Verify Preorder Serialization of a Binary Tree 问题及解法

问题描述：

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 #.

     _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 nullpointer.

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

示例:
"9,3,4,#,#,1,#,#,2,#,6,#,#"
Return true

"1,#"
Return false

"9,#,#,1"
Return false

问题分析：

本题给的树所有节点都有子节点，除了空节点外。那么我们就可以利用树的出度和入度的性质来求解该问题。

过程详见代码：

class Solution {public:    bool isValidSerialization(string preorder) {stringstream ss(preorder);vector<string> vs;while (!ss.eof()){string str;getline(ss, str, ',');vs.emplace_back(str);}int count = 1;for (auto node : vs){if (--count < 0)return false;if (node != "#") count += 2;}return count == 0;}};