OR-Tools LP Limit Number of Elements in Solution

[idratherbecoding]

I have a relatively simple binary integer optimization problem and I am using Google OR-Tools' linear solver. I started the project in C#, but have since decided to port to Python and finish from there. The problem I having is making sure that the solution uses exactly n elements from those available. In C#, this line had the desired result:

solver.Add(solver.LinearExprArrayHelper.Sum(x) == n);

What I believe to be the equivalent line in Python, results in no optimal solution to the problem:

solver.Add(solver.Sum(x) == n)

The full code is based largely on the example on the OR-Tools page for mixed integer programming using arrays to define the model. Any guidance would be much appreciated. Thanks!

from ortools.linear_solver import pywraplp
import random


def create_data_model(points, salaries, capacity, num_vars, num_constraints):
    """Stores the data for the problem."""
    data = {'constraint_coeffs': [salaries], 'bounds': [capacity], 'obj_coeffs': points, 'num_vars': num_vars,
            'num_constraints': num_constraints}
    return data


def main():
    points = []
    for i in range(20):
        points.append(random.randint(5, 40))

    salaries = []
    for i in range(20):
        salaries.append(round_nearest_hundred(random.randint(5000, 10000)))

    data = create_data_model(points, salaries, 35000, len(salaries), 1)
    # Create the mip solver with the SCIP backend.
    solver = pywraplp.Solver.CreateSolver('SCIP')
    if not solver:
        return

    x = {}
    for j in range(data['num_vars']):
        x[j] = solver.IntVar(0, 1, 'x[%i]' % j)
    print('Number of variables =', solver.NumVariables())

    for i in range(data['num_constraints']):
        constraint = solver.RowConstraint(0, data['bounds'][i], '')
        for j in range(data['num_vars']):
            constraint.SetCoefficient(x[j], data['constraint_coeffs'][i][j])
    print('Number of constraints =', solver.NumConstraints())
    # In Python, you can also set the constraints as follows.
    # for i in range(data['num_constraints']):
    #  constraint_expr = \
    # [data['constraint_coeffs'][i][j] * x[j] for j in range(data['num_vars'])]
    #  solver.Add(sum(constraint_expr) <= data['bounds'][i])

    solver.Add(solver.Sum(x) == 5) # <-- This is the line causing me issues. 

    objective = solver.Objective()
    for j in range(data['num_vars']):
        objective.SetCoefficient(x[j], data['obj_coeffs'][j])
    objective.SetMaximization()
    # In Python, you can also set the objective as follows.
    # obj_expr = [data['obj_coeffs'][j] * x[j] for j in range(data['num_vars'])]
    # solver.Maximize(solver.Sum(obj_expr))

    status = solver.Solve()

    if status == pywraplp.Solver.OPTIMAL:
        print('Objective value =', solver.Objective().Value())
        for j in range(data['num_vars']):
            print(x[j].name(), ' = ', x[j].solution_value())
        print()
        print('Problem solved in %f milliseconds' % solver.wall_time())
        print('Problem solved in %d iterations' % solver.iterations())
        print('Problem solved in %d branch-and-bound nodes' % solver.nodes())
    else:
        print('The problem does not have an optimal solution.')


def round_nearest_hundred(a: int):
    return round(a / 100) * 100


if __name__ == '__main__':
    main()