<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:
    bool isValid(string s) {
        return stoi(s) <= 255;
    }
    vector<string> addAll(string prefix, vector<string> v) {
        for (int i = 0; i<v.size(); i++) {
            if (v[i] == "") v[i] = prefix;
            else {
             v[i] = prefix + "." + v[i];
            }
        }
        return v;
    } 
    vector<string> restoreIpAddressesUtil(string &s, int index, int dotsLeft) {
        if (index == s.size() && dotsLeft == 0) return vector<string>(1, "");
        if (index == s.size()) return vector<string> ();
        vector<string> ans;
        if (s[index]!='0') {
            string cur = {s[index]};
            vector<string> v1 = addAll(cur, restoreIpAddressesUtil(s, index+1, dotsLeft-1));
            ans.insert(ans.end(), v1.begin(), v1.end());
            if (index+1<s.size()) {
                cur += s[index+1];
                vector<string> v2 = addAll(cur, restoreIpAddressesUtil(s, index+2, dotsLeft-1));
                ans.insert(ans.end(), v2.begin(), v2.end());
                if (index+2<s.size()) {
                    cur += s[index+2];
                    if (isValid(cur)) {
                       vector<string> v3 = addAll(cur, restoreIpAddressesUtil(s, index+3, dotsLeft-1));
            ans.insert(ans.end(), v3.begin(), v3.end());
                    }
                }
            }
        } else {
            string cur = {s[index]};
            vector<string> v1 = addAll(cur, restoreIpAddressesUtil(s, index+1, dotsLeft-1));
            ans.insert(ans.end(), v1.begin(), v1.end());
        }
        return ans;
    }
    vector<string> restoreIpAddresses(string s) {
        return restoreIpAddressesUtil(s, 0, 4);
    }
};
14158