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
class Solution {
public:
    string largestNumber(vector<int>& cost, int target) {
        const int inf = 1 << 30;
        vector<vector<int>> f(10, vector<int>(target + 1, -inf));
        vector<vector<int>> g(10, vector<int>(target + 1));
        f[0][0] = 0;
        for (int i = 1; i <= 9; ++i) {
            int c = cost[i - 1];
            for (int 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";
        }
        string ans;
        for (int i = 9, j = target; i;) {
            if (g[i][j] == j) {
                --i;
            } else {
                ans += '0' + i;
                j = g[i][j];
            }
        }
        return ans;
    }
};