Part 2: Domains, Variables, Constraints

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Theoretical Questions

Domain with an Arbitrary Set of Values

Implement the missing constructor in

public IntVarImpl(Solver cp, Set<Integer> values) {
    throw new NotImplementedException();

This exercise is straightforward: just create a dense domain and then remove the values not present in the set.

Check that your implementation passes the tests

Implement a Domain Iterator

Many filtering algorithms require iteration over the values of a domain.

A naive (but correct) way of iterating over a domain is:

for (int v = x.min(); v <= x.max(); x++) {
    if (x.contains(i)) {
        // do something

This method is rather inefficient because it will also consider the values that are not present in the domain. Instead, the fillArray method from allows filling an array with all the values present in the sparse set. In case of an offset value of 0, you could even use the very efficient System.arraycopy.

The main advantage over the iterator mechanism is that no object is created (and thus garbage collected). Indeed dest is typically a container array stored as an instance variable and reused many times. It is important for efficiency to avoid creating objects on the heap at each execution of a propagator. Never forget that a propagate() method of Constraint may be called thousands of times per second. This implementation using fillArray avoids the ConcurrentModificationException discussion when implementing an Iterator: should we allow modifying a domain while iterating on it? The answer here is very clear: you get a snapshot of the domain at the time of the call to fillArray and you can thus safely iterate over this dest array and modify the domain at the same time.

To do:

The Absolute Value Constraint


Several directions of implementation are possible:

  1. The full domain-consistent version (use the fillArray method to iterate over domains).

  2. A hybrid domain-bound consistent one.

Check that your implementation passes the tests

The Maximum Constraint


Implement a bound-consistent filtering algorithm.

Check that your implementation passes the tests