<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>

vector<vector<int>> permutations;

void perms(vector<int>& indices, int count){
    if(count == 3){
        permutations.push_back(indices);
    } else {
        perms(indices, count + 1);
        for(int i = count + 1; i < indices.size(); i++){
            swap(indices[count], indices[i]);
            perms(indices, count + 1);
            swap(indices[count], indices[i]);
        }
    }
}

class Solution {
public:
    string largestTimeFromDigits(vector<int>& arr) {
        
        auto isValid = [&arr](vector<int>& permutations) -> bool {
            return arr[permutations[2]] < 6 &&
                (arr[permutations[0]] * 10 + arr[permutations[1]] < 24);
        };

        vector<int> indices = {0,1,2,3};
        perms(indices, 0);

        string ans = "";
        for(int i = 0; i < permutations.size(); i++){
            if(isValid(permutations[i])){
                auto& p = permutations[i];
                string candidate =  
                    to_string(arr[p[0]]) +
                    to_string(arr[p[1]]) +
                    ":" +
                    to_string(arr[p[2]]) +
                    to_string(arr[p[3]]);
                ans = max(ans, candidate);
            }
        }

        return ans;
    }
};
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