Solving a problem using constraint programming consists of finding a value for each variable that satisfies the constraints. In this problem, there will be more than one solution that satisfies the constraints. You can use Solver to find multiple solutions for the problem and display them.

You start by creating an instance of the class IloSolver to solve the problem expressed in the model.

Add the following code after the comment //Create an instance of IloSolver

    IloSolver solver(model);

Add the following code after the comment //Search for a solution

    solver.startNewSearch();

Next, you use a while loop and the member function IloSolver::next to search for multiple solutions. IloSolver::next searches for the next solution in the search tree.

The member function IloSolver::next, like IloSolver::solve, controls the execution of goals. The first time one of these member functions is called, it creates a goal stack, an internal data structure that Solver uses to manage goals during a solution search.

The member function IloSolver::next returns a Boolean value of type IloBool. If a solution is found, an IloTrue value is returned and the program displays the solution.

After the while loop terminates, you must use the member function IloSolver::endSearch to terminate the search and delete internal objects created by Solver to carry out the search (such as the search tree, goal stack, and so on).

The member functions and streams IloAlgorithm::out and IloSolver::getValue are used to display the solution. The following code is provided for you:

    IloInt solutionCounter = 0;
    while(solver.next()) {
      solver.out() << "solution  " << ++solutionCounter << ":\t";
      for (IloInt i = 0; i < nCoins; i++)
        solver.out() << solver.getValue(coins[i]) << " ";
      solver.out() << endl;
    }
    solver.endSearch();

Compile and run the program. You should get the following results:

[1, 10, 20, 100]
solution  1:    3 0 1 1
solution  2:    3 0 6 0
solution  3:    3 2 0 1
solution  4:    3 2 5 0
solution  5:    3 4 4 0
solution  6:    3 6 3 0
solution  7:    3 8 2 0
solution  8:    3 10 1 0
solution  9:    3 12 0 0

As you can see, there are nine solutions: