<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:
    string largestTimeFromDigits(vector<int>& arr) {
        vector<int> v(10,0);
        for(auto it:arr){
            v[it]++;
        }
        string ans="";
        for(int i=2;i>=0;i--){
            string curr="";
            if(v[i]>0){
                curr+=to_string(i);
                v[i]--;
            }
            else{
                continue;
            }
            if(i==2){
                for(int j=3;j>=0;j--){
                    if(v[j]>0){
                        curr+=to_string(j);
                        v[j]--;
                        curr+=':';
                        for(int k=5;k>=0;k--){
                            if(v[k]>0){
                                curr+=to_string(k);
                                v[k]--;
                                for(int l=9;l>=0;l--){
                                    if(v[l]>0){
                                        curr+=to_string(l);
                                        ans=max(ans,curr);
                                        curr.pop_back();
                                    }
                                }
                                curr.pop_back();
                                v[k]++;
                            }
                        }
                        curr.pop_back();
                        v[j]++;
                    }
                }
                curr.pop_back();
                v[i]++;
            }
            else if(i==0||i==1){
                for(int j=9;j>=0;j--){
                    if(v[j]>0){
                        curr+=to_string(j);
                        v[j]--;
                        curr+=':';
                        for(int k=5;k>=0;k--){
                            if(v[k]>0){
                                curr+=to_string(k);
                                v[k]--;
                                for(int l=9;l>=0;l--){
                                    if(v[l]>0){
                                        curr+=to_string(l);
                                        ans=max(ans,curr);
                                        curr.pop_back();
                                    }
                                }
                                curr.pop_back();
                                v[k]++;
                            }
                        }
                        curr.pop_back();
                        v[j]++;
                    }
                }
                curr.pop_back();
                v[i]++;
            }
        }
        return ans;
    }
};
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