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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.iterator.TIntIterator;
import gnu.trove.set.hash.TIntHashSet;
import org.chocosolver.solver.ISelf;
import org.chocosolver.solver.Model;
import org.chocosolver.solver.constraints.extension.Tuples;
import org.chocosolver.solver.constraints.nary.automata.FA.IAutomaton;
import org.chocosolver.solver.variables.BoolVar;
import org.chocosolver.solver.variables.IntVar;
import org.chocosolver.util.tools.ArrayUtils;
import java.util.Arrays;
import java.util.stream.IntStream;
import java.util.stream.Stream;
import static java.lang.Integer.MAX_VALUE;
import static java.lang.Integer.MIN_VALUE;
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.String.format;
/**
* An interface dedicated to list decomposition of some constraints.
*
* Project: choco-solver.
*
* @author Charles Prud'homme
* @since 12/06/2018.
*/
public interface IDecompositionFactory extends ISelf {
/**
* Creates and posts a decomposition of a cumulative constraint: associates a boolean
* variable to each task and each point of time sich that the scalar product of boolean
* variables per heights for each time never exceed capacity.
*
* @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
* @see org.chocosolver.solver.constraints.IIntConstraintFactory#cumulative(IntVar[], int[],
* int[], int)
*/
default void cumulativeTimeDec(IntVar[] starts, int[] durations, int[] heights, int capacity) {
int n = starts.length;
// 1. find range of 't' parameters while creating variables
int min_t = MAX_VALUE, max_t = MIN_VALUE;
for (int i = 0; i < n; i++) {
min_t = min(min_t, starts[i].getLB());
max_t = max(max_t, starts[i].getUB() + durations[i]);
}
for (int t = min_t; t <= max_t; t++) {
BoolVar[] bit = ref().boolVarArray(format("b_%s_", t), n);
for (int i = 0; i < n; i++) {
ref().addClausesBoolAndArrayEqVar(
new BoolVar[]{
ref().intLeView(starts[i], t),
ref().intGeView(starts[i], t - durations[i] + 1)
},
bit[i]);
}
ref().scalar(
bit,
Arrays.stream(heights, 0, n).toArray(),
"<=",
capacity
).post();
}
}
/**
* Creates an element constraint: value = matrix[rowIndex-offset][colIndex-colOffset]
*
* @param value an integer variable taking its value in matrix
* @param matrix a matrix of integer values
* @param rowIndex index of the selected row
* @param rowOffset offset for row index
* @param colIndex index of the selected column
* @param colOffset offset for column index
*/
default IntVar[] element(IntVar value, int[][] matrix, IntVar rowIndex, int rowOffset, IntVar colIndex, int colOffset) {
IntVar[] results = new IntVar[matrix.length];
for (int r = 0; r < matrix.length; r++) {
int min = IntStream.of(matrix[r]).min().orElse(IntVar.MIN_INT_BOUND);
int max = IntStream.of(matrix[r]).max().orElse(IntVar.MAX_INT_BOUND);
results[r] = ref().intVar("val[" + r + "]", min, max);
ref().element(results[r], matrix[r], colIndex, colOffset).post();
}
ref().element(value, results, rowIndex, rowOffset).post();
return results;
}
/**
* Creates an element constraint: value = matrix[rowIndex-offset][colIndex-colOffset]
*
* @param value an integer variable taking its value in matrix
* @param matrix a matrix of integer variables
* @param rowIndex index of the selected row
* @param rowOffset offset for row index
* @param colIndex index of the selected column
* @param colOffset offset for column index
*/
default IntVar[] element(IntVar value, IntVar[][] matrix, IntVar rowIndex, int rowOffset, IntVar colIndex, int colOffset) {
IntVar[] results = new IntVar[matrix.length];
for (int r = 0; r < matrix.length; r++) {
int min = Stream.of(matrix[r]).mapToInt(IntVar::getLB).min().orElse(IntVar.MIN_INT_BOUND);
int max = Stream.of(matrix[r]).mapToInt(IntVar::getUB).max().orElse(IntVar.MAX_INT_BOUND);
results[r] = ref().intVar("val[" + r + "]", min, max);
ref().element(results[r], matrix[r], colIndex, colOffset).post();
}
ref().element(value, results, rowIndex, rowOffset).post();
return results;
}
/**
* Creates and posts a decomposition of 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
* @return array of variables that encodes the states, which can optionally be constrained too.
*/
@SuppressWarnings("UnusedReturnValue")
default IntVar[] regularDec(IntVar[] vars, IAutomaton automaton) {
int n = vars.length;
IntVar[] states = new IntVar[n + 1];
TIntHashSet[] layer = new TIntHashSet[n + 1];
for (int i = 0; i <= n; i++) {
layer[i] = new TIntHashSet();
}
layer[0].add(automaton.getInitialState());
states[0] = ref().intVar("Q_" + ref().nextId(), layer[0].toArray());
TIntHashSet nexts = new TIntHashSet();
for (int i = 0; i < n; i++) {
int ub = vars[i].getUB();
Tuples tuples = new Tuples(true);
for (int j = vars[i].getLB(); j <= ub; j = vars[i].nextValue(j)) {
TIntIterator layerIter = layer[i].iterator();
while (layerIter.hasNext()) {
int k = layerIter.next();
nexts.clear();
automaton.delta(k, j, nexts);
for (TIntIterator it = nexts.iterator(); it.hasNext(); ) {
int succ = it.next();
if (i + 1 < n || automaton.isFinal(succ)) {
layer[i + 1].add(succ);
tuples.add(k, succ, j);
}
}
}
}
states[i + 1] = ref().intVar("Q_" + ref().nextId(), layer[i + 1].toArray());
ref().table(new IntVar[]{states[i], states[i + 1], vars[i]}, tuples, "CT+").post();
}
return states;
}
/**
* Creates and posts a decomposition of a bin packing constraint. Bin Packing
* formulation: forall b in [0,binLoad.length-1], load[b]=sum(w[i] | i in [0,w.length-1], bin[i]
* = b+offset) forall i in [0,w.length-1], bin is in [offset,load.length-1+offset],
*
* @param bin IntVar representing the bin of each item
* @param w int representing the size of each item
* @param load 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 void binPackingDec(IntVar[] bin, int[] w, IntVar[] load, int offset) {
ref().sum(load, "=", Arrays.stream(w).sum()).post();
for (int i = 0; i < bin.length; i++) {
ref().member(bin[i], offset, load.length - 1 + offset).post();
}
for (int i = 0; i < load.length; i++) {
BoolVar[] in = new BoolVar[bin.length];
for (int j = 0; j < bin.length; j++) {
in[j] = ref().intEqView(bin[j], i + offset);
}
ref().scalar(in, w, "=", load[i]).post();
}
}
/**
*
* Creates and posts a decomposition of the {@link IIntConstraintFactory#circuit(IntVar[], int)} constraint.
*
*
* It relies on two {@link IIntConstraintFactory#allDifferent(IntVar[], String)} constraints and some
* {@link IIntConstraintFactory#element(IntVar, IntVar[], IntVar, int)} constraints.
*
*
* @param S successors variables
* @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 void circuitDec(IntVar[] S, int offset) {
int n = S.length;
ref().allDifferent(S, "AC").post();
IntVar[] t = ref().intVarArray("t", n - 1, 1 + offset, n - 1 + offset);
ref().allDifferent(t, "AC3").post();
ref().element(t[0], S, ref().intVar(offset), 0).post();
for (int i = 1; i < n - 2; i++) {
ref().element(t[i], S, t[i - 1], 0).post();
}
ref().element(ref().intVar(offset), S, t[n - 2], 0).post();
}
/**
* Creates a decomposition of the 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 void argmaxDec(IntVar z, int offset, IntVar[] vars) {
int n = vars.length;
//noinspection OptionalGetWithoutIsPresent
int min = Stream.of(vars).mapToInt(IntVar::getLB).min().getAsInt();
int max = Stream.of(vars).mapToInt(IntVar::getUB).max().getAsInt();
IntVar[] q = new IntVar[n];
IntVar M = ref().intVar("M", n * min, n * (max + 1));
z.ge(0).post();
z.lt(vars.length).post();
for (int j = 0; j < n; j++) {
q[j] = ref().intAffineView(n, vars[j], n - j);
z.ne(j + offset).iff(M.gt(q[j])).post();
}
ref().max(M, q).post();
}
/**
* Creates a decomposition of the Argmin constraint.
* z is the index of the minimum 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 void argminDec(IntVar z, int offset, IntVar[] vars) {
int n = vars.length;
//noinspection OptionalGetWithoutIsPresent
int min = Stream.of(vars).mapToInt(IntVar::getLB).min().getAsInt();
int max = Stream.of(vars).mapToInt(IntVar::getUB).max().getAsInt();
IntVar[] q = new IntVar[n];
IntVar M = ref().intVar("M", n * min, n * (max + 1));
for (int j = 0; j < n; j++) {
q[j] = ref().intAffineView(n, vars[j], j);
z.ne(j + offset).iff(M.lt(q[j])).post();
}
ref().min(M, q).post();
}
/**
*
* Creates a decomposition that encodes an "if-then-else" constraint.
*
*
* If c[0] then y = x[0]
*
else if c[1] then y = x[1]
*
...
*
else y is not constrained.
*
*
* @param c array of boolean variables
* @param x array of ints
* @param y a integer variable
* @implNote This is encoded thanks to a table constraint.
*/
default void ifThenElseDec(BoolVar[] c, int[] x, IntVar y) {
Tuples tuples = new Tuples();
int star = Math.max(2, y.getUB() + 1);
tuples.setUniversalValue(star);
int[] t = new int[c.length + 1];
Arrays.fill(t, 0);
t[c.length] = star;
tuples.add(t.clone());
Arrays.fill(t, star);
for (int i = 0; i < c.length; i++) {
if (i > 0) t[i - 1] = 0;
t[i] = 1;
t[c.length] = x[i];
tuples.add(t.clone());
}
ref().table(ArrayUtils.append(c, new IntVar[]{y}), tuples).post();
}
/**
*
* Creates a decomposition that encodes an "if-then-else" constraint.
*
*
* If c[0] then y = x[0]
*
else if c[1] then y = x[1]
*
...
*
else y is not constrained.
*
*
* @param c array of boolean variables
* @param x array of integer variables
* @param y a integer variable
* @implNote This introduces an additional variable
* and is based on a table constraint and an element constraint.
*/
default void ifThenElseDec(BoolVar[] c, IntVar[] x, IntVar y) {
/*
BoolVar[] d = ref().boolVarArray(c.length);
d[0] = ref().boolVar(true);
//y.eq(x[0]).decompose().impliedBy(c[0]);
c[0].imp(y.eq(x[0])).post();
for (int i = 1; i < c.length; i++) {
d[i].eq(c[i - 1].not().and(d[i - 1])).post();
//y.eq(x[i]).decompose().impliedBy(c[i].and(d[i]).boolVar());
c[i].and(d[i]).imp(y.eq(x[i])).post();
}/*/
Tuples tuples = new Tuples();
int univ = Math.max(2, y.getUB() + 1);
tuples.setUniversalValue(univ);
int[] t = new int[c.length + 1];
Arrays.fill(t, 0);
t[c.length] = c.length;
tuples.add(t.clone());
Arrays.fill(t, univ);
for (int i = 0; i < c.length; i++) {
if (i > 0) t[i - 1] = 0;
t[i] = 1;
t[c.length] = i;
tuples.add(t.clone());
}
IntVar idx = ref().intVar(0, c.length);
ref().table(ArrayUtils.append(c, new IntVar[]{idx}), tuples).post();
ref().element(y, ArrayUtils.append(x, new IntVar[]{y}), idx, 0).post();
//*/
}
/**
* Matrix multiplication A x B = C.
* @param A a m x n matrix
* @param B a n x p matrix
* @param C a m x p matrix
*/
default void product(IntVar[][] A, IntVar[][] B, IntVar[][] C) {
assert A.length > 0 && B.length > 0 && C.length > 0;
assert A[0].length > 0 && B[0].length > 0 && C[0].length > 0;
assert A[0].length == B[0].length;
assert A.length == C.length;
assert B[0].length == C[0].length;
int n = B.length;
int m = C.length;
int p = C[0].length;
Model model = C[0][0].getModel();
for(int i = 0; i < m; i++){
for(int j = 0; j < p; j++){
int finalI = i;
int finalJ = j;
model.sum(IntStream.range(0, n)
.mapToObj(k -> A[finalI][k].mul(B[k][finalJ]).intVar())
.toArray(IntVar[]::new),
"=", C[i][j]).post();
}
}
}
default void product(BoolVar[][] A, BoolVar[][] B, BoolVar[][] C) {
assert A.length > 0 && B.length > 0 && C.length > 0;
assert A[0].length > 0 && B[0].length > 0 && C[0].length > 0;
assert A[0].length == B[0].length;
assert A.length == C.length;
assert B[0].length == C[0].length;
int n = B.length;
int m = C.length;
int p = C[0].length;
Model model = C[0][0].getModel();
for (int i = 0; i < m; i++) {
for (int j = 0; j < p; j++) {
int finalI = i;
int finalJ = j;
model.addClausesBoolOrArrayEqVar(
IntStream.range(0, n)
.mapToObj(k -> A[finalI][k].and(B[k][finalJ]).boolVar())
.toArray(BoolVar[]::new)
, C[i][j]);
}
}
}
}