Largest Multiple of Three
<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>
Greedy; Array; Math; Dynamic Programming; Sorting
func largestMultipleOfThree(digits []int) string {
	sort.Ints(digits)
	n := len(digits)
	const inf = 1 << 30
	f := make([][]int, n+1)
	for i := range f {
		f[i] = make([]int, 3)
		for j := range f[i] {
			f[i][j] = -inf
		}
	}
	f[0][0] = 0
	for i := 1; i <= n; i++ {
		for j := 0; j < 3; j++ {
			f[i][j] = max(f[i-1][j], f[i-1][(j-digits[i-1]%3+3)%3]+1)
		}
	}
	if f[n][0] <= 0 {
		return ""
	}
	ans := []byte{}
	for i, j := n, 0; i > 0; i-- {
		k := (j - digits[i-1]%3 + 3) % 3
		if f[i][j] == f[i-1][k]+1 {
			ans = append(ans, byte('0'+digits[i-1]))
			j = k
		}
	}
	i := 0
	for i < len(ans)-1 && ans[i] == '0' {
		i++
	}
	return string(ans[i:])
}