<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 {
    bool valid(const string& s, int start, int length) {
        return length == 1 ||
               (s[start] != '0' &&
                (length < 3 || s.substr(start, length) <= "255"));
    }

public:
    vector<string> restoreIpAddresses(string s) {
        vector<string> ans;
        int length = s.length();
        for (int len1 = max(1, length - 9); len1 <= 3 && len1 <= length - 3;
             ++len1) {
            if (!valid(s, 0, len1)) {
                continue;
            }
            for (int len2 = max(1, length - len1 - 6);
                 len2 <= 3 && len2 <= length - len1 - 2; ++len2) {
                if (!valid(s, len1, len2)) {
                    continue;
                }
                for (int len3 = max(1, length - len1 - len2 - 3);
                     len3 <= 3 && len3 <= length - len1 - len2 - 1; ++len3) {
                    if (valid(s, len1 + len2, len3) &&
                        valid(s, len1 + len2 + len3,
                              length - len1 - len2 - len3)) {
                        ans.push_back(s.substr(0, len1) + "." +
                                      s.substr(len1, len2) + "." +
                                      s.substr(len1 + len2, len3) + "." +
                                      s.substr(len1 + len2 + len3));
                    }
                }
            }
        }
        return ans;
    }
};
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