<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:
    bool isValid(string s) {
        int hour = stoi(s.substr(0, 2));
        int minute = stoi(s.substr(2, 2));
        return hour < 24 && minute < 60;
    }

    void createPermutations(vector<int>& arr, int ind, int curr_time, string temp, string& ans) {
        if (ind == 4) {
            if (isValid(temp) && curr_time > time) {
                time = curr_time;
                ans = temp;
            }
            return;
        }

        for (int i = ind; i < 4; i++) {
            swap(arr[i], arr[ind]);

            int ind_time = curr_time;
            if (ind == 0) ind_time += arr[0] * 60 * 10;
            else if (ind == 1) ind_time += arr[1] * 60;
            else if (ind == 2) ind_time += arr[2] * 10;
            else if (ind == 3) ind_time += arr[3];

            createPermutations(arr, ind + 1, ind_time, temp + to_string(arr[ind]), ans);

            swap(arr[i], arr[ind]);
        }
    }

    int time = -1;
    string largestTimeFromDigits(vector<int>& arr) {
        string ans = "";
        createPermutations(arr, 0, 0, "", ans);
        if (ans.length() == 4) {
            ans.insert(2, ":");
        }
        return ans;
    }
};

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