<p>A <strong>valid IP address</strong> consists of exactly four integers separated by single dots. Each integer is between <code>0</code> and <code>255</code> (<strong>inclusive</strong>) and cannot have leading zeros.</p>

<ul>
	<li>For example, <code>&quot;0.1.2.201&quot;</code> and <code>&quot;192.168.1.1&quot;</code> are <strong>valid</strong> IP addresses, but <code>&quot;0.011.255.245&quot;</code>, <code>&quot;192.168.1.312&quot;</code> and <code>&quot;192.168@1.1&quot;</code> are <strong>invalid</strong> IP addresses.</li>
</ul>

<p>Given a string <code>s</code> containing only digits, return <em>all possible valid IP addresses that can be formed by inserting dots into </em><code>s</code>. You are <strong>not</strong> allowed to reorder or remove any digits in <code>s</code>. You may return the valid IP addresses in <strong>any</strong> order.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;25525511135&quot;
<strong>Output:</strong> [&quot;255.255.11.135&quot;,&quot;255.255.111.35&quot;]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;0000&quot;
<strong>Output:</strong> [&quot;0.0.0.0&quot;]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;101023&quot;
<strong>Output:</strong> [&quot;1.0.10.23&quot;,&quot;1.0.102.3&quot;,&quot;10.1.0.23&quot;,&quot;10.10.2.3&quot;,&quot;101.0.2.3&quot;]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 20</code></li>
	<li><code>s</code> consists of digits only.</li>
</ul>

class Solution {
public:
    void solve(int index , string &s , string &path , vector<string>&ans, int cnt)
    {
        int n = s.size();
        if(index == n && cnt == 4)
        {
            path.pop_back();
            ans.push_back(path);
            return;
        }
        if(index==n) return;

        //pick one digit   
        path.push_back(s[index]);
        path.push_back('.');
        solve(index+1 , s , path , ans , cnt+1);
        path.pop_back();
        if(path.size() > 0)
        path.pop_back();

        //pick two digit
        if(index+1 < n)
        {
            int num = stoi(s.substr(index , 2));
            if(num>=10 && num <= 99)
            {
                string sub = s.substr(index , 2);
                string temp = path;
                path+=sub;
                path.push_back('.');
                solve(index+2 , s , path ,ans , cnt+1);
                path = temp;
            }
        }
        //pick three digit
        if(index+2 < n)
        {
            int num = stoi(s.substr(index , 3));
            if(num>=100 && num <= 255)
            {
                string sub = s.substr(index , 3);
                string temp = path;
                path+=sub;
                path.push_back('.');
                solve(index+3 , s , path ,ans , cnt+1);
                path = temp;
            }
        }
    }
    vector<string> restoreIpAddresses(string s) {
        int n = s.size();
        string path = "";
        vector<string>ans;
        int cnt = 0 ;
        solve(0 , s , path , ans , cnt);
        return ans;   
    }
};
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