<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 {
    string res;
    int cur_max = -1;
    
    bool IsValidH(string cur){
        int val = atoi(cur.c_str());
        if(val > 23) return false;
        return true;
    }
    bool IsValidM(string cur){
        int val = atoi(cur.c_str());
        if(val > 59) return false;
        return true;
    }

    int GetSec(string H, string M){
        return atoi(H.c_str())*60 + atoi(M.c_str());
    }

    void check(string cur){
        // hour
        string sH = cur.substr(0,2);
        string sM = cur.substr(2,2);
        
        if( (!IsValidH(sH)) || (!IsValidM(sM))) return;
        
        int curSec = GetSec(sH, sM);
        if( curSec > cur_max){
            cur_max = curSec;
            res = sH + ":" +sM;
        }
        
    }
    
    void helper(vector<int>& arr, vector<int>& visited, string cur){
        if(cur.length() == 4){
            check(cur);
            return;
        }
        
        for(int i = 0;i<4;i++){
            if(visited[i] == 1) continue;
            visited[i] = 1;
            helper(arr, visited, cur + to_string(arr[i]));
            visited[i] = 0;
        }
    }
    
public:
    string largestTimeFromDigits(vector<int>& arr) {
        res = "";
        
        string cur = "";
        vector<int> visited(4, 0);
        helper(arr, visited, cur);
        
        return res;
    }
};
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