<p>Given an array <code>arr</code> of 4 digits, find the latest 24-hour time that can be made using each digit <strong>exactly once</strong>.</p>

<p>24-hour times are formatted as <code>&quot;HH:MM&quot;</code>, where <code>HH</code> is between <code>00</code> and <code>23</code>, and <code>MM</code> is between <code>00</code> and <code>59</code>. The earliest 24-hour time is <code>00:00</code>, and the latest is <code>23:59</code>.</p>

<p>Return <em>the latest 24-hour time in <code>&quot;HH:MM&quot;</code> format</em>. If no valid time can be made, return an empty string.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr = [1,2,3,4]
<strong>Output:</strong> &quot;23:41&quot;
<strong>Explanation:</strong> The valid 24-hour times are &quot;12:34&quot;, &quot;12:43&quot;, &quot;13:24&quot;, &quot;13:42&quot;, &quot;14:23&quot;, &quot;14:32&quot;, &quot;21:34&quot;, &quot;21:43&quot;, &quot;23:14&quot;, and &quot;23:41&quot;. Of these times, &quot;23:41&quot; is the latest.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr = [5,5,5,5]
<strong>Output:</strong> &quot;&quot;
<strong>Explanation:</strong> There are no valid 24-hour times as &quot;55:55&quot; is not valid.
</pre>

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

<ul>
	<li><code>arr.length == 4</code></li>
	<li><code>0 &lt;= arr[i] &lt;= 9</code></li>
</ul>

class Solution {
public:
    void dfs(set<int>& used, vector<string>& ans, string time, vector<int>& arr, bool H) {
        // for(auto u : used) cout << u << " ";
        cout << endl;
        if(used.size() == 4) ans.emplace_back(time);
        for(int i = 0; i < 4; i++) {
            if(used.count(i)) continue;
            for(int j = 0; j < 4; j++) {
                if(used.count(j)) continue;
                if(j == i) continue;
                used.insert(i);
                used.insert(j);
                if(H) {
                    if(arr[i] * 10 + arr[j] <= 24) dfs(used, ans, time + to_string(arr[i]) + to_string(arr[j]) + ":", arr, false);
                } else {
                    if(!(time[0] == '2' && time[1] == '4') && arr[i] * 10 + arr[j] <= 59) dfs(used, ans, time + to_string(arr[i]) + to_string(arr[j]), arr, false);
                }
                used.erase(i);
                used.erase(j);
            }
        }
    }
    string largestTimeFromDigits(vector<int>& arr) {
        sort(arr.begin(), arr.end());
        set<int> used;
        vector<string> ans;
        string time = "";
        dfs(used, ans, time, arr, true);
        if(ans.empty()) return "";
        sort(ans.begin(), ans.end());
        return ans.back();
    }
};
15000