递归函数中的Python参数

Question

I am trying to implement a recursive function to solve a 3-SAT problem as described in the this great Udacity course https://www.udacity.com/course/cs313 I am new of Python programming and I have noticed a behavior I find strange.

The fact is that when the recursive3SatSolver ends returning None and the algorithm backtracks to a new branch the solution variable (passed as parameter at each iteration) is not set to the previous state but remains with the latest value (the one modified within the ended function)

it behaves as if the parameter was passed by reference and not by value

def solve_3SAT(num_variables, clauses):
    solution = [-1]*(num_variables+1)
    satisfiedClauses = [0]*len(clauses)
    for i in range(0, num_variables+1):
        positive = False
        negative = False
        for idClause,clause in enumerate(clauses):
            positive = positive or (i in clause)
            negative = negative or (-i in clause)
        candidate = positive ^ negative
        for idClause,clause in enumerate(clauses):
            if i in clause:
                if candidate:
                    satisfiedClauses[idClause]=1
        if candidate:
            if positive:
                solution[i]=1
            else:
                solution[i]=0
    solution[0]=0
    print 'preprocessing: ',solution
    solution = recursive3SatSolver(num_variables,solution,clauses)
    if solution != None:
        for idS,s in enumerate(solution):
            if solution[idS]<0:
                solution[idS]=0
    return solution    

def recursive3SatSolver(num_variables, solution, clauses):
    if is_satisfiable(clauses,solution)==False:
        return None
    satisfiedClauses = satisfied_clauses(clauses,solution)
    for idC,sat in enumerate(satisfiedClauses):
        if sat == 0:
            chosenClause=idC
            clause = clauses[chosenClause]
            for idVar,var in enumerate(clause):
                absVar = abs(var)
                if solution[absVar]<0:
                    value=-1
                    if var>0:
                        value=1
                    else:
                        value=0
                    solution[absVar]=value
                    if is_satisfied(num_variables,clauses,solution):
                        return solution
                    else:
                        finalSolution = recursive3SatSolver(num_variables,solution,clauses)
                        if finalSolution!=None:
                            #print 'returning ...'
                            return finalSolution
                        else:
                            print 'changing branch: ',solution,'=>'
                            solution[absVar]=1-solution[absVar]
                            continue
            print 'finished possibilities for this clause'        
            return None

    if is_satisfied(num_variables,clauses,solution):
        return solution
    else:
        print 'no more clauses'
        return None

def satisfied_clauses(clauses,assignment):
    satisfiedClauses= [0]*len(clauses)
    for idClause,clause in enumerate(clauses):
        if is_clause_satisfied(clause,assignment):
            satisfiedClauses[idClause]=1
    return satisfiedClauses

def is_satisfiable(clauses, assignment):
    for clause in clauses:
        if is_clause_satisfiable(clause,assignment):
            continue
        else:
            return False
    return True

def is_clause_satisfiable(clause,assignment):
    sat = is_clause_satisfied(clause,assignment)
    if sat :
        return True
    else:
        for idVar, var in enumerate(clause):
            absVar = abs(var)
            if assignment[absVar]==-1:
                return True
        return False

def is_clause_satisfied(clause,assignment):
    for idVar,var in enumerate(clause):
        absVar = abs(var)
        if assignment[absVar]<0:
            continue
        if var>0:
            if assignment[absVar]==1:
                return True
        else:
            if assignment[absVar]==0:
                return True
    return False

def is_satisfied(num_variables, clauses, assignment):
    if assignment==None:
        return False
    check=True
    for clause in clauses:
        clauseVal = False;
        for var in clause:
            val=False;
            if var<0:
                val = not assignment[abs(var)]
            else:
                val = assignment[var]
            clauseVal = clauseVal or val
        check = check and clauseVal
    return check

def test():
    clauses = [[-2, -3, -1], [3, -2, 1], [-3, 2, 1],
               [2, -3, -1], [3, -2, 1], [3, -2, 1]]
    solutions = [[0, 0, 0, 0],
                 [0, 0, 1, 1],
                 [0, 1, 0, 0],
                 [0, 1, 1, 0],
                 [1, 0, 0, 0],
                 [1, 0, 1, 1],
                 [1, 1, 0, 0],
                 [1, 1, 1, 0]]
    assert solve_3SAT(3,clauses) in solutions

    clauses = [[2, 1, 3], [-2, -1, 3], [-2, 3, -1], [-2, -1, 3],
               [2, 3, 1], [-1, 3, -2], [-3, 2, 1], [1, -3, -2],
               [-2, -1, 3], [1, -2, -3], [-2, -1, 3], [-1, -2, -3],
               [3, -2, 1], [2, 1, 3], [-3, -1, 2], [-3, -2, 1],
               [-1, 3, -2], [1, 2, -3], [-3, -1, 2], [2, -1, 3]]
    assert solve_3SAT(3,clauses) == None
    print 'Tests passed'

clauses = [[2, 1, 3], [-2, -1, 3], [-2, 3, -1], [-2, -1, 3],
               [2, 3, 1], [-1, 3, -2], [-3, 2, 1], [1, -3, -2],
               [-2, -1, 3], [1, -2, -3], [-2, -1, 3], [-1, -2, -3],
               [3, -2, 1], [2, 1, 3], [-3, -1, 2], [-3, -2, 1],
               [-1, 3, -2], [1, 2, -3], [-3, -1, 2], [2, -1, 3]]
assert solve_3SAT(3,clauses) == None
print 'Tests passed'

UPDATE I have been wondering why I have needed some time to get this. And I have understood the reason is that I was used to program back tracking on boolean clauses/predicates in Prolog where the variables are automatically set to the previous step when a branch fail.

Answer 1

it behaves as if the parameter was passed by reference and not by value

Every object is passed by reference in Python. In your case if solution is a list you should probably make a copy of it.

Some methods you can use:

>>> l = [0,1,2]
>>> list(l) # creates a new list from the old one
[0, 1, 2]
>>> l[:] # slices also create a new object
[0, 1, 2]
>>> import copy
>>> copy.deepcopy(l) # create a deep copy of the object
[0, 1, 2]
>>> [i for i in l] # manually copy an object
[0, 1, 2]

My preferred way is to use the list(...) constructor.