[LeetCode] Restore IP Addresses

[Problem]

Given a string containing only digits, restore it by returning all possible valid IP address combinations.

For example:
Given "25525511135",

return ["255.255.11.135", "255.255.111.35"]. (Order does not matter)

[Analysis]
（1）合法的IP所有数字的长度不超过12，对于超过12的字符串，直接判为非法；
（2）对于长度小于等于12的字符串，枚举每一位的长度，每一位的长度为1~3；
（3）每一位除了单独为0外，不能以0开头；

[Solution]

class Solution {
public:
    // is s valid for a part of IP
    bool valid(string s){
        // empty string
        if(s.length() == 0){
            return false;
        }
        else if(s.length() > 1 && s[0] == '0'){
            return false;
        }
   
        // non-empty string
        int val = 0;
        for(int i = 0; i < s.length(); ++i){
            val = val * 10 + (s[i] - '0');
        }
   
        // valid
        if(val <= 255){
            return true;
        }
        else{
            return false;
        }
    }
   
    // restore IP addresses
    vector<string> restoreIpAddresses(string s, int nth){
        vector<string> res;
   
        // invalid string
        if(s.length() > (5 - nth) * 3){
            return res;
        }
   
        // the last value
        if(nth == 4){
            if(valid(s)){
                res.push_back(s);
            }
        }
        else{
            // the length of each part should between 1 and 3
            for(int i = 1; i <= 3 && i <= s.length(); ++i){
                string str = s.substr(0, i);
   
                // invalid
                if(!valid(str))continue;
   
                // search
                vector<string> r = restoreIpAddresses(s.substr(i, s.length()-i), nth+1);
                for(int j = 0; j < r.size(); ++j){
                    res.push_back(str + "." + r[j]);
                }
            }
        }
        return res;
    }
   
    // restore IP addresses
    vector<string> restoreIpAddresses(string s) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        return restoreIpAddresses(s, 1);
    }
};

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