Questionnaire-2024/smt_and_z3/0005_sol.tex

\item \lect Complete the following python script with the necessary statements.

The final script should map each integer of a list of five integers to four possible colours such that the mapping returns different colours for adjacent integers.
% You need to declare and populate a z3 \texttt{Datatype}
% Furthermore, you need to create a list of five distinct integers and bound them.
% Finally, enforce the constraints on the uninterpreted function ....

  \begin{pythonSourceCode}
    from itertools import combinations
    from z3 import *

    solver = Solver()

    # Declare a Datatype and populate it with 4 colours.
    Colours = Datatype("Colours")
    Colours.declare("RED")
    Colours.declare("BLUE")
    Colours.declare("GREEN")
    Colours.declare("YELLOW")

    Colour = Colours.create()
    # Declare a function from integers to your custom datatype
    f    = Function('f', IntSort(), Colour)

    variables = list()
    for i in range(0,5):
        variables.append(Int(i))
        # Bound each integer i such that 0 <= i < 5

        solver.add(0 <= variables[-1])
        solver.add(variables[-1] <= 5)

    # Enfore that all i are distinct
    solver.add(Distinct(variables))


    # Enforce that colours are different for adjacent integers
    for combi in combinations(variables,2):
        solver.add(Implies(Abs(combi[0] - combi[1]) == 1, f(combi[0]) != f(combi[1])))


    result = solver.check()
    if result == sat:
        print(solver.model())
  \end{pythonSourceCode}