<p>Given an array of digits <code>digits</code>, return <em>the largest multiple of <strong>three</strong> that can be formed by concatenating some of the given digits in <strong>any order</strong></em>. If there is no answer return an empty string.</p>

<p>Since the answer may not fit in an integer data type, return the answer as a string. Note that the returning answer must not contain unnecessary leading zeros.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> digits = [8,1,9]
<strong>Output:</strong> &quot;981&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> digits = [8,6,7,1,0]
<strong>Output:</strong> &quot;8760&quot;
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> digits = [1]
<strong>Output:</strong> &quot;&quot;
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= digits.length &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= digits[i] &lt;= 9</code></li>
</ul>

class Solution {
public:
    string largestMultipleOfThree(vector<int>& d) {
        sort(d.rbegin(),d.rend());
        int n=d.size();
        if(d[0]==0)
            return "0";
        vector<vector<int>> dp(n+1,vector<int> (3,-1));
        function<int(int,int)> fx=[&](int i,int j){
            if(dp[i][j]!=-1)
                return dp[i][j];
            if(i==n){
                if(!j)
                    return dp[i][j]=0;
                return dp[i][j]=-1e7;
            }
            int ans=fx(i+1,j);
            ans=max(ans,fx(i+1,(j+d[i])%3)+1);
            return dp[i][j]=ans;
        };
        fx(0,0);
        if(!fx(0,0))
            return "";
        string ans;
        int m=0;
        // cout<<fx(0,0)<<" ";
        for(int i=0;i<n;i++){
            //take
            // cout<<d[i]<<" ";
            int  x=dp[i+1][(m+d[i])%3];
            int y=dp[i+1][m];
            if(y>x+1)
                continue;
            ans.push_back(d[i]+'0'),m=(m+d[i])%3;
        }
        if(ans[0]=='0')
            return "0";
        return ans;
    }
};
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