> For the complete documentation index, see [llms.txt](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/tree/331.-verify-preorder-serialization-of-a-binary-tree.md).

# 331. Verify Preorder Serialization of a Binary Tree

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 `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:**

```
Input: "9,3,4,#,#,1,#,#,2,#,6,#,#"
Output: true
```

**Example 2:**

```
Input: "1,#"
Output: false
```

**Example 3:**

```
Input: "9,#,#,1"
Output: false
```

{% hint style="info" %}
preorder字串的最後一個一定是#，且井字號的數量比數字數量多1。
{% endhint %}

```cpp
bool isValidSerialization(string preorder) { // time: O(n); space: O(n)
    istringstream in(preorder);
    vector<string> v;
    string buf;
    int cnt = 0;
    while (getline(in, buf, ',')) v.push_back(buf);
    for (int i = 0; i < v.size() - 1; ++i) {
        if (v[i] == "#") {
            if (cnt == 0) return false;
            --cnt;
        } else {
            ++cnt;
        }
    }
    return cnt == 0 && v.back() == "#";
}
```

```cpp
bool isValidSerialization(string preorder) { // time: O(n); space: O(1)
    istringstream in(preorder);
    string buf;
    int degree = 1; // the number of # can be accommodated
    bool degree_is_zero = false;
    while (getline(in, buf, ',')) {
        if (degree_is_zero) return false;
        if (buf == "#") {
            if (--degree == 0) degree_is_zero = true;
        } else ++degree;
    }
    return degree == 0;
}
```

```cpp
bool isValidSerialization(string preorder) { // time: O(n); space: O(1)
    int capacity = 1; // the number of # can be accommodated
    preorder += ",";
    for (int i = 0; i < preorder.length(); ++i) {
        if (preorder[i] != ',') continue;
        if (--capacity < 0) return false;
        if (preorder[i - 1] != '#') capacity += 2;
    }
    return capacity == 0;
}
```