<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 comp(string &a, string &b){
        if(b == "~" )return a;
        if(a == "~")return b;
        if(a.size() < b.size())return b;
        else if(a.size() > b.size())return a;
        else {
            for(int i = 0; i < a.size(); i++){
                if(a[i] > b[i])return a;
                else if( a[i] < b[i])return b;
            }
            return a;
        }
    }
    // string dp[10][5001];
    map<pair<int,int>,string> dp;
    string solve(vector<int> &cost, int ind, int target){
        if(ind < 0){
            if(!target)return "";
            return "~";
        }
        if(dp.count({target, ind}))return dp[{target,ind}];
        string t;
        if (target >= cost[ind]){
            string temp = solve(cost, ind, target - cost[ind]);
            if(temp == "~"){
                temp = solve(cost, ind - 1, target);
                return dp[{target,ind}] = temp;
            } else {
                string w ;
                w += (char)((ind + 1) +'0');
                w += temp;
                string p = solve(cost, ind - 1, target);
                if(p == "~")return dp[{target,ind}] = w;
                else  return dp[{target,ind}] =  comp(p, w);
            }
        }
        else{
            string s = solve(cost, ind - 1, target);
            return dp[{target,ind}] = s;
        }
    }
    string largestNumber(vector<int>& cost, int target) {
        // string ans;
        int ind = 8;
        // memset(dp, "!", sizeof(dp));
        string ans = solve(cost, ind, target);
        if(ans == "~")return "0";
        return ans;
    }
};
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