<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"));
    }

    void helper(const string& s, int startIndex, vector<int>& dots,
                vector<string>& ans) {
        const int remainingLength = s.length() - startIndex;
        const int remainingNumberOfIntegers = 4 - dots.size();

        if (remainingLength > remainingNumberOfIntegers * 3 ||
            remainingLength < remainingNumberOfIntegers) {
            return;
        }
        if (dots.size() == 3) {
            if (valid(s, startIndex, remainingLength)) {
                string temp;
                int last = 0;
                for (int dot : dots) {
                    temp.append(s.substr(last, dot));
                    last += dot;
                    temp.append(".");
                }
                temp.append(s.substr(startIndex));
                ans.push_back(temp);
            }
            return;
        }
        for (int curPos = 1; curPos <= 3 && curPos <= remainingLength;
             ++curPos) {
            // Append a dot at the current position.
            dots.push_back(curPos);
            // Try making all combinations with the remaining string.
            if (valid(s, startIndex, curPos)) {
                helper(s, startIndex + curPos, dots, ans);
            }
            // Backtrack, i.e. remove the dot to try placing it at the next
            // position.
            dots.pop_back();
        }
    }

public:
    vector<string> restoreIpAddresses(string s) {
        vector<int> dots;
        vector<string> ans;
        helper(s, 0, dots, ans);
        return ans;
    }
};
8730