Form Largest Integer With Digits That Add up to Target
<p>Given an array of integers <code>cost</code> and an integer <code>target</code>, return <em>the <strong>maximum</strong> integer you can paint under the following rules</em>:</p>

<ul>
	<li>The cost of painting a digit <code>(i + 1)</code> is given by <code>cost[i]</code> (<strong>0-indexed</strong>).</li>
	<li>The total cost used must be equal to <code>target</code>.</li>
	<li>The integer does not have <code>0</code> digits.</li>
</ul>

<p>Since the answer may be very large, return it as a string. If there is no way to paint any integer given the condition, return <code>&quot;0&quot;</code>.</p>

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

<pre>
<strong>Input:</strong> cost = [4,3,2,5,6,7,2,5,5], target = 9
<strong>Output:</strong> &quot;7772&quot;
<strong>Explanation:</strong> The cost to paint the digit &#39;7&#39; is 2, and the digit &#39;2&#39; is 3. Then cost(&quot;7772&quot;) = 2*3+ 3*1 = 9. You could also paint &quot;977&quot;, but &quot;7772&quot; is the largest number.
<strong>Digit    cost</strong>
  1  -&gt;   4
  2  -&gt;   3
  3  -&gt;   2
  4  -&gt;   5
  5  -&gt;   6
  6  -&gt;   7
  7  -&gt;   2
  8  -&gt;   5
  9  -&gt;   5
</pre>

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

<pre>
<strong>Input:</strong> cost = [7,6,5,5,5,6,8,7,8], target = 12
<strong>Output:</strong> &quot;85&quot;
<strong>Explanation:</strong> The cost to paint the digit &#39;8&#39; is 7, and the digit &#39;5&#39; is 5. Then cost(&quot;85&quot;) = 7 + 5 = 12.
</pre>

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

<pre>
<strong>Input:</strong> cost = [2,4,6,2,4,6,4,4,4], target = 5
<strong>Output:</strong> &quot;0&quot;
<strong>Explanation:</strong> It is impossible to paint any integer with total cost equal to target.
</pre>

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

<ul>
	<li><code>cost.length == 9</code></li>
	<li><code>1 &lt;= cost[i], target &lt;= 5000</code></li>
</ul>
Array; Dynamic Programming
func largestNumber(cost []int, target int) string {
	const inf = 1 << 30
	f := make([][]int, 10)
	g := make([][]int, 10)
	for i := range f {
		f[i] = make([]int, target+1)
		g[i] = make([]int, target+1)
		for j := range f[i] {
			f[i][j] = -inf
		}
	}
	f[0][0] = 0
	for i := 1; i <= 9; i++ {
		c := cost[i-1]
		for j := 0; j <= target; j++ {
			if j < c || f[i][j-c]+1 < f[i-1][j] {
				f[i][j] = f[i-1][j]
				g[i][j] = j
			} else {
				f[i][j] = f[i][j-c] + 1
				g[i][j] = j - c
			}
		}
	}
	if f[9][target] < 0 {
		return "0"
	}
	ans := []byte{}
	for i, j := 9, target; i > 0; {
		if g[i][j] == j {
			i--
		} else {
			ans = append(ans, '0'+byte(i))
			j = g[i][j]
		}
	}
	return string(ans)
}