# 【LeetCode】 Check If a String Is a Valid Sequence from Root to Leaves Path in a Binary Tree

## Description
> Given a binary tree where each path going from the root to any leaf form a valid sequence, check if a given string is a valid sequence in such binary tree.

> We get the given string from the concatenation of an array of integers `arr` and the concatenation of all values of the nodes along a path results in a sequence in the given binary tree.

> Constraints:
> * `1 <= arr.length <= 5000`
> * `0 <= arr[i] <= 9`
> * Each node's value is between [0 - 9].

> 給予一個二元樹，每個從樹根到樹葉的路徑都可以組成一段合法序列，檢查給予的字串是否和任意路徑的合法序列相同。

> 我們從整數陣列`arr`中得到給定的字串，且我們可以在二元樹中每個節點中的值組合起來得到一段序列。

> 限制：
> * `1 <= arr.length <= 5000`
> * `0 <= arr[i] <= 9`
> * 每個節點中的值介於 [0 - 9].

## Example:

Example 1:

Input: root = [0,1,0,0,1,0,null,null,1,0,0], arr = [0,1,0,1]
Output: true
Explanation: 
The path 0 -> 1 -> 0 -> 1 is a valid sequence (green color in the figure). 
Other valid sequences are: 
0 -> 1 -> 1 -> 0 
0 -> 0 -> 0



Example 2:

Input: root = [0,1,0,0,1,0,null,null,1,0,0], arr = [0,0,1]
Output: false 
Explanation: The path 0 -> 0 -> 1 does not exist, therefore it is not even a sequence.



Example 3:

Input: root = [0,1,0,0,1,0,null,null,1,0,0], arr = [0,1,1]
Output: false
Explanation: The path 0 -> 1 -> 1 is a sequence, but it is not a valid sequence.


## Solution

* 用DFS去跑每個路徑查看是否吻合即可。
* 成功條件：
* `arr`已經都配對完畢，且節點是樹葉。
* 剪枝條件：
* `arr`已經都配對完畢，但節點不是樹葉。
* 節點和`arr`不吻合。
* 節點不存在(`NULL`)

### Code

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    bool isValidSequence(TreeNode* root, vector<int>& arr) {
        if(!root) return false;
        if(root->val == arr[0])
        {
            if(arr.size() == 1)
            {
                if(!root->left && !root->right)
                    return true;
                return false;
            }
            vector<int> sub_arr(arr.begin() + 1, arr.end());
            return isValidSequence(root->left, sub_arr) ||
                   isValidSequence(root->right, sub_arr);
        }
        return false;
    }
};

###### tags: `LeetCode` `C++`