Serialize and Deserialize Binary Tree

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
/*
Logic:
step1: We will traverse the tree levelwise using BFS in serialize function and store in string.
while stroing tree in string,we will give one space between every node and "null" for NULL node.

step2: In deserialize function,we will store the nodes into vector of string and pass to fun.
fun will traverse the tree levelwise using BFS and push the elements into tree.
*/
class Codec {
public:
    string serialize(TreeNode* root) {
        if(!root) return "";
        deque<TreeNode*> q;
        q.push_back(root);
        string res="";
        while(!q.empty()){
            int k=q.size();
            for(int i=0;i<k;i++){
                TreeNode* temp=q.front();
                q.pop_front();
                if(!temp){
                    res+="null ";
                }
                else{
                    res+=to_string(temp->val);
                    res+=" ";
                    q.push_back(temp->left);
                    q.push_back(temp->right);
                }
            }
        }
        return res;


    }
    int _stoi(string s){
        int ans=0,i=0;
        bool sign=false;
        if(s[i]=='-'){ sign=true;i++;}
        while(i<s.size()){
            ans=ans*10+(s[i++]-'0');
        }
        if(sign) ans=-ans;
        return ans;
    }
    TreeNode* fun(vector <string> arr){
        if(arr.size()==0) return NULL;
        deque<TreeNode*> q;
        TreeNode* res=new TreeNode(_stoi(arr[0]));
        q.push_back(res);
        int i=1;
        while(!q.empty()){
            int k=q.size();
            for(int j=0;j<k;j++){
                TreeNode* temp=q.front();
                q.pop_front();
                if(arr[i]!="null"){
                    temp->left=new TreeNode(_stoi(arr[i++]));
                    q.push_back(temp->left);
                }
                else i++;
                if(arr[i]!="null"){
                    temp->right=new TreeNode(_stoi(arr[i++]));
                    q.push_back(temp->right);
                }
                else i++;
            }
        }
        return res;
    }

    TreeNode* deserialize(string s) {
        if(s=="") return NULL;
        vector <string> arr;
        int i=0;
        while(i<s.size()){
            if(s[i]=='n'){ arr.push_back("null"); i+=5;}
            else if(s[i]=='-' || isdigit(s[i])){   //number can be negative also
                bool sign=false;
                if(s[i]=='-'){ sign=true;i++;}
                string val="";
                while(isdigit(s[i])){
                    val+=s[i++];
                }
                if(sign) val="-"+val;
                arr.push_back(val);
                i++;
            }
        }
        return fun(arr);
    }
};