<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:
  vector<string> restoreIpAddresses(const string& s) {
    vector<string> ans;
    dfs(s, 0, {}, ans);
    return ans;
  }

 private:
  void dfs(const string& s, int start, vector<string>&& path,
           vector<string>& ans) {
    if (path.size() == 4 && start == s.length()) {
      ans.push_back(path[0] + "." + path[1] + "." + path[2] + "." + path[3]);
      return;
    }
    if (path.size() == 4 || start == s.length())
      return;

    for (int length = 1; length <= 3; ++length) {
      if (start + length > s.length())
        return;  // out-of-bounds
      if (length > 1 && s[start] == '0')
        return;  // leading '0'
      const string& num = s.substr(start, length);
      if (stoi(num) > 255)
        return;
      path.push_back(num);
      dfs(s, start + length, std::move(path), ans);
      path.pop_back();
    }
  }
};
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