<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:
    void solve(int index,vector<int> &maxi,vector<int> &freq,vector<int> &ans,vector<int> temp){
        if(index==4){
            ans=temp;
            return;
        }
        if(index==1) {
            if(temp[0]==2)
                maxi[1]=3;
            else maxi[1]=9;
        }
        for(int i=maxi[index];i>=0;i--){
                if(freq[i]>0){
                    freq[i]--;
                    temp.push_back(i);
                    solve(index+1,maxi,freq,ans,temp);
                    if(ans.size()==4) return;

                    freq[i]++;
                    temp.pop_back();
            }
            }    
    }
    string largestTimeFromDigits(vector<int>& arr) {
        vector<int> freq(10,0);
        for(auto a:arr)
           freq[a]++;
        vector<int> maxi={2,9,5,9};
        vector<int> ans;
        solve(0,maxi,freq,ans,{});
        if(ans.size()!=4) return "";
        string res="";
        //res+=to_string(ans[0]*10+ans[1])+':'+to_string(ans[2]*10+ans[3]);
        res+=to_string(ans[0])+to_string(ans[1])+':'+to_string(ans[2])+to_string(ans[3]);
        return res;

    }
};
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