<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>

#include <string>
#include <vector>
class Solution {
public:
    string largestMultipleOfThree(vector<int>& digits) {
        int freq[10] = { 0 };
        int total = 0;
        for(const int d : digits){
            ++freq[d];
            total += d;
        }
        if(total % 3 == 1){
            bool satisfied = false;
            for(int i = 1; i < 10 && !satisfied; i += 3){
                if(freq[i] && !satisfied){
                    --freq[i];
                    satisfied = true;
                }
            }
            int count = 2;
            for(int i = 2; i < 10 && !satisfied; i += 3){
                if(freq[i] && !satisfied){
                    --freq[i];
                    --count;
                    satisfied = !count;
                }
                if(freq[i] && !satisfied){
                    --freq[i];
                    --count;
                    satisfied = !count;
                }
            }
        }
        if(total % 3 == 2){
            bool satisfied = false;
            for(int i = 2; i < 10 && !satisfied; i += 3){
                if(freq[i] && !satisfied){
                    --freq[i];
                    satisfied = true;
                }
            }
            int count = 2;
            for(int i = 1; i < 10 && !satisfied; i += 3){
                if(freq[i] && !satisfied){
                    --freq[i];
                    --count;
                    satisfied = !count;
                }
                if(freq[i] && !satisfied){
                    --freq[i];
                    --count;
                    satisfied = !count;
                }
            }
        }
        int sz = 0;
        for(int i = 0; i < 10; ++i){
            sz += freq[i];
        }
        std::string result(sz, '0');
        auto pos = result.begin();
        for(int i = 9; i >= 0; --i){
            //if(freq[i] > 0){
                std::fill(pos, pos + freq[i], '0' + i);
            //}
            pos += freq[i];
            //result += std::string(freq[i], '0' + i);
        }
        if(!result.empty() && result[0] == '0'){
            result = "0";
        }
        return result;
    }
};
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