<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 valid(const string& s, int left, int right) {
        if (left >= s.size()) {
            return false;
        }
        if (right < left) {
            return false;
        }
        if (right - left >= 3) {
            return false;
        }
        if (right - left == 2) {
            if (s[left] == '0') {
                return false;
            }
            if (s[left] >= '3') {
                return false;
            }
            if (s[left] == '2') {
                if (s[left + 1] >= '6') {
                    return false;
                } else if (s[left+1] == '5') {
                    if (s[right] >= '6'){
                        return false;
                    }
                }
            }
        }
        if (right - left == 1) {
            if (s[left] == '0') {
                return false;
            }
        }
        return true;
    }

    string construct(const string& s, vector<int>& dots) {
        string ans;
        size_t dot_idx = 0;
        for (int i=0; i < s.size(); i++) {
            ans.push_back(s[i]);
            if (dot_idx < dots.size() && dots[dot_idx] == i) {
                ans.push_back('.');
                dot_idx++;
            }
        }
        return ans;
    }

    void placedots(int start_idx, vector<int>& positions_before_dot, const string& s, vector<string>& ans) {

        if (positions_before_dot.size() == 3) {
            if (valid(s, positions_before_dot.back() + 1, s.size() - 1)) {
                ans.push_back(construct(s, positions_before_dot));
            }
            return;
        }

        for (int i=start_idx; i < s.size() && i <= (start_idx + 2); i++) {
            if (valid(s, start_idx, i)) {
                positions_before_dot.push_back(i);
                placedots(i + 1, positions_before_dot, s, ans);
                positions_before_dot.pop_back();
            }
        }
    }


    vector<string> restoreIpAddresses(string s) {
        if (s.size() <= 3) {
            return {};
        }
        vector<int> dots;
        vector<string> ans;
        placedots(0, dots, s, ans);
        return ans;
    }
};
8313