<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) {
        set<char> exists;
        for(int i=0; i<target.length(); i++) {
            exists.insert(target[i]);
        }

        for(auto itr: stickers) {
            for(int i=0;i<itr.length();i++) {
                exists.erase(itr[i]);
            }
        }

        if (exists.size() != 0) {
            return -1;
        }
        unordered_map<string, int> cache;

        string reduce = reduceString(target, "");
        return backtrack(stickers, reduce, cache);
    }

    int backtrack(vector<string>& stickers, string target, unordered_map<string, int>& cache) {
        if (target.length() == 0) {
            return 0;
        }

        if (cache[target]) {
            return cache[target];
        }

        int ans = INT_MAX;

        for(int i=0; i<stickers.size(); i++) {
            string reduced = reduceString(target, stickers[i]);
            if (reduced.length() < target.length()) {
                ans = min(ans, 1+backtrack(stickers, reduced, cache));
            }
        }

        cache[target] = ans;

        return ans;
    }

    string reduceString(string& s, string sticker) {
        vector<int> freq(26, 0);
        string answer = "";
        for(int i=0;i<s.length();i++){
            freq[s[i] - 97]++;
        }

        for(int i=0; i<sticker.length();i++) {
            if(freq[sticker[i]-97]) {
                freq[sticker[i]-97]--;
            }
        }

        for(int i=0; i<26; i++) {
            while(freq[i] != 0) {
                answer += (97+i);
                freq[i]--;
            }
        }

        return answer;
    }
};
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