<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) {
        int n = stickers.size();

        unordered_set<string> visited;

        vector<vector<int>> stickerFrequencies(n, vector<int>(26, 0));
        for(int i=0;i < n;i++){
            for(auto ch : stickers[i]){
                stickerFrequencies[i][ch-'a']++;
            }
        }

        vector<int> targetFrequency(26, 0);
        for(auto ch : target){
            targetFrequency[ch-'a']++;
        }

        queue<pair<vector<int>, int>> q;
        q.push(make_pair(targetFrequency, 0));
        while(!q.empty()){
            auto tFreq = q.front().first; int numStickers = q.front().second; q.pop();

            string tStr = "";
            for(int i=0;i<26;i++){
                if(tFreq[i] > 0){
                    tStr += string(tFreq[i], i);
                }
            }

            if(tStr == ""){
                return numStickers;
            }

            if(visited.count(tStr)){
                continue;
            }

            visited.insert(tStr);

            char seeking = tStr[0];
            for(auto sticker : stickerFrequencies){
                if(sticker[seeking] > 0){
                    q.push(make_pair(tFreq, numStickers + 1));
                    for(int i=0;i<26;i++){
                        q.back().first[i] -= sticker[i];
                    }
                }
            }
        }

        return -1;      
    }
};
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