Test if a number is constructable from a set of numbers through arithmetic operations

construcable.py

class P:
    def __init__(self, value, mask, left, right, operation):
        self.value = value
        self.mask = mask
        self.left = left
        self.right = right
        self.operation = operation
        
        if self.left == None and self.right == None:
            self.expression = str(value)
        else:
            self.expression = "(" + self.left.expression + self.operation + self.right.expression + ")"
            
def generateExpressions(g, A):
    values = [(x, "0"*i + "1") for i, x in enumerate(A)]
    E = [P(x, "1" + "0"*i, None, None, None) for i, x in enumerate(A)]
    Q = [P(x, "1" + "0"*i, None, None, None) for i, x in enumerate(A)]
    goal = []
    
    while Q != []:
        a = Q.pop(0)
        if a.value == g:
            print(a.expression)
            goal.append(a)
            
        for b in E:
            if bin(int(a.mask, 2) & int(b.mask, 2))[2:] == "0": #We have not used a number twice
                newmask = bin(int(a.mask, 2) | int(b.mask, 2))[2:]
                
                #Addition
                c = P(a.value + b.value, newmask, a, b, "+")
                if (c.value, c.mask) not in values:
                    values.append((c.value, c.mask))
                    Q.append(c)
                    E.append(c)
                
                #Subtraction
                if a.value - b.value > 0:
                    c = P(a.value - b.value, newmask, a, b, "-")
                    if (c.value, c.mask) not in values:
                        values.append((c.value, c.mask))
                        Q.append(c)
                        E.append(c)
                
                #Multiplication
                c = P(a.value * b.value, newmask, a, b, "*")
                if (c.value, c.mask) not in values:
                    values.append((c.value, c.mask))
                    Q.append(c)
                    E.append(c)
                
                #Division
                if a.value % b.value == 0:
                    c = P(a.value // b.value, newmask, a, b, "/")
                    if (c.value, c.mask) not in values:
                        values.append((c.value, c.mask))
                        Q.append(c)
                        E.append(c)
                
    if goal == []:
        return 0
    
    v = []
    for x in goal:
        total = 0
        for i, y in enumerate(x.mask[::-1]):
            if y == "1":
                total += A[i]
        v.append(total)
    return min(v)