<p>You are given a list of airline <code>tickets</code> where <code>tickets[i] = [from<sub>i</sub>, to<sub>i</sub>]</code> represent the departure and the arrival airports of one flight. Reconstruct the itinerary in order and return it.</p>

<p>All of the tickets belong to a man who departs from <code>&quot;JFK&quot;</code>, thus, the itinerary must begin with <code>&quot;JFK&quot;</code>. If there are multiple valid itineraries, you should return the itinerary that has the smallest lexical order when read as a single string.</p>

<ul>
	<li>For example, the itinerary <code>[&quot;JFK&quot;, &quot;LGA&quot;]</code> has a smaller lexical order than <code>[&quot;JFK&quot;, &quot;LGB&quot;]</code>.</li>
</ul>

<p>You may assume all tickets form at least one valid itinerary. You must use all the tickets once and only once.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/14/itinerary1-graph.jpg" style="width: 382px; height: 222px;" />
<pre>
<strong>Input:</strong> tickets = [[&quot;MUC&quot;,&quot;LHR&quot;],[&quot;JFK&quot;,&quot;MUC&quot;],[&quot;SFO&quot;,&quot;SJC&quot;],[&quot;LHR&quot;,&quot;SFO&quot;]]
<strong>Output:</strong> [&quot;JFK&quot;,&quot;MUC&quot;,&quot;LHR&quot;,&quot;SFO&quot;,&quot;SJC&quot;]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/14/itinerary2-graph.jpg" style="width: 222px; height: 230px;" />
<pre>
<strong>Input:</strong> tickets = [[&quot;JFK&quot;,&quot;SFO&quot;],[&quot;JFK&quot;,&quot;ATL&quot;],[&quot;SFO&quot;,&quot;ATL&quot;],[&quot;ATL&quot;,&quot;JFK&quot;],[&quot;ATL&quot;,&quot;SFO&quot;]]
<strong>Output:</strong> [&quot;JFK&quot;,&quot;ATL&quot;,&quot;JFK&quot;,&quot;SFO&quot;,&quot;ATL&quot;,&quot;SFO&quot;]
<strong>Explanation:</strong> Another possible reconstruction is [&quot;JFK&quot;,&quot;SFO&quot;,&quot;ATL&quot;,&quot;JFK&quot;,&quot;ATL&quot;,&quot;SFO&quot;] but it is larger in lexical order.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= tickets.length &lt;= 300</code></li>
	<li><code>tickets[i].length == 2</code></li>
	<li><code>from<sub>i</sub>.length == 3</code></li>
	<li><code>to<sub>i</sub>.length == 3</code></li>
	<li><code>from<sub>i</sub></code> and <code>to<sub>i</sub></code> consist of uppercase English letters.</li>
	<li><code>from<sub>i</sub> != to<sub>i</sub></code></li>
</ul>

class Solution {
public:
    vector<string> findItinerary(vector<vector<string>>& tickets) {
        for (auto ticket : tickets)
        targets[ticket[0]].insert(ticket[1]);
        visit("JFK");
        return vector<string>(route.rbegin(), route.rend());
    }

    map<string, multiset<string>> targets;
    vector<string> route;

    void visit(string airport) {
        while (targets[airport].size()) {
            string next = *targets[airport].begin();
            targets[airport].erase(targets[airport].begin());
            visit(next);
        }
        route.push_back(airport);
    }
    
    vector<string> findItineraryTLE(vector<vector<string>>& tickets) {
        
        int ticket_size = tickets.size();
        
        unordered_map<string, deque<string>> um;
        vector<string> result;
        sort(tickets.rbegin(), tickets.rend());
        
        for(auto& each : tickets)
        {
            um[each[0]].emplace_back(each[1]);
        }
        
        
        
        
        string jfk = "JFK";
        
        result.push_back(jfk);
        
        DFS(um, jfk, result, tickets.size());
        
        return result;
    }
    
    bool DFS(unordered_map<string, deque<string>>& um, string& cur, vector<string>& result, int ticket_size)
    {
        if(result.size() == ticket_size+1)
        {
            return true;
        }
        
        if(!um.count(cur))
        {
            cout << cur << endl;
            return false;
        }
        
        auto copy_um = um;
        for(auto& u : copy_um[cur])
        {
            auto back = um[cur].back();
            um[cur].pop_back();
            result.push_back(back);
            
            if(DFS(um, back, result, ticket_size))
            {
                return true;
            }
            
            um[cur].push_front(back);
            result.pop_back();
        }
        return false;
    }
};

// JFK -> NRT, KUL
// NRT -> JFK


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