prob.py

class Solution(object):
    def getProbability(self, balls):
        """
        :type balls: List[int]
        :rtype: float
        """

        trie =  {}

        newballs = balls + balls[0:-1]

        perBall = []
        stack = []

        for x in range(0, len(balls)):
            stack.append([[],len(perBall)])
            perBall += [x+1 for _ in range(balls[x])]


        newSeqList = []

        # DFS and create set of balls in box 1 which are uniq.
        # We do one box because, box 2 values can be induced by box 1
        # Uniq in the sense that the order doesn't matter only the amount of ball matter
        # [1,1,2] and [1,2,1] values in box 1 are considered same
        # [1,1,2] and [1,1,1] values in box 1 are considered different
        while stack:
            theSeq, newPointer = stack.pop()

            theSeq.append(perBall[newPointer])

            if len(theSeq) == (len(perBall) /2):
                newSeqList.append(theSeq)
                continue

            prev = None

            for i in range(newPointer, len(perBall) - 1):
                # Make new copy for the new seq
                newSeq = theSeq[:]
                 
                if prev == None or prev != perBall[i + 1]:
                    stack.append([newSeq, i+1])
                    prev = perBall[i + 1]


        for x in newSeqList:
            print('- ' + str(x))


s = Solution()

balls = [1,2,1]
# balls = [3,2,1]
s.getProbability(balls)