, var2, var4).post();
return arithm(var4, op2, var3);
}
case "/":
// v1 / v2 = v3
if (Operator.EQ.name().equals(op2)) {
return div(var1, var2, var3);
} else {
// v1 / v2 OP v3
int[] bounds = VariableUtils.boundsForDivision(var1, var2);
IntVar var4 = ref().intVar(bounds[0], bounds[1]);
ref().div(var1, var2, var4).post();
return arithm(var4, op2, var3);
}
default:
switch (op2) {
case "*":
// v1 = v2 * v3
if (Operator.EQ.name().equals(op1)) {
return times(var2, var3, var1);
} else {
// v1 OP v2 * v3
int[] bounds = VariableUtils.boundsForMultiplication(var2, var3);
IntVar var4 = ref().intVar(bounds[0], bounds[1]);
ref().times(var2, var3, var4).post();
return arithm(var1, op1, var4);
}
case "/":
// v1 = v2 / v3
if (Operator.EQ.name().equals(op1)) {
return div(var2, var3, var1);
} else {
// v1 OP v2 / v3
int[] bounds = VariableUtils.boundsForDivision(var2, var3);
IntVar var4 = ref().intVar(bounds[0], bounds[1]);
ref().div(var2, var3, var4).post();
return arithm(var1, op1, var4);
}
case "+":
return scalar(new IntVar[]{var1, var3}, new int[]{1, -1}, op1, var2);
case "-":
return scalar(new IntVar[]{var1, var3}, new int[]{1, 1}, op1, var2);
default:
throw new SolverException("Unknown operators for arithm constraint");
}
}
}
/**
* Creates a distance constraint: |var1-var2| op var3
*
* where op can take its value among {"=", ">", "<"}
*
* @param var1 first variable
* @param var2 second variable
* @param op an operator
* @param var3 resulting variable
*/
default Constraint distance(IntVar var1, IntVar var2, String op, IntVar var3) {
switch (Operator.get(op)) {
case EQ:
return new Constraint(ConstraintsName.DISTANCE, new PropEQDistanceXYZ(ArrayUtils.toArray(var1, var2, var3)));
case LE:
return new Constraint(ConstraintsName.DISTANCE, new PropLEDistanceXYZ(ArrayUtils.toArray(var1, var2, var3)));
case GE:
return new Constraint(ConstraintsName.DISTANCE, new PropGEDistanceXYZ(ArrayUtils.toArray(var1, var2, var3)));
case LT:
return new Constraint(ConstraintsName.DISTANCE, new PropLTDistanceXYZ(ArrayUtils.toArray(var1, var2, var3)));
case GT:
return new Constraint(ConstraintsName.DISTANCE, new PropGTDistanceXYZ(ArrayUtils.toArray(var1, var2, var3)));
default:
throw new SolverException("Unexpected operator for distance: " + op);
}
}
/**
* Creates an euclidean division constraint.
* Ensures dividend / divisor = result, rounding towards 0
* Also ensures divisor != 0
*
* @param dividend dividend
* @param divisor divisor
* @param result result
*/
default Constraint div(IntVar dividend, IntVar divisor, IntVar result) {
return new Constraint(ConstraintsName.DIVISION, new PropDivXYZ(dividend, divisor, result));
}
/**
* Creates a maximum constraint : max = max(var1, var2)
* (Bound Consistency)
*
* @param max a variable
* @param var1 a variable
* @param var2 a variable
*/
default Constraint max(IntVar max, IntVar var1, IntVar var2) {
return new Constraint(ConstraintsName.MAX, new PropMaxBC(max, var1, var2));
}
/**
* Creates a minimum constraint: min = min(var1, var2)
* (Bound Consistency)
*
* @param min a variable
* @param var1 a variable
* @param var2 a variable
*/
default Constraint min(IntVar min, IntVar var1, IntVar var2) {
return new Constraint(ConstraintsName.MIN, new PropMinBC(min, var1, var2));
}
/**
*
* Ensures X % Y = Z.
*
*
* Creates a modulo constraint, that uses truncated division:
* the quotient is defined by truncation q = trunc(a/n)
* and the remainder would have same sign as the dividend.
* The quotient is rounded towards zero: equal to the first integer
* in the direction of zero from the exact rational quotient.
*
*
* @param X first variable
* @param Y second variable
* @param Z result
*/
default Constraint mod(IntVar X, IntVar Y, IntVar Z) {
if (Y.isInstantiated() && Y.getValue() == 0) {
throw new SolverException("Y variable should not be instantiated to 0 for constraint "
+ X.getName() + " MOD " + Y.getName() + " = " + Z.getName());
}
if (Y.isInstantiated()) {
return mod(X, Y.getValue(), Z);
} else if (TuplesFactory.canBeTupled(X, Y, Z)) {
return table(new IntVar[]{X, Y, Z}, TuplesFactory.modulo(X, Y, Z));
} else {
return new Constraint(X.getName() + " MOD " + Y.getName() + " = " + Z.getName(), new PropModXYZ(X, Y, Z));
}
}
/**
* Creates a multiplication constraint: X * Y = Z
*
* @param X first variable
* @param Y second variable
* @param Z result variable
*/
@SuppressWarnings("SuspiciousNameCombination")
default Constraint times(IntVar X, IntVar Y, IntVar Z) {
if (Y.isInstantiated()) {
return times(X, Y.getValue(), Z);
} else if (X.isInstantiated()) {
return times(Y, X.getValue(), Z);
} else if (TuplesFactory.canBeTupled(X, Y, Z)) {
return table(new IntVar[]{X, Y, Z}, TuplesFactory.times(X, Y, Z));
} else {
return new Constraint(ConstraintsName.TIMES, new PropTimesNaive(X, Y, Z));
}
}
//##################################################################################################################
//GLOBALS ##########################################################################################################
//##################################################################################################################
/**
* Creates an allDifferent constraint.
* Ensures that all variables from vars take a different value.
* Uses BC plus a probabilistic AC propagator to get a compromise between BC and AC
*
* @param vars list of variables
*/
default Constraint allDifferent(IntVar... vars) {
return allDifferent(vars, "DEFAULT");
}
/**
* Creates an allDifferent constraint.
* Ensures that all variables from vars take a different value.
* The consistency level should be chosen among "BC", "AC" and "DEFAULT".
*
* @param vars list of variables
* @param CONSISTENCY consistency level, among {"BC", "AC_REGIN", "AC", "AC_ZHANG", "DEFAULT"}
*
* BC:
* Based on: "A Fast and Simple Algorithm for Bounds Consistency of the AllDifferent Constraint"
* A. Lopez-Ortiz, CG. Quimper, J. Tromp, P.van Beek
*
* AC_REGIN:
* Uses Regin algorithm
* Runs in O(m.n) worst case time for the initial propagation and then in O(n+m) on average.
*
* AC, AC_ZHANG:
* Uses Zhang improvement of Regin algorithm
*
* DEFAULT:
*
* Uses BC plus a probabilistic AC_ZHANG propagator to get a compromise between BC and AC_ZHANG
*/
default Constraint allDifferent(IntVar[] vars, String CONSISTENCY) {
if (vars.length <= 1) return ref().trueConstraint();
return new AllDifferent(vars, CONSISTENCY);
}
/**
* Creates an allDifferent constraint subject to the given condition. More precisely:
*
* IF singleCondition
* for all X,Y in vars, condition(X) => X != Y
* ELSE
* for all X,Y in vars, condition(X) AND condition(Y) => X != Y
*
* @param vars collection of variables
* @param condition condition defining which variables should be constrained
* @param singleCondition specifies how to apply filtering
*/
default Constraint allDifferentUnderCondition(IntVar[] vars, Condition condition, boolean singleCondition) {
if (singleCondition) {
return new Constraint(ConstraintsName.ALLDIFFERENT,
new PropCondAllDiffInst(vars, condition, singleCondition),
new PropCondAllDiff_AC(vars, condition)
);
}
return new Constraint(ConstraintsName.ALLDIFFERENT, new PropCondAllDiffInst(vars, condition, singleCondition));
}
/**
* Creates an allDifferent constraint for variables that are not equal to 0.
* There can be multiple variables equal to 0.
*
* @param vars collection of variables
*/
default Constraint allDifferentExcept0(IntVar[] vars) {
return allDifferentUnderCondition(vars, Condition.EXCEPT_0, true);
}
/**
* Creates an AllDiffPrec constraint. The predecessors and successors matrix are built as following:
* with n = |variables|, for all i in [0,n-1], if there is k such that predecessors[i][k] = j then variables[j] is a predecessor of variables[i].
* Similarly, with n = |variables|, for all i in [0,n-1], if there is k such that successors[i][k] = j then variables[j] is a successor of variables[i].
* The matrix should be built such that, if variables[i] is a predecessor of variables[j], then i is in successors[j] and vice versa.
*
* filter should be one of the following (depending on the wanted filtering algorithm): BESSIERE, GREEDY, GREEDY_RC, GODET_RC, GODET_BC or DEFAULT (which is GODET_BC).
*
* @param variables the variables
* @param predecessors the predecessors matrix
* @param successors the successors matrix
* @param filter the name of the filtering scheme
*/
default Constraint allDiffPrec(IntVar[] variables, int[][] predecessors, int[][] successors, String filter) {
return new Constraint(
ConstraintsName.ALLDIFFPREC,
new PropAllDiffPrec(variables, predecessors, successors, filter)
);
}
/**
* Creates an AllDiffPrec constraint. The predecessors and successors matrix are built as following:
* with n = |variables|, for all i in [0,n-1], if there is k such that predecessors[i][k] = j then variables[j] is a predecessor of variables[i].
* Similarly, with n = |variables|, for all i in [0,n-1], if there is k such that successors[i][k] = j then variables[j] is a successor of variables[i].
* The matrix should be built such that, if variables[i] is a predecessor of variables[j], then i is in successors[j] and vice versa.
*
* @param variables the variables
* @param predecessors the predecessors matrix
* @param successors the successors matrix
*/
default Constraint allDiffPrec(IntVar[] variables, int[][] predecessors, int[][] successors) {
return allDiffPrec(variables, predecessors, successors, "GODET_BC");
}
/**
* Creates an AllDiffPrec constraint. The precedence matrix is built as following:
* with n = |variables|, for all i,j in [0,n-1], precedence[i][j] = true iff precedence[j][i] = false iff variables[i] precedes variables[j].
*
* filter should be one of the following (depending on the wanted filtering algorithm): BESSIERE, GREEDY, GREEDY_RC, GODET_RC, GODET_BC or DEFAULT (which is GODET_BC).
*
* @param variables the variables
* @param precedence the precedence matrix
* @param filter the name of the filtering scheme
*/
default Constraint allDiffPrec(IntVar[] variables, boolean[][] precedence, String filter) {
return new Constraint(
ConstraintsName.ALLDIFFPREC,
new PropAllDiffPrec(variables, precedence, filter)
);
}
/**
* Creates an AllDiffPrec constraint. The precedence matrix is built as following:
* with n = |variables|, for all i,j in [0,n-1], precedence[i][j] = true iff precedence[j][i] = false iff variables[i] precedes variables[j].
*
* @param variables the variables
* @param precedence the precedence matrix
*/
default Constraint allDiffPrec(IntVar[] variables, boolean[][] precedence) {
return allDiffPrec(variables, precedence, "GODET_BC");
}
/**
* Creates an allEqual constraint.
* Ensures that all variables from vars take the same value.
*
* @param vars list of variables
*/
default Constraint allEqual(IntVar... vars) {
return atMostNValues(vars, ref().intVar(1), false);
}
/**
* Creates a notAllEqual constraint.
* Ensures that all variables from vars take more than a single value.
*
* @param vars list of variables
*/
default Constraint notAllEqual(IntVar... vars) {
return atLeastNValues(vars, ref().intVar(2), false);
}
/**
* Creates an among constraint.
* nbVar is the number of variables of the collection vars that take their value in values.
*
gccat among
*
* Propagator :
* C. Bessiere, E. Hebrard, B. Hnich, Z. Kiziltan, T. Walsh,
* Among, common and disjoint Constraints
* CP-2005
*
* @param nbVar a variable
* @param vars vector of variables
* @param values set of values
*/
default Constraint among(IntVar nbVar, IntVar[] vars, int[] values) {
int[] vls = new TIntHashSet(values).toArray(); // remove double occurrences
Arrays.sort(vls); // sort
return new Constraint(ConstraintsName.AMONG, new PropAmongGAC(ArrayUtils.concat(vars, nbVar), vls));
}
/**
* Creates an and constraint that is satisfied if all boolean variables in bools are true
*
* @param bools an array of boolean variable
* @return a constraint and ensuring that variables in bools are all set to true
*/
default Constraint and(BoolVar... bools) {
Model s = bools[0].getModel();
IntVar sum = s.intVar(0, bools.length, true);
s.sum(bools, "=", sum).post();
return s.arithm(sum, "=", bools.length);
}
/**
* Creates an and constraint that is satisfied if all constraints in cstrs are satisfied
* BEWARE: this should not be used to post several constraints at once but in a reification context
*
* @param cstrs an array of constraints
* @return a constraint and ensuring that all constraints in cstrs are satisfied
*/
default Constraint and(Constraint... cstrs) {
BoolVar[] bools = new BoolVar[cstrs.length];
for (int i = 0; i < cstrs.length; i++) {
bools[i] = cstrs[i].reify();
}
return and(bools);
}
/**
* Creates an atLeastNValue constraint.
* Let N be the number of distinct values assigned to the variables of the vars collection.
* Enforce condition N >= nValues to hold.
*
* This embeds a light propagator by default.
* Additional filtering algorithms can be added.
*
* @param vars collection of variables
* @param nValues limit variable
* @param AC additional filtering algorithm, domain filtering algorithm derivated from (Soft)AllDifferent
*/
default Constraint atLeastNValues(IntVar[] vars, IntVar nValues, boolean AC) {
int[] vals = getDomainUnion(vars);
if (AC) {
return new Constraint(ConstraintsName.ATLEASTNVALUES, new PropAtLeastNValues(vars, vals, nValues),
new PropAtLeastNValues_AC(vars, vals, nValues));
} else {
return new Constraint(ConstraintsName.ATLEASTNVALUES, new PropAtLeastNValues(vars, vals, nValues));
}
}
/**
* Creates an atMostNValue constraint.
* Let N be the number of distinct values assigned to the variables of the vars collection.
* Enforce condition N <= nValues to hold.
*
* This embeds a light propagator by default.
* Additional filtering algorithms can be added.
*
* @param vars collection of variables
* @param nValues limit variable
* @param STRONG "AMNV" Filters the conjunction of AtMostNValue and disequalities
* (see Fages and Lapègue Artificial Intelligence 2014)
* automatically detects disequalities and allDifferent constraints.
* Presumably useful when nValues must be minimized.
*/
default Constraint atMostNValues(IntVar[] vars, IntVar nValues, boolean STRONG) {
int[] vals = getDomainUnion(vars);
if (STRONG) {
Gci gci = new Gci(vars);
R[] rules = new R[]{new R1(), new R3(vars.length, nValues.getModel())};
return new Constraint(ConstraintsName.ATMOSTNVALUES, new PropAtMostNValues(vars, vals, nValues),
new PropAMNV(vars, nValues, gci, new MDRk(gci), rules));
} else {
return new Constraint(ConstraintsName.ATMOSTNVALUES, new PropAtMostNValues(vars, vals, nValues));
}
}
/**
* Creates a BinPacking constraint.
* Bin Packing formulation:
* forall b in [0,binLoad.length-1],
* binLoad[b]=sum(itemSize[i] | i in [0,itemSize.length-1], itemBin[i] = b+offset
* forall i in [0,itemSize.length-1], itemBin is in [offset,binLoad.length-1+offset],
*
* @param itemBin IntVar representing the bin of each item
* @param itemSize int representing the size of each item
* @param binLoad IntVar representing the load of each bin (i.e. the sum of the size of the items in it)
* @param offset 0 by default but typically 1 if used within MiniZinc
* (which counts from 1 to n instead of from 0 to n-1)
*/
default Constraint binPacking(IntVar[] itemBin, int[] itemSize, IntVar[] binLoad, int offset) {
if (itemBin.length != itemSize.length) {
throw new SolverException("itemBin and itemSize arrays should have same size");
}
Model model = itemBin[0].getModel();
// redundant filtering
int sum = 0;
for (int i = 0; i < itemSize.length; i++) {
sum += itemSize[i];
}
int maxCapa = binLoad[0].getUB();
for (int j = 1; j < binLoad.length; j++) {
maxCapa = Math.max(maxCapa, binLoad[j].getUB());
}
int thresholdCapa = (int) Math.ceil(1.0 * maxCapa / 2);
List list = new ArrayList<>(itemBin.length);
for (int i = 0; i < itemBin.length; i++) {
if (itemSize[i] > thresholdCapa) {
list.add(itemBin[i]);
}
}
return Constraint.merge(
ConstraintsName.BINPACKING,
new Constraint(ConstraintsName.BINPACKING, new PropBinPacking(itemBin, itemSize, binLoad, offset)),
model.sum(binLoad, "=", sum),
model.allDifferent(list.toArray(new IntVar[0]))
);
}
/**
* Creates an channeling constraint between an integer variable and a set of boolean variables.
* Maps the boolean assignments variables bVars with the standard assignment variable var.
* var = i <-> bVars[i-offset] = 1
*
* @param bVars array of boolean variables
* @param var observed variable. Should presumably have an enumerated domain
* @param offset 0 by default but typically 1 if used within MiniZinc
* (which counts from 1 to n instead of from 0 to n-1)
*/
default Constraint boolsIntChanneling(BoolVar[] bVars, IntVar var, int offset) {
if (var.hasEnumeratedDomain()) {
return new Constraint(ConstraintsName.BOOLCHANNELING, new PropEnumDomainChanneling(bVars, var, offset));
} else {
IntVar enumV = var.getModel().intVar(var.getName() + "_enumImage", var.getLB(), var.getUB(), false);
enumV.eq(var).post();
return new Constraint(ConstraintsName.BOOLCHANNELING,
new PropEnumDomainChanneling(bVars, enumV, offset)
);
}
}
/**
* Creates an channeling constraint between an integer variable and a set of bit variables.
* Ensures that var = 20*BIT_1 + 21*BIT_2 + ... 2n-1*BIT_n.
*
* BIT_1 is related to the first bit of OCTET (2^0),
* BIT_2 is related to the first bit of OCTET (2^1), etc.
*
* The upper bound of var is given by 2n, where n is the size of the array bits.
*
* @param bits the array of bits
* @param var the numeric value
* @implNote This constraint is transformed into a table constraint
* @see #table(IntVar[], Tuples)
*/
default Constraint bitsIntChanneling(BoolVar[] bits, IntVar var) {
int s = bits.length;
int max = (int) Math.pow(2, s) - 1;
Tuples tuples = new Tuples(true);
for (int v = 0; v <= max; v++) {
if (var.contains(v)) {
int[] t = new int[s + 1];
for (int b = 0; b < s; b++) {
t[b] = ((v >>> b) & 1) != 0 ? 1 : 0;
}
t[s] = v;
tuples.add(t);
}
}
return table(ArrayUtils.append(bits, new IntVar[]{var}), tuples);
}
/**
* Creates an channeling constraint between an integer variable and a set of clauses.
* Link each value from the domain of var to two boolean variable:
* one reifies the equality to the i^th value of the variable domain,
* the other reifies the less-or-equality to the i^th value of the variable domain.
* Contract: eVars.lenght == lVars.length == var.getUB() - var.getLB() + 1
* Contract: var is not a boolean variable
*
* @param var an Integer variable
* @param eVars array of EQ boolean variables
* @param lVars array of LQ boolean variables
*/
default Constraint clausesIntChanneling(IntVar var, BoolVar[] eVars, BoolVar[] lVars) {
return new Constraint(ConstraintsName.CLAUSESINTCHANNELING, new PropClauseChanneling(var, eVars, lVars));
}
/**
* Creates a circuit constraint which ensures that
* the elements of vars define a covering circuit
* where vars[i] = offset+j means that j is the successor of i.
*
* Filtering algorithms:
*
subtour elimination : Caseau & Laburthe (ICLP'97)
* allDifferent GAC algorithm: Régin (AAAI'94)
* dominator-based filtering: Fages & Lorca (CP'11)
* Strongly Connected Components based filtering (Cambazar & Bourreau JFPC'06 and Fages and Lorca TechReport'12)
*
* @param vars vector of variables which take their value in [offset,offset+|vars|-1]
* @return a circuit constraint
*/
default Constraint circuit(IntVar[] vars) {
return circuit(vars, 0);
}
/**
* Creates a circuit constraint which ensures that
* the elements of vars define a covering circuit
* where vars[i] = offset+j means that j is the successor of i.
*
* Filtering algorithms:
*
subtour elimination : Caseau & Laburthe (ICLP'97)
* allDifferent GAC algorithm: Régin (AAAI'94)
* dominator-based filtering: Fages & Lorca (CP'11)
* Strongly Connected Components based filtering (Cambazar & Bourreau JFPC'06 and Fages and Lorca TechReport'12)
*
* @param vars vector of variables which take their value in [offset,offset+|vars|-1]
* @param offset 0 by default but typically 1 if used within MiniZinc
* (which counts from 1 to n instead of from 0 to n-1)
* @return a circuit constraint
*/
default Constraint circuit(IntVar[] vars, int offset) {
return circuit(vars, offset, CircuitConf.RD);
}
/**
* Creates a circuit constraint which ensures that
* the elements of vars define a covering circuit
* where vars[i] = offset+j means that j is the successor of i.
*
* Filtering algorithms:
*
subtour elimination : Caseau & Laburthe (ICLP'97)
* allDifferent GAC algorithm: Régin (AAAI'94)
* dominator-based filtering: Fages & Lorca (CP'11)
* Strongly Connected Components based filtering (Cambazard & Bourreau JFPC'06 and Fages and Lorca TechReport'12)
* See Fages PhD Thesis (2014) for more information
*
* @param vars vector of variables which take their value in [offset,offset+|vars|-1]
* @param offset 0 by default but typically 1 if used within MiniZinc
* (which counts from 1 to n instead of from 0 to n-1)
* @param conf filtering options
* @return a circuit constraint
*/
default Constraint circuit(IntVar[] vars, int offset, CircuitConf conf) {
Propagator[] props;
if (conf == CircuitConf.LIGHT) {
props = new Propagator[]{new PropNoSubtour(vars, offset)};
} else {
props = new Propagator[]{
new PropNoSubtour(vars, offset),
new PropCircuit_ArboFiltering(vars, offset, conf),
new PropCircuit_AntiArboFiltering(vars, offset, conf),
new PropCircuitSCC(vars, offset, conf)
};
}
Constraint alldiff = allDifferent(vars, "AC");
alldiff.ignore();
return new Constraint(ConstraintsName.CIRCUIT, ArrayUtils.append(alldiff.propagators, props));
}
/**
* Creates a regular constraint that supports a cost function.
* Ensures that the assignment of a sequence of variables is recognized by costAutomaton, a deterministic finite automaton,
* and that the sum of the costs associated to each assignment is bounded by the cost variable.
* This version allows to specify different costs according to the automaton state at which the assignment occurs
* (i.e. the transition starts)
*
* @param vars sequence of variables
* @param cost cost variable
* @param costAutomaton a deterministic finite automaton defining the regular language and the costs
* Can be built with method CostAutomaton.makeSingleResource(...)
*/
default Constraint costRegular(IntVar[] vars, IntVar cost, ICostAutomaton costAutomaton) {
return new CostRegular(vars, cost, costAutomaton);
}
/**
* Creates a count constraint.
* Let N be the number of variables of the vars collection assigned to value value;
* Enforce condition N = limit to hold.
*
*
* @param value an int
* @param vars a vector of variables
* @param limit a variable
*/
default Constraint count(int value, IntVar[] vars, IntVar limit) {
return new Constraint(ConstraintsName.COUNT, new PropCount_AC(vars, value, limit));
}
/**
* Creates a count constraint.
* Let N be the number of variables of the vars collection assigned to value value;
* Enforce condition N = limit to hold.
*
*
* @param value a variable
* @param vars a vector of variables
* @param limit a variable
*/
default Constraint count(IntVar value, IntVar[] vars, IntVar limit) {
if (value.isInstantiated()) {
return count(value.getValue(), vars, limit);
} else if (value.hasEnumeratedDomain()) {
return new Constraint(ConstraintsName.COUNT, new PropCountVar(vars, value, limit));
} else {
Model model = value.getModel();
IntVar Evalue = model.intVar(model.generateName("COUNT_"), value.getLB(), value.getUB(), false);
Evalue.eq(value).post();
return new Constraint(ConstraintsName.COUNT,
new PropCountVar(vars, Evalue, limit));
}
}
/**
* Creates a cumulative constraint: Enforces that at each point in time,
* the cumulated height of the set of tasks that overlap that point
* does not exceed a given limit.
*
* Task duration and height should be >= 0
* Discards tasks whose duration or height is equal to zero
*
* @param tasks Task objects containing start, duration and end variables
* @param heights integer variables representing the resource consumption of each task
* @param capacity integer variable representing the resource capacity
* @return a cumulative constraint
*/
default Constraint cumulative(Task[] tasks, IntVar[] heights, IntVar capacity) {
return cumulative(tasks, heights, capacity, true);
}
/**
* Creates a cumulative constraint: Enforces that at each point in time,
* the cumulated height of the set of tasks that overlap that point
* does not exceed a given limit.
*
* Task duration and height should be >= 0
* Discards tasks whose duration or height is equal to zero
*
* @param tasks Task objects containing start, duration and end variables
* @param heights integer variables representing the resource consumption of each task
* @param capacity integer variable representing the resource capacity
* @param incremental specifies if an incremental propagation should be applied
* @return a cumulative constraint
*/
default Constraint cumulative(Task[] tasks, IntVar[] heights, IntVar capacity, boolean incremental) {
return cumulative(tasks, heights, capacity, incremental, Cumulative.Filter.DEFAULT.make(tasks.length));
}
/**
* Creates a cumulative constraint: Enforces that at each point in time,
* the cumulated height of the set of tasks that overlap that point
* does not exceed a given limit.
*
* Task duration and height should be >= 0
* Discards tasks whose duration or height is equal to zero
*
* @param tasks Task objects containing start, duration and end variables
* @param heights integer variables representing the resource consumption of each task
* @param capacity integer variable representing the resource capacity
* @param incremental specifies if an incremental propagation should be applied
* @param filters specifies which filtering algorithms to apply
* @return a cumulative constraint
*/
default Constraint cumulative(Task[] tasks, IntVar[] heights, IntVar capacity, boolean incremental, Cumulative.Filter... filters) {
return cumulative(tasks, heights, capacity, incremental, Arrays.stream(filters).map(f -> f.make(tasks.length)).toArray(CumulFilter[]::new));
}
/**
* Creates a cumulative constraint: Enforces that at each point in time,
* the cumulated height of the set of tasks that overlap that point
* does not exceed a given limit.
*
* Task duration and height should be >= 0
* Discards tasks whose duration or height is equal to zero
*
* @param tasks Task objects containing start, duration and end variables
* @param heights integer variables representing the resource consumption of each task
* @param capacity integer variable representing the resource capacity
* @param incremental specifies if an incremental propagation should be applied
* @param filters specifies which filtering algorithms to apply
* @return a cumulative constraint
*/
default Constraint cumulative(Task[] tasks, IntVar[] heights, IntVar capacity, boolean incremental, CumulFilter... filters) {
if (tasks.length != heights.length) {
throw new SolverException("Tasks and heights arrays should have same size");
}
int nbUseFull = 0;
for (int h = 0; h < heights.length; h++) {
if (heights[h].getUB() > 0 && tasks[h].getDuration().getUB() > 0) {
nbUseFull++;
}
}
// remove tasks that have no impact on resource consumption
if (nbUseFull < tasks.length) {
if (nbUseFull == 0) return arithm(capacity, ">=", 0);
Task[] T2 = new Task[nbUseFull];
IntVar[] H2 = new IntVar[nbUseFull];
int idx = 0;
for (int h = 0; h < heights.length; h++) {
if (heights[h].getUB() > 0 && tasks[h].getDuration().getUB() > 0) {
T2[idx] = tasks[h];
H2[idx] = heights[h];
idx++;
}
}
tasks = T2;
heights = H2;
}
return new Cumulative(tasks, heights, capacity, incremental, filters);
}
/**
* Creates and posts a decomposition of a cumulative constraint:
* Enforces that at each point in time,
* the cumulated height of the set of tasks that overlap that point
* does not exceed a given limit.
*
* Task duration and height should be >= 0
* Discards tasks whose duration or height is equal to zero
*
* @param starts starting time of each task
* @param durations processing time of each task
* @param heights resource consumption of each task
* @param capacity resource capacity
*/
default void cumulative(IntVar[] starts, int[] durations, int[] heights, int capacity) {
int n = starts.length;
final IntVar[] d = new IntVar[n];
final IntVar[] h = new IntVar[n];
final IntVar[] e = new IntVar[n];
Task[] tasks = new Task[n];
for (int i = 0; i < n; i++) {
d[i] = ref().intVar(durations[i]);
h[i] = ref().intVar(heights[i]);
e[i] = ref().intVar(starts[i].getName() + "_e",
starts[i].getLB() + durations[i],
starts[i].getUB() + durations[i],
true);
tasks[i] = new Task(starts[i], d[i], e[i]);
}
ref().cumulative(tasks, h, ref().intVar(capacity), false, Cumulative.Filter.NAIVETIME).post();
}
/**
* Creates a diffN constraint. Constrains each rectanglei, given by their origins Xi,Yi
* and sizes widthi,heighti, to be non-overlapping.
*
* @param X collection of coordinates in first dimension
* @param Y collection of coordinates in second dimension
* @param width collection of width (each duration should be > 0)
* @param height collection of height (each height should be >= 0)
* @param addCumulativeReasoning indicates whether or not redundant cumulative constraints should be put on each dimension (advised)
* @return a non-overlapping constraint
*/
default Constraint diffN(IntVar[] X, IntVar[] Y, IntVar[] width, IntVar[] height, boolean addCumulativeReasoning) {
Model model = X[0].getModel();
Constraint diffNCons = new Constraint(
ConstraintsName.DIFFN,
new PropDiffN(X, Y, width, height)
);
if (addCumulativeReasoning) {
IntVar[] EX = new IntVar[X.length];
IntVar[] EY = new IntVar[X.length];
Task[] TX = new Task[X.length];
Task[] TY = new Task[X.length];
int minx = Integer.MAX_VALUE / 2;
int maxx = Integer.MIN_VALUE / 2;
int miny = Integer.MAX_VALUE / 2;
int maxy = Integer.MIN_VALUE / 2;
for (int i = 0; i < X.length; i++) {
EX[i] = model.intVar(model.generateName("diffN_"), X[i].getLB() + width[i].getLB(), X[i].getUB() + width[i].getUB(), true);
EY[i] = model.intVar(model.generateName("diffN_"), Y[i].getLB() + height[i].getLB(), Y[i].getUB() + height[i].getUB(), true);
TX[i] = new Task(X[i], width[i], EX[i]);
TY[i] = new Task(Y[i], height[i], EY[i]);
minx = Math.min(minx, X[i].getLB());
miny = Math.min(miny, Y[i].getLB());
maxx = Math.max(maxx, X[i].getUB() + width[i].getUB());
maxy = Math.max(maxy, Y[i].getUB() + height[i].getUB());
}
IntVar maxX = model.intVar(model.generateName("diffN_"), minx, maxx, true);
IntVar minX = model.intVar(model.generateName("diffN_"), minx, maxx, true);
IntVar diffX = model.intVar(model.generateName("diffN_"), 0, maxx - minx, true);
IntVar maxY = model.intVar(model.generateName("diffN_"), miny, maxy, true);
IntVar minY = model.intVar(model.generateName("diffN_"), miny, maxy, true);
IntVar diffY = model.intVar(model.generateName("diffN_"), 0, maxy - miny, true);
return Constraint.merge(ConstraintsName.DIFFNWITHCUMULATIVE,
diffNCons,
min(minX, X), max(maxX, EX), scalar(new IntVar[]{maxX, minX}, new int[]{1, -1}, "=", diffX),
cumulative(TX, height, diffY),
min(minY, Y), max(maxY, EY), scalar(new IntVar[]{maxY, minY}, new int[]{1, -1}, "=", diffY),
cumulative(TY, width, diffX)
);
} else {
return diffNCons;
}
}
/**
* Creates a element constraint: value = table[index-offset]
* where table is an array of variables.
*
* @param value value variable
* @param table array of variables
* @param index index variable in range [offset,offset+|table|-1]
* @param offset int offset, generally 0
*/
default Constraint element(IntVar value, IntVar[] table, IntVar index, int offset) {
if (Stream.of(table).allMatch(Variable::isAConstant)) {
return element(value, Stream.of(table).mapToInt(IntVar::getValue).toArray(), index, offset);
} else {
// uses two propagator to perform a fix point
return new Constraint(
ConstraintsName.ELEMENT,
new PropElementV_fast(value, table, index, offset));
}
}
/**
* Creates a global cardinality constraint (GCC):
* Each value values[i] should be taken by exactly occurrences[i] variables of vars.
*
* This constraint does not ensure any well-defined level of consistency, yet.
*
* @param vars collection of variables
* @param values collection of constrained values
* @param occurrences collection of cardinality variables
* @param closed restricts domains of vars to values if set to true
*/
default Constraint globalCardinality(IntVar[] vars, int[] values, IntVar[] occurrences, boolean closed) {
assert values.length == occurrences.length;
if (!closed) {
return new GlobalCardinality(vars, values, occurrences);
} else {
TIntArrayList toAdd = new TIntArrayList();
TIntSet givenValues = new TIntHashSet();
for (int i : values) {
assert !givenValues.contains(i);
givenValues.add(i);
}
for (IntVar var : vars) {
int ub = var.getUB();
for (int k = var.getLB(); k <= ub; k = var.nextValue(k)) {
if (!givenValues.contains(k)) {
if (!toAdd.contains(k)) {
toAdd.add(k);
}
}
}
}
if (toAdd.size() > 0) {
int n2 = values.length + toAdd.size();
int[] v2 = new int[n2];
IntVar[] cards = new IntVar[n2];
System.arraycopy(values, 0, v2, 0, values.length);
System.arraycopy(occurrences, 0, cards, 0, values.length);
for (int i = values.length; i < n2; i++) {
v2[i] = toAdd.get(i - values.length);
cards[i] = vars[0].getModel().intVar(0);
}
return new GlobalCardinality(vars, v2, cards);
} else {
return new GlobalCardinality(vars, values, occurrences);
}
}
}
/**
* Creates an inverse channeling between vars1 and vars2:
* vars1[i] = j <=> vars2[j] = i
* Performs AC if domains are enumerated.
* If not, then it works on bounds without guaranteeing BC
* (enumerated domains are strongly recommended)
*
* Beware you should have |vars1| = |vars2|
*
* @param vars1 vector of variables which take their value in [0,|vars2|-1]
* @param vars2 vector of variables which take their value in [0,|vars1|-1]
*/
default Constraint inverseChanneling(IntVar[] vars1, IntVar[] vars2) {
return inverseChanneling(vars1, vars2, 0, 0);
}
/**
* Creates an inverse channeling between vars1 and vars2:
* vars1[i-offset2] = j <=> vars2[j-offset1] = i
* Performs AC if domains are enumerated.
* If not, then it works on bounds without guaranteeing BC
* (enumerated domains are strongly recommended)
*
* Beware you should have |vars1| = |vars2|
*
* @param vars1 vector of variables which take their value in [offset1,offset1+|vars2|-1]
* @param vars2 vector of variables which take their value in [offset2,offset2+|vars1|-1]
* @param offset1 lowest value in vars1 (most often 0)
* @param offset2 lowest value in vars2 (most often 0)
*/
default Constraint inverseChanneling(IntVar[] vars1, IntVar[] vars2, int offset1, int offset2) {
return inverseChanneling(vars1, vars2, offset1, offset2, false);
}
/**
* Creates an inverse channeling between vars1 and vars2:
* vars1[i-offset2] = j <=> vars2[j-offset1] = i
* Performs AC if domains are enumerated.
* If not, then it works on bounds without guaranteeing BC
* (enumerated domains are strongly recommended)
*
* Beware you should have |vars1| = |vars2|
*
* @param vars1 vector of variables which take their value in [offset1,offset1+|vars2|-1]
* @param vars2 vector of variables which take their value in [offset2,offset2+|vars1|-1]
* @param offset1 lowest value in vars1 (most often 0)
* @param offset2 lowest value in vars2 (most often 0)
* @param ac use AC level for embedded alldifferent, if false, domains are scanned
*/
default Constraint inverseChanneling(IntVar[] vars1, IntVar[] vars2, int offset1, int offset2, boolean ac) {
if (vars1.length != vars2.length)
throw new SolverException(Arrays.toString(vars1) + " and " + Arrays.toString(vars2) + " should have same size");
boolean allEnum = true;
for (int i = 0; i < vars1.length && allEnum; i++) {
if (!(vars1[i].hasEnumeratedDomain() && vars2[i].hasEnumeratedDomain())) {
allEnum = false;
}
}
if (ac) {
allEnum = true;
}
Propagator ip = allEnum ? new PropInverseChannelAC(vars1, vars2, offset1, offset2)
: new PropInverseChannelBC(vars1, vars2, offset1, offset2);
Constraint alldiff1 = allDifferent(vars1, ac ? "AC" : "");
alldiff1.ignore();
Constraint alldiff2 = allDifferent(vars2, ac ? "AC" : "");
alldiff2.ignore();
return new Constraint(ConstraintsName.INVERSECHANNELING, ArrayUtils.append(
alldiff1.getPropagators(),
alldiff2.getPropagators(),
new Propagator[]{ip}
));
}
/**
* Creates an intValuePrecedeChain constraint.
* Ensure that if there exists j such that X[j] = T, then, there must exist i < j such that
* X[i] = S.
*
* @param X an array of variables
* @param S a value
* @param T another value
*/
default Constraint intValuePrecedeChain(IntVar[] X, int S, int T) {
return new Constraint(ConstraintsName.INT_VALUE_PRECEDE, new PropIntValuePrecedeChain(X, S, T));
}
/**
* Creates an intValuePrecedeChain constraint.
* Ensure that, for each pair of V[k] and V[l] of values in V, such that k < l,
* if there exists j such that X[j] = V[l], then, there must exist i < j such that
* X[i] = V[k].
*
* @param X array of variables
* @param V array of (distinct) values
*/
default Constraint intValuePrecedeChain(IntVar[] X, int[] V) {
if (V.length > 1) {
TIntHashSet values = new TIntHashSet();
PropIntValuePrecedeChain[] ps = new PropIntValuePrecedeChain[V.length - 1];
values.add(V[0]);
for (int i = 1; i < V.length; i++) {
if (values.contains(V[i])) {
throw new SolverException("\"int_value_precede\" requires V to be made of distinct values");
}
values.add(V[i]);
ps[i - 1] = new PropIntValuePrecedeChain(X, V[i - 1], V[i]);
}
return new Constraint(ConstraintsName.INT_VALUE_PRECEDE, ps);
} else {
return ref().trueConstraint();
}
}
/**
* Creates a knapsack constraint.
* Ensures that :
*
- occurrences[i] * weight[i] = weightSum
*
- occurrences[i] * energy[i] = energySum
*
and maximizing the value of energySum.
*
*
* A knapsack constraint
* wikipedia:
* "Given a set of items, each with a weight and an energy value,
* determine the count of each item to include in a collection so that
* the total weight is less than or equal to a given limit and the total value is as large as possible.
* It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack
* and must fill it with the most useful items."
* The limit over weightSum has to be specified either in its domain or with an additional constraint:
*
* model.post(solver.arithm(weightSum, "<=", limit);
*
*
* @param occurrences number of occurrences of every item
* @param weightSum load of the knapsack
* @param energySum profit of the knapsack
* @param weight weight of each item (must be >=0)
* @param energy energy of each item (must be >=0)
*/
default Constraint knapsack(IntVar[] occurrences, IntVar weightSum, IntVar energySum,
int[] weight, int[] energy) {
Constraint scalar1 = scalar(occurrences, weight, "=", weightSum);
scalar1.ignore();
Constraint scalar2 = scalar(occurrences, energy, "=", energySum);
scalar2.ignore();
return new Constraint(ConstraintsName.KNAPSACK, ArrayUtils.append(
scalar1.propagators,
scalar2.propagators,
new Propagator[]{new PropKnapsack(occurrences, weightSum, energySum, weight, energy)}
));
}
/**
* Creates a keySort constraint which ensures that the variables of SORTEDvars correspond to the variables
* of vars according to a permutation stored in PERMvars (optional, can be null).
* The variables of SORTEDvars are also sorted in increasing order wrt to K-size tuples.
* The sort is stable, that is, ties are broken using the position of the tuple in vars.
*
*
* For example:
* - vars= (<4,2,2>,<2,3,1>,<4,2,1>,<1,3,0>)
* - SORTEDvars= (<1,3,0>,<2,3,1>,<4,2,2>,<4,2,1>)
* - PERMvars= (4,2,1,3)
* - K = 2
*
* @param vars a tuple of array of variables
* @param PERMvars array of permutation variables, domains should be [1,vars.length] -- Can be null
* @param SORTEDvars a tuple of array of variables sorted in increasing order
* @param K key prefix size (0 ≤ k ≤ m, where m is the size of the array of variable)
* @return a keySort constraint
*/
default Constraint keySort(IntVar[][] vars, IntVar[] PERMvars, IntVar[][] SORTEDvars, int K) {
if (PERMvars == null) {
int n = vars.length;
PERMvars = new IntVar[n];
for (int p = 0; p < n; p++) {
PERMvars[p] = vars[0][0].getModel().intVar("p_" + (p + 1), 1, n, true);
}
}
return new Constraint(ConstraintsName.KEYSORT, new PropKeysorting(vars, SORTEDvars, PERMvars, K));
}
/**
* Creates a lexChainLess constraint.
* For each pair of consecutive vectors varsi and varsi+1 of the vars collection
* varsi is lexicographically strictly less than than varsi+1
*
* @param vars collection of vectors of variables
*/
default Constraint lexChainLess(IntVar[]... vars) {
return new Constraint(ConstraintsName.LEXCHAIN, new PropLexChain(vars, true));
}
/**
* Creates a lexChainLessEq constraint.
* For each pair of consecutive vectors varsi and varsi+1 of the vars collection
* varsi is lexicographically less or equal than than varsi+1
*
* @param vars collection of vectors of variables
*/
default Constraint lexChainLessEq(IntVar[]... vars) {
return new Constraint(ConstraintsName.LEXCHAIN, new PropLexChain(vars, false));
}
/**
* Creates a lexLess constraint.
* Ensures that vars1 is lexicographically strictly less than vars2.
*
* @param vars1 vector of variables
* @param vars2 vector of variables
*/
default Constraint lexLess(IntVar[] vars1, IntVar[] vars2) {
if (vars1.length != vars2.length) {
throw new SolverException("vars1 and vars2 should have the same length for lexLess constraint");
}
return new Constraint(ConstraintsName.LEX, new PropLex(vars1, vars2, true));
}
/**
* Creates a lexLessEq constraint.
* Ensures that vars1 is lexicographically less or equal than vars2.
*
* @param vars1 vector of variables
* @param vars2 vector of variables
*/
default Constraint lexLessEq(IntVar[] vars1, IntVar[] vars2) {
if (vars1.length != vars2.length) {
throw new SolverException("vars1 and vars2 should have the same length for lexLess constraint");
}
return new Constraint(ConstraintsName.LEX, new PropLex(vars1, vars2, false));
}
/**
* Creates an Argmax constraint.
* z is the index of the maximum value of the collection of domain variables vars.
*
* @param z a variable
* @param offset offset wrt to 'z'
* @param vars a vector of variables, of size > 0
*/
default Constraint argmax(IntVar z, int offset, IntVar[] vars) {
return new Constraint(ConstraintsName.ARGMAX, new PropArgmax(z, offset, vars));
}
/**
* Creates an Argmin constraint.
* z is the index of the minimum value of the collection of domain variables vars.
* @implNote This introduces {@link org.chocosolver.solver.variables.view.integer.IntMinusView}[]
* and returns an {@link #argmax(IntVar, int, IntVar[])} constraint
* on this views.
*
* @param z a variable
* @param offset offset wrt to 'z'
* @param vars a vector of variables, of size > 0
*/
default Constraint argmin(IntVar z, int offset, IntVar[] vars) {
IntVar[] views = Arrays.stream(vars).map(v -> ref().intMinusView(v)).toArray(IntVar[]::new);
return new Constraint(ConstraintsName.ARGMAX, new PropArgmax(z, offset, views));
}
/**
* Creates a maximum constraint.
* max is the maximum value of the collection of domain variables vars
*
* @param max a variable
* @param vars a vector of variables, of size > 0
*/
default Constraint max(IntVar max, IntVar[] vars) {
if (vars.length == 1) {
return max.eq(vars[0]).decompose();
} else if (vars.length == 2) {
return max(max, vars[0], vars[1]);
} else {
return new Constraint(ConstraintsName.MAX, new PropMax(vars, max));
}
}
/**
* Creates a maximum constraint.
* max is the maximum value of the collection of boolean variables vars
*
* @param max a boolean variable
* @param vars a vector of boolean variables, of size > 0
*/
default Constraint max(BoolVar max, BoolVar[] vars) {
if (vars.length == 1) {
return max.eq(vars[0]).decompose();
} else if (vars.length == 2) {
return max(max, vars[0], vars[1]);
} else {
return new Constraint(ConstraintsName.MAX, new PropBoolMax(vars, max));
}
}
/**
* Create a constraint where solutions (tuples) are encoded by a multi-valued decision diagram.
* The order of the variables in vars is important and must refer to the MDD.
*
* @param vars the array of variables
* @param MDD the multi-valued decision diagram encoding solutions
*/
default Constraint mddc(IntVar[] vars, MultivaluedDecisionDiagram MDD) {
return new Constraint(ConstraintsName.MDDC, new PropLargeMDDC(MDD, vars));
}
/**
* Creates a minimum constraint.
* min is the minimum value of the collection of domain variables vars
*
* @param min a variable
* @param vars a vector of variables, of size > 0
*/
default Constraint min(IntVar min, IntVar[] vars) {
if (vars.length == 1) {
return min.eq(vars[0]).decompose();
} else if (vars.length == 2) {
return min(min, vars[0], vars[1]);
} else {
return new Constraint(ConstraintsName.MIN, new PropMin(vars, min));
}
}
/**
* Creates a minimum constraint.
* min is the minimum value of the collection of boolean variables vars
*
* @param min a boolean variable
* @param vars a vector of boolean variables, of size > 0
*/
default Constraint min(BoolVar min, BoolVar[] vars) {
if (vars.length == 1) {
return min.eq(vars[0]).decompose();
} else if (vars.length == 2) {
return min(min, vars[0], vars[1]);
} else {
return new Constraint(ConstraintsName.MIN, new PropBoolMin(vars, min));
}
}
/**
* Creates a regular constraint that supports a multiple cost function.
* Ensures that the assignment of a sequence of vars is recognized by costAutomaton, a deterministic finite automaton,
* and that the sum of the cost vector associated to each assignment is bounded by the variable vector costVars.
* This version allows to specify different costs according to the automaton state at which the assignment occurs
* (i.e. the transition starts).
* The precision is set to {@code 1e-4d}.
*
* @param vars sequence of variables
* @param costVars cost variables
* @param costAutomaton a deterministic finite automaton defining the regular language and the costs
* Can be built from method CostAutomaton.makeMultiResources(...)
*/
default Constraint multiCostRegular(IntVar[] vars, IntVar[] costVars, ICostAutomaton costAutomaton) {
return multiCostRegular(vars, costVars, costAutomaton, 1e-4d);
}
/**
* Creates a regular constraint that supports a multiple cost function.
* Ensures that the assignment of a sequence of vars is recognized by costAutomaton, a deterministic finite automaton,
* and that the sum of the cost vector associated to each assignment is bounded by the variable vector costVars.
* This version allows to specify different costs according to the automaton state at which the assignment occurs
* (i.e. the transition starts)
*
* @param vars sequence of variables
* @param costVars cost variables
* @param costAutomaton a deterministic finite automaton defining the regular language and the costs
* Can be built from method CostAutomaton.makeMultiResources(...)
* @param precision the smallest used double for MCR algorithm
*/
default Constraint multiCostRegular(IntVar[] vars, IntVar[] costVars,
ICostAutomaton costAutomaton, double precision) {
return new Constraint(ConstraintsName.MULTICOSTREGULAR,
new PropMultiCostRegular(vars, costVars, costAutomaton, precision));
}
/**
* Creates an nValue constraint.
* Let N be the number of distinct values assigned to the variables of the vars collection.
* Enforce condition N = nValues to hold.
*
* This embeds a light propagator by default.
* Additional filtering algorithms can be added.
*
* see atleast_nvalue and atmost_nvalue
*
* @param vars collection of variables
* @param nValues limit variable
* @return the conjunction of atleast_nvalue and atmost_nvalue
*/
default Constraint nValues(IntVar[] vars, IntVar nValues) {
int[] vals = getDomainUnion(vars);
Gci gci = new Gci(vars);
R[] rules = new R[]{new R1(), new R3(vars.length, nValues.getModel())};
return new Constraint(
ConstraintsName.NVALUES,
new PropNValue(vars, nValues),
// at least
// new PropAtLeastNValues(vars, vals, nValues),
// at most
// new PropAtMostNValues(vars, vals, nValues),
new PropAMNV(vars, nValues, gci, new MDRk(gci), rules)
);
}
/**
* Creates an or constraint that is satisfied if at least one boolean variables in bools is true
*
* @param bools an array of boolean variable
* @return a constraint that is satisfied if at least one boolean variables in bools is true
*/
default Constraint or(BoolVar... bools) {
Model s = bools[0].getModel();
IntVar sum = s.intVar(0, bools.length, true);
s.sum(bools, "=", sum).post();
return s.arithm(sum, ">=", 1);
}
/**
* Creates an or constraint that is satisfied if at least one constraint in cstrs are satisfied
*
* @param cstrs an array of constraints
* @return a constraint and ensuring that at least one constraint in cstrs are satisfied
*/
default Constraint or(Constraint... cstrs) {
BoolVar[] bools = new BoolVar[cstrs.length];
for (int i = 0; i < cstrs.length; i++) {
bools[i] = cstrs[i].reify();
}
return or(bools);
}
/**
* Creates a path constraint which ensures that
*
the elements of vars define a covering path from start to end
* where vars[i] = j means that j is the successor of i.
* Moreover, vars[end] = |vars|
* Requires : |vars|>0
*
* Filtering algorithms: see circuit constraint
*
* @param vars vector of variables which take their value in [0,|vars|]
* @param start variable indicating the index of the first variable in the path
* @param end variable indicating the index of the last variable in the path
* @return a path constraint
*/
default Constraint path(IntVar[] vars, IntVar start, IntVar end) {
return path(vars, start, end, 0);
}
/**
* Creates a path constraint which ensures that
*
the elements of vars define a covering path from start to end
* where vars[i] = offset+j means that j is the successor of i.
* Moreover, vars[end-offset] = |vars|+offset
* Requires : |vars|>0
*
* Filtering algorithms: see circuit constraint
*
* @param vars vector of variables which take their value in [offset,offset+|vars|]
* @param start variable indicating the index of the first variable in the path
* @param end variable indicating the index of the last variable in the path
* @param offset 0 by default but typically 1 if used within MiniZinc
* (which counts from 1 to n instead of from 0 to n-1)
* @return a path constraint
*/
default Constraint path(IntVar[] vars, IntVar start, IntVar end, int offset) {
assert start != null && end != null && vars != null;
switch (vars.length) {
case 0:
throw new SolverException("|vars| Should be strictly greater than 0");
case 1:
return Constraint.merge(ConstraintsName.PATH,
arithm(start, "=", offset),
arithm(end, "=", offset),
arithm(vars[0], "=", 1 + offset)
);
default:
if (start == end) {
return start.getModel().falseConstraint();
} else {
return Constraint.merge(ConstraintsName.PATH,
arithm(start, "!=", end),
circuit(ArrayUtils.concat(vars, start), offset),
element(end.getModel().intVar(vars.length + offset), vars, end, offset)
);
}
}
}
/**
* Creates a regular constraint.
* Enforces the sequence of vars to be a word
* recognized by the deterministic finite automaton.
* For example regexp = "(1|2)(3*)(4|5)";
* The same dfa can be used for different propagators.
*
* @param vars sequence of variables
* @param automaton a deterministic finite automaton defining the regular language
*/
default Constraint regular(IntVar[] vars, IAutomaton automaton) {
return new Constraint(ConstraintsName.REGULAR, new PropRegular(vars, automaton));
}
/**
* Creates a scalar constraint which ensures that Sum(vars[i]*coeffs[i]) operator scalar
*
* @param vars a collection of IntVar
* @param coeffs a collection of int, for which |vars|=|coeffs|
* @param operator an operator in {"=", "!=", ">","<",">=","<="}
* @param scalar an integer
* @return a scalar constraint
*/
default Constraint scalar(IntVar[] vars, int[] coeffs, String operator, int scalar) {
return scalar(vars, coeffs, operator, scalar, ref().getSettings().getMinCardForSumDecomposition());
}
/**
* Creates a scalar constraint which ensures that Sum(vars[i]*coeffs[i]) operator scalar
*
* @param vars a collection of IntVar
* @param coeffs a collection of int, for which |vars|=|coeffs|
* @param operator an operator in {"=", "!=", ">","<",">=","<="}
* @param scalar an integer
* @param minCardForDecomp minimum number of cardinality threshold to a sum constraint to be decomposed
* @return a scalar constraint
*/
default Constraint scalar(IntVar[] vars, int[] coeffs, String operator, int scalar, int minCardForDecomp) {
assert vars.length > 0;
Model s = vars[0].getModel();
IntVar scalarVar = s.intVar(scalar);
return scalar(vars, coeffs, operator, scalarVar, minCardForDecomp);
}
/**
* Creates a scalar constraint which ensures that Sum(vars[i]*coeffs[i]) operator scalar
*
* @param vars a collection of IntVar
* @param coeffs a collection of int, for which |vars|=|coeffs|
* @param operator an operator in {"=", "!=", ">","<",">=","<="}
* @param scalar an IntVar
* @return a scalar constraint
*/
default Constraint scalar(IntVar[] vars, int[] coeffs, String operator, IntVar scalar) {
return scalar(vars, coeffs, operator, scalar,
ref().getSettings().getMinCardForSumDecomposition());
}
/**
* Creates a scalar constraint which ensures that Sum(vars[i]*coeffs[i]) operator scalar
*
* @param vars a collection of IntVar
* @param coeffs a collection of int, for which |vars|=|coeffs|
* @param operator an operator in {"=", "!=", ">","<",">=","<="}
* @param scalar an IntVar
* @param minCardForDecomp minimum number of cardinality threshold to a sum constraint to be decomposed
* @return a scalar constraint
*/
default Constraint scalar(IntVar[] vars, int[] coeffs, String operator, IntVar scalar,
int minCardForDecomp) {
if (vars.length != coeffs.length) {
throw new SolverException("vars and coeffs arrays should have same size");
}
return IntLinCombFactory.reduce(vars, coeffs, Operator.get(operator), scalar, minCardForDecomp);
}
/**
* Creates a sort constraint which ensures that the variables of sortedVars correspond to the variables
* of vars according to a permutation. The variables of sortedVars are also sorted in increasing order.
*
*
* For example:
* - X= (4,2,1,3)
* - Y= (1,2,3,4)
*
* @param vars an array of variables
* @param sortedVars an array of variables sorted in increasing order
* @return a sort constraint
*/
default Constraint sort(IntVar[] vars, IntVar[] sortedVars) {
if (vars.length != sortedVars.length) {
throw new SolverException("vars and sortedVars arrays should have same size");
}
// return new Constraint("Sort", new PropSort(vars, sortedVars));
IntVar[][] X = new IntVar[vars.length][1];
IntVar[][] Y = new IntVar[sortedVars.length][1];
for (int i = 0; i < vars.length; i++) {
X[i][0] = vars[i];
Y[i][0] = sortedVars[i];
}
return keySort(X, null, Y, 1);
}
/**
* Creates a subCircuit constraint which ensures that
*
the elements of vars define a single circuit of subcircuitSize nodes where
* vars[i] = offset+j means that j is the successor of i.
* and vars[i] = offset+i means that i is not part of the circuit
* the constraint ensures that |{vars[i] =/= offset+i}| = subCircuitLength
*
*
Filtering algorithms:
* subtour elimination : Caseau & Laburthe (ICLP'97)
* allDifferent GAC algorithm: Régin (AAAI'94)
* dominator-based filtering: Fages & Lorca (CP'11) (adaptive scheme by default, see implementation)
*
* @param vars a vector of variables
* @param offset 0 by default but 1 if used within MiniZinc
* (which counts from 1 to n instead of from 0 to n-1)
* @param subCircuitLength expected number of nodes in the circuit
* @return a subCircuit constraint
*/
default Constraint subCircuit(IntVar[] vars, int offset, IntVar subCircuitLength) {
int n = vars.length;
Model model = vars[0].getModel();
IntVar nbLoops = model.intVar("nLoops", 0, n, true);
nbLoops.add(subCircuitLength).eq(n).post();
Constraint alldiff = allDifferent(vars, "AC");
alldiff.ignore();
return new Constraint(ConstraintsName.SUBCIRCUIT, ArrayUtils.append(
alldiff.getPropagators(),
ArrayUtils.toArray(
new PropKLoops(vars, offset, nbLoops),
new PropSubcircuit(vars, offset, subCircuitLength),
new PropSubcircuitDominatorFilter(vars, offset, true)
)
));
}
/**
* Creates a subPath constraint which ensures that
* the elements of vars define a path of SIZE vertices, leading from start to end
* where vars[i] = offset+j means that j is the successor of i.
* where vars[i] = offset+i means that vertex i is excluded from the path.
* Moreover, vars[end-offset] = |vars|+offset
* Requires : |vars|>0
*
* Filtering algorithms: see subCircuit constraint
*
* @param vars vector of variables which take their value in [offset,offset+|vars|]
* @param start variable indicating the index of the first variable in the path
* @param end variable indicating the index of the last variable in the path
* @param offset 0 by default but typically 1 if used within MiniZinc
* (which counts from 1 to n instead of from 0 to n-1)
* @param SIZE variable indicating the number of variables to belong to the path
* @return a subPath constraint
*/
default Constraint subPath(IntVar[] vars, IntVar start, IntVar end, int offset, IntVar SIZE) {
assert start != null && end != null && vars != null;
switch (vars.length) {
case 0:
throw new SolverException("|vars| Should be strictly greater than 0");
case 1:
return Constraint.merge(ConstraintsName.SUBPATH,
arithm(start, "=", offset),
arithm(end, "=", offset),
arithm(vars[0], "=", 1 + offset),
arithm(SIZE, "=", 1)
);
default:
return Constraint.merge(ConstraintsName.SUBPATH,
arithm(start, "<", vars.length + offset),
subCircuit(ArrayUtils.concat(vars, start), offset, end.getModel().intOffsetView(SIZE, 1)),
element(end.getModel().intVar(vars.length + offset), vars, end, offset)
);
}
}
/**
* Creates a sum constraint.
* Enforces that ∑i in |vars|varsi operator sum.
*
* @param vars a collection of IntVar
* @param operator operator in {"=", "!=", ">","<",">=","<="}
* @param sum an integer
* @return a sum constraint
*/
default Constraint sum(IntVar[] vars, String operator, int sum) {
return sum(vars, operator, sum, ref().getSettings().getMinCardForSumDecomposition());
}
/**
* Creates a sum constraint.
* Enforces that ∑x in vars1x operator ∑y in vars2y.
*
* @param vars1 a collection of IntVar
* @param operator operator in {"=", "!=", ">","<",">=","<="}
* @param vars2 a collection of IntVar
* @return a sum constraint
*/
default Constraint sum(IntVar[] vars1, String operator, IntVar[] vars2) {
int[] coeffs = new int[vars1.length+ vars2.length];
Arrays.fill(coeffs, 0, vars1.length, 1);
Arrays.fill(coeffs, vars1.length, vars1.length + vars2.length, -1);
return scalar(ArrayUtils.append(vars1, vars2), coeffs, operator, 0, ref().getSettings().getMinCardForSumDecomposition());
}
/**
* Creates a sum constraint.
* Enforces that ∑i in |vars|varsi operator sum.
*
* @param vars a collection of IntVar
* @param operator operator in {"=", "!=", ">","<",">=","<="}
* @param sum an integer
* @param minCardForDecomp minimum number of cardinality threshold to a sum constraint to be decomposed
* @return a sum constraint
*/
default Constraint sum(IntVar[] vars, String operator, int sum, int minCardForDecomp) {
assert vars.length > 0;
Model s = vars[0].getModel();
IntVar sumVar = s.intVar(sum);
return IntLinCombFactory.reduce(vars, Operator.get(operator), sumVar, minCardForDecomp);
}
/**
* Creates a sum constraint.
* Enforces that ∑i in |vars|varsi operator sum.
*
* @param vars a collection of IntVar
* @param operator operator in {"=", "!=", ">","<",">=","<="}
* @param sum an IntVar
* @return a sum constraint
*/
default Constraint sum(IntVar[] vars, String operator, IntVar sum) {
return sum(vars, operator, sum, ref().getSettings().getMinCardForSumDecomposition());
}
/**
* Creates a sum constraint.
* Enforces that ∑i in |vars|varsi operator sum.
*
* @param vars a collection of IntVar
* @param operator operator in {"=", "!=", ">","<",">=","<="}
* @param sum an IntVar
* @param minCardForDecomp minimum number of cardinality threshold to a sum constraint to be decomposed
* @return a sum constraint
*/
default Constraint sum(IntVar[] vars, String operator, IntVar sum, int minCardForDecomp) {
return IntLinCombFactory.reduce(vars, Operator.get(operator), sum, minCardForDecomp);
}
/**
* Creates a sum constraint.
* Enforces that ∑i in |vars|varsi operator sum.
* This constraint is much faster than the one over integer variables
*
* @param vars a vector of boolean variables
* @param sum an integer
*/
default Constraint sum(BoolVar[] vars, String operator, int sum) {
assert vars.length > 0;
Model s = vars[0].getModel();
IntVar sumVar = s.intVar(sum);
return sum(vars, operator, sumVar);
}
/**
* Creates a sum constraint.
* Enforces that ∑i in |vars|varsi operator sum.
* This constraint is much faster than the one over integer variables
*
* @param vars a vector of boolean variables
* @param sum a variable
*/
default Constraint sum(BoolVar[] vars, String operator, IntVar sum) {
return sum(vars, operator, sum, ref().getSettings().getMinCardForSumDecomposition());
}
/**
* Creates a sum constraint.
* Enforces that ∑i in |vars|varsi operator sum.
* This constraint is much faster than the one over integer variables
*
* @param vars a vector of boolean variables
* @param sum a variable
* @param minCardForDecomp minimum number of cardinality threshold to a sum constraint to be decomposed
*/
default Constraint sum(BoolVar[] vars, String operator, IntVar sum, int minCardForDecomp) {
if (sum.getModel().getSettings().enableDecompositionOfBooleanSum()) {
int[] bounds = VariableUtils.boundsForAddition(vars);
IntVar p = sum.getModel().intVar(sum.getModel().generateName("RSLT_"), bounds[0], bounds[1], true);
IntLinCombFactory.reduce(vars, Operator.EQ, p, minCardForDecomp).post();
return arithm(p, operator, sum);
} else {
return IntLinCombFactory.reduce(vars, Operator.get(operator), sum, minCardForDecomp);
}
}
/**
* Creates a table constraint specifying that the sequence of variables vars must belong to the list of tuples
* (or must NOT belong in case of infeasible tuples)
*
* Default configuration with GACSTR+ algorithm for feasible tuples and GAC3rm otherwise
*
* @param vars variables forming the tuples
* @param tuples the relation between the variables (list of allowed/forbidden tuples)
*/
default Constraint table(IntVar[] vars, Tuples tuples) {
String algo = "GAC3rm";
if (tuples.isFeasible()) {
//noinspection OptionalGetWithoutIsPresent
if (tuples.nbTuples() > 512 &&
(IntStream.range(0, vars.length)
.map(i -> tuples.max(i) - tuples.min(i))
.max().getAsInt()) < 512) {
algo = "CT+";
} else if (tuples.allowUniversalValue()) {
// STR2+ or CT+, depending on dom size
algo = "STR2+";
} else {
algo = "GACSTR+";
}
}
return table(vars, tuples, algo);
}
/**
* Creates a table constraint, with the specified algorithm defined algo
*
* - CT+: Compact-Table algorithm (AC),
*
* - GAC2001: Arc Consistency version 2001 for tuples,
*
* - GAC2001+: Arc Consistency version 2001 for allowed tuples,
*
* - GAC3rm: Arc Consistency version AC3 rm for tuples,
*
* - GAC3rm+ (default): Arc Consistency version 3rm for allowed tuples,
*
* - GACSTR+: Arc Consistency version STR for allowed tuples,
*
* - STR2+: Arc Consistency version STR2 for allowed tuples,
*
* - FC: Forward Checking.
*
* - MDD+: uses a multi-valued decision diagram for allowed tuples (see mddc constraint),
*
* @param vars variables forming the tuples
* @param tuples the relation between the variables (list of allowed/forbidden tuples). Should not be modified once passed to the constraint.
* @param algo to choose among {"CT+", "GAC3rm", "GAC2001", "GACSTR", "GAC2001+", "GAC3rm+", "FC", "STR2+"}
*/
default Constraint table(IntVar[] vars, Tuples tuples, String algo) {
if (!tuples.allowUniversalValue() && vars.length == 2) {
switch (algo) {
case "FC":
return table(vars[0], vars[1], tuples, algo);
case "GAC2001":
return table(vars[0], vars[1], tuples, "AC2001");
case "CT+":
return table(vars[0], vars[1], tuples, "CT+");
case "GAC3rm":
return table(vars[0], vars[1], tuples, "AC3rm");
default:
return table(vars[0], vars[1], tuples);
}
}
if (algo.contains("+") && !tuples.isFeasible()) {
throw new SolverException(algo + " table algorithm cannot be used with forbidden tuples.");
}
if (tuples.allowUniversalValue() && !(algo.contains("CT+") || algo.contains("STR2+"))) {
throw new SolverException(algo + " table algorithm cannot be used with short tuples.");
}
Propagator p;
switch (algo) {
case "CT+": {
if (tuples.allowUniversalValue()) {
p = new PropCompactTableStar(vars, tuples);
} else {
p = new PropCompactTable(vars, tuples);
}
}
break;
case "MDD+":
p = new PropLargeMDDC(new MultivaluedDecisionDiagram(vars, tuples), vars);
break;
case "FC":
p = new PropLargeFC(vars, tuples);
break;
case "GAC3rm":
p = new PropLargeGAC3rm(vars, tuples);
break;
case "GAC2001":
p = new PropLargeGAC2001(vars, tuples);
break;
case "GACSTR+":
p = new PropLargeGACSTRPos(vars, tuples);
break;
case "GAC2001+":
p = new PropLargeGAC2001Positive(vars, tuples);
break;
case "GAC3rm+":
p = new PropLargeGAC3rmPositive(vars, tuples);
break;
case "STR2+":
p = new PropTableStr2(vars, tuples);
break;
default:
throw new SolverException("Table algorithm " + algo + " is unkown");
}
return new Constraint(ConstraintsName.TABLE, p);
}
/**
* Creates a tree constraint.
* Partition succs variables into nbTrees (anti) arborescences
* succs[i] = j means that j is the successor of i.
* and succs[i] = i means that i is a root
*
*
dominator-based filtering: Fages & Lorca (CP'11)
* However, the filtering over nbTrees is quite light here
*
* @param succs successors variables, taking their domain in [0,|succs|-1]
* @param nbTrees number of arborescences (=number of loops)
* @return a tree constraint
*/
default Constraint tree(IntVar[] succs, IntVar nbTrees) {
return tree(succs, nbTrees, 0);
}
/**
* Creates a tree constraint.
* Partition succs variables into nbTrees (anti) arborescences
* succs[i] = offset+j means that j is the successor of i.
* and succs[i] = offset+i means that i is a root
*
*
dominator-based filtering: Fages & Lorca (CP'11)
* However, the filtering over nbTrees is quite light here
*
* @param succs successors variables, taking their domain in [offset,|succs|-1+offset]
* @param nbTrees number of arborescences (=number of loops)
* @param offset 0 by default but 1 if used within MiniZinc
* (which counts from 1 to n instead of from 0 to n-1)
* @return a tree constraint
*/
default Constraint tree(IntVar[] succs, IntVar nbTrees, int offset) {
return new Constraint(ConstraintsName.TREE,
new PropAntiArborescences(succs, offset, false),
new PropKLoops(succs, offset, nbTrees)
);
}
/**
* Get the list of values in the domains of vars
*
* @param vars an array of integer variables
* @return the list of values in the domains of vars
*/
default int[] getDomainUnion(IntVar... vars) {
int m = vars[0].getLB(), M = vars[0].getUB(), j, k;
for (int i = 1; i < vars.length; i++) {
if (m > (k = vars[i].getLB())) {
m = k;
}
if (M < (j = vars[i].getUB())) {
M = j;
}
}
BitSet values = new BitSet(M - m + 1);
DisposableRangeIterator rit;
for (IntVar v : vars) {
rit = v.getRangeIterator(true);
while (rit.hasNext()) {
int from = rit.min();
int to = rit.max();
// operate on range [from,to] here
values.set(from - m, to - m + 1);
rit.next();
}
rit.dispose();
}
int[] vs = new int[values.cardinality()];
k = 0;
for (int i = values.nextSetBit(0); i >= 0; i = values.nextSetBit(i + 1)) {
vs[k++] = i + m;
}
return vs;
}
}