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

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。

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() == "#";
}

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;
}

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;
}