<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:
    struct DPValidAddress
{
    set<string> firstSubset;
    set<string> secondSubset;
    set<string> thirdSubset;
    set<string> forthSubset;
};

void printSubnet(std::set<string> subnet)
{
  for_each(subnet.begin(), subnet.end(), [](string str){
      std::cout << str << "    " ;
      });
  std::cout << std::endl;
}
void updateNewSubnet(set<string>& vecSubnetUpdate, const set<string> vecNxtSubnet, char ch)
{
    for_each(vecNxtSubnet.begin(), vecNxtSubnet.end(), [&](const string& subnet) {
        string str(1,ch);
        string strCheck(str);
        int nIdx = subnet.find('.');
        if(nIdx > 0)
        {
          strCheck.append(subnet.substr(0, nIdx));
        }
        else
        {
          strCheck.append(subnet);
        }
        stringstream stream(strCheck);
        int nSubnet;
        stream >> nSubnet;
        if (nSubnet <= 255)
        {
          str.append(subnet);
          vecSubnetUpdate.insert(str);
        }
    });
}

void addNewSubnet(set<string>& vecSubnetUpdate, const set<string>& vecDiagSubnet, char ch)
{
    for_each(vecDiagSubnet.begin(), vecDiagSubnet.end(), [&](string subnet) {
         string str{ch};
         str.append(".");
         str.append(subnet);
         vecSubnetUpdate.insert(str);
    });
}

void recuseValidIPAddr(char ch, vector<DPValidAddress>& vecDP, int nIdx)
{
    set<string> vecNxt;
    set<string> vecDiag;
    //populating firstSubset
    {
        vecNxt = vecDP[nIdx +1].firstSubset;
        //std::cout << "Populating first Subset of Index " << nIdx << " with char value " << ch <<  std::endl;
        updateNewSubnet(vecDP[nIdx].firstSubset, vecNxt, ch);
        //printSubnet(vecDP[nIdx].firstSubset);
    }
    //populating secondSubset
    {
        vecNxt = vecDP[nIdx +1].secondSubset;
        vecDiag = vecDP[nIdx +1].firstSubset;
        //std::cout << "Populating second Subset of Index " << nIdx << " with char value " << ch <<  std::endl;
        addNewSubnet(vecDP[nIdx].secondSubset, vecDiag, ch);
        updateNewSubnet(vecDP[nIdx].secondSubset, vecNxt, ch);
        //printSubnet(vecDP[nIdx].secondSubset);
    }
    //populating thirdSubset
    {
        vecNxt = vecDP[nIdx +1].thirdSubset;
        vecDiag = vecDP[nIdx +1].secondSubset;
        //std::cout << "Populating third Subset of Index " << nIdx << " with char value " << ch <<  std::endl;
        addNewSubnet(vecDP[nIdx].thirdSubset, vecDiag, ch);
        updateNewSubnet(vecDP[nIdx].thirdSubset, vecNxt, ch);
        //printSubnet(vecDP[nIdx].thirdSubset);
    }
    //populating forthSubset
    {
        vecNxt = vecDP[nIdx +1].forthSubset;
        vecDiag = vecDP[nIdx +1].thirdSubset;
        //std::cout << "Populating forth Subset of Index " << nIdx << " with char value " << ch <<  std::endl;
        addNewSubnet(vecDP[nIdx].forthSubset, vecDiag, ch);
        updateNewSubnet(vecDP[nIdx].forthSubset, vecNxt, ch);
        //printSubnet(vecDP[nIdx].forthSubset);
    }
}

std::vector<std::string> restoreIpAddresses(std::string s) {
    std::vector<DPValidAddress> vecDP;
    vecDP.resize(s.size());
    //std::cout << "input value is " << s << std::endl;
    string str{s[s.size()-1]};
    //std::cout << str <<std::endl;
    vecDP[s.size()-1].firstSubset.insert(str);
    for (int nIdx = s.size() -2; nIdx >= 0; nIdx--)
    {
        recuseValidIPAddr(s[nIdx], vecDP, nIdx);
    }
    std::vector<string> retResult;
    
    std::copy_if(vecDP[0].forthSubset.begin(), vecDP[0].forthSubset.end(), std::back_inserter(retResult), [](const std::string& sIPAddr)
    {
        stringstream stream(sIPAddr);
        string intermediate;
        while(getline(stream, intermediate, '.'))
        {
            if (intermediate.size() != 1 && intermediate[0] == '0')
            {
                return false;
            }
        }
        return true;
    });
    
    return retResult;
}
};
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