<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:
    int max_time=INT_MIN;
    string ans="";

    int getTime(string res){
        int first = res[0] - '0';
        int second = res[1] - '0';
        int third = res[2] - '0';
        int fourth = res[3] - '0';

        int hours = first * 10 +second;
        int minutes = third * 10 + fourth;

        if(hours > 23 or minutes > 59) return INT_MIN;
        return hours * 60 + minutes;
    }
    void solve(vector<int> &arr, string res, vector<bool> &visited){
        if(visited[0] && visited[1] && visited[2] && visited[3]){
            int current_time = getTime(res);
            if(current_time >  max_time){
                max_time = current_time;
                ans = res;
            }
            return;
        }
        for(int i=0;i<4; i++){
            if(!visited[i]){
                visited[i] = true;
                res += to_string(arr[i]);
                solve(arr, res, visited);
                if(ans != "") return;
                visited[i] = false;
                res.pop_back();
            }
        }
    }
    string largestTimeFromDigits(vector<int>& arr) {
        sort(arr.begin(), arr.end(), greater<int>());
        vector<bool> visited(4, false);
        solve(arr, "", visited);
        if(ans != ""){
            return ans.substr(0,2) + ":" + ans.substr(2);
        }
        return ans;
    }
};
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