<p>We are given <code>n</code> different types of <code>stickers</code>. Each sticker has a lowercase English word on it.</p>

<p>You would like to spell out the given string <code>target</code> by cutting individual letters from your collection of stickers and rearranging them. You can use each sticker more than once if you want, and you have infinite quantities of each sticker.</p>

<p>Return <em>the minimum number of stickers that you need to spell out </em><code>target</code>. If the task is impossible, return <code>-1</code>.</p>

<p><strong>Note:</strong> In all test cases, all words were chosen randomly from the <code>1000</code> most common US English words, and <code>target</code> was chosen as a concatenation of two random words.</p>

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

<pre>
<strong>Input:</strong> stickers = [&quot;with&quot;,&quot;example&quot;,&quot;science&quot;], target = &quot;thehat&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong>
We can use 2 &quot;with&quot; stickers, and 1 &quot;example&quot; sticker.
After cutting and rearrange the letters of those stickers, we can form the target &quot;thehat&quot;.
Also, this is the minimum number of stickers necessary to form the target string.
</pre>

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

<pre>
<strong>Input:</strong> stickers = [&quot;notice&quot;,&quot;possible&quot;], target = &quot;basicbasic&quot;
<strong>Output:</strong> -1
Explanation:
We cannot form the target &quot;basicbasic&quot; from cutting letters from the given stickers.
</pre>

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

<ul>
	<li><code>n == stickers.length</code></li>
	<li><code>1 &lt;= n &lt;= 50</code></li>
	<li><code>1 &lt;= stickers[i].length &lt;= 10</code></li>
	<li><code>1 &lt;= target.length &lt;= 15</code></li>
	<li><code>stickers[i]</code> and <code>target</code> consist of lowercase English letters.</li>
</ul>

class Solution {
public:
    int minStickers(vector<string>& stickers, string target) {
        
        unordered_map<string, unordered_map<int,int>> dp;
        
        function<int(string,int)> traverse = [&](string toMake, int index){
          //  if(index == stickers.size() || toMake.empty()) return 0;
            if(toMake.empty()) return 0;
            if(index == stickers.size()) return -1;
            
            if(dp.find(toMake) != dp.end() &&
               dp[toMake].find(index) != dp[toMake].end()) return dp[toMake][index];
            
            // not including sticker case
            int notInclude = traverse(toMake, index+1);
            
            // check if can be included
            vector<int> charRequired(26,0);
            for(char& c: toMake) {
                charRequired[c-'a']++;
            }
            bool hasCommon = false;
            for(char& c: stickers[index]) {
                if(charRequired[c-'a'] == 0) continue;
                hasCommon = true;
                charRequired[c-'a']--;
            }
            int included = -1;
            if (hasCommon) {
                string next = "";
                for (int i=0; i<26; i++) {
                    if (charRequired[i] == 0) continue;
                    next += string(charRequired[i], (i+'a'));
                }
                included = traverse(next, index);
                if (included != -1) included++;
            }
            int res = -1;
            if (notInclude != -1 && included != -1) res = min(notInclude, included);
            else if (notInclude != -1 ) res = notInclude;
            else if (included != -1) res = included;
            dp[toMake][index] = res;
            return res;
        };
        return traverse(target,0);
    }
};
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