<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>

class Solution {
public:
    string largestNumber(vector<int>& cost, int target) {
        map<int, int> costs;
        int max_cost = 0;
        for (int i = 0; i < 9; i++) {
            costs[cost[i]] = i+1;
            max_cost = max(max_cost, cost[i]);
        }
        vector<int> costvec;
        vector<int> numvec;
        for (auto& ele : costs) {
            costvec.push_back(ele.first);
            numvec.push_back(ele.second);
        }
        int n_cost = costs.size();
        vector<priority_queue<int>> dp(max_cost);
        for (int i = 1; i <= target; i++) {
            //cout << i << endl;
            priority_queue<int> cur;
            int maxx = 0;
            for (int j = 0; j < n_cost; j++) {
                if (costvec[j] == i) {
                    maxx = max(maxx, numvec[j]);
                }
            }
            if (maxx != 0) cur.push(maxx);
            for (int j = 0; j < n_cost; j++) {
                int c = costvec[j];
                auto tmp = dp[max_cost - c];
                if (tmp.size() == 0) continue;
                tmp.push(numvec[j]);
                
                bool cur_big = bigger(cur, tmp);

                //bool cur_big = false;
                if (!cur_big) {
                    cur = tmp;
                }
            }
            dp.erase(dp.begin());
            dp.push_back(cur);
        }
        auto& targ = dp[max_cost-1];
        if (targ.size() == 0) return "0";

        string res = "";
        
        while (!targ.empty()) {
            res = res+char('0'+targ.top());
            targ.pop();
        }
        return res;
    }

    bool bigger(priority_queue<int> a, priority_queue<int> b) {
        if (a.size() > b.size()) return true;
        if (a.size() < b.size()) return false;

        while (!a.empty()) {
            if (a.top() > b.top()) return true;
            if (a.top() < b.top()) return false;
            a.pop();
            b.pop();
        }
        return false;
    }
};
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