One way to serialize a binary tree is to use pre-order traversal. When we encounter a non-null node, we record the node’s value. If it is a null node, we record using a sentinel value such as #.

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     _9_
    /   \
   3     2
  / \   / \
 4   1  #  6
/ \ / \   / \
# # # #   # #

For example, the above binary tree can be serialized to the string “9,3,4,#,#,1,#,#,2,#,6,#,#”, where # represents a null node.

Given a string of comma separated values, verify whether it is a correct preorder traversal serialization of a binary tree. Find an algorithm without reconstructing the tree.

Each comma separated value in the string must be either an integer or a character ‘#’ representing null pointer.

You may assume that the input format is always valid, for example it could never contain two consecutive commas such as “1,,3”.

Example 1:

“9,3,4,#,#,1,#,#,2,#,6,#,#” Return true

Example 2:

“1,#” Return false

Example 3:

“9,#,#,1” Return false

Solution

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class Solution(object):
    def isValidSerialization(self, preorder):
        """
        :type preorder: str
        :rtype: bool
        """
        nodes = preorder.split(",")
        print nodes
        diff=1
        for i in range(len(nodes)):
            diff -= 1
            if diff < 0:
                return False

            if nodes[i] != '#':
                diff += 2
        print diff
        if diff == 0:
            return True
        else:
            return False
if __name__ == "__main__":
    sol = Solution()
    print(sol.isValidSerialization("9,3,4,#,#,1,#,#,2,#,6,#,#"))