<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();

        // Populate sticker freqs
        vector<vector<int>> stickerFreqs(n, vector<int>(26, 0));
        for (int i = 0; i < n; ++i)
            for (char c : stickers[i])
                ++stickerFreqs[i][c - 'a'];
        
        // Target freqs
        vector<int> targetFreqs(26, 0);
        for (char c : target)
            ++targetFreqs[c - 'a'];
        
        // Find the minimum no of stickers needed to make target empty
        return bfs(targetFreqs, stickerFreqs);
    }

    int bfs(const vector<int>& targetFreqs, const vector<vector<int>>& stickerFreqs) {
        queue<string> qq;
        unordered_set<string> seen;
        string root = decode(targetFreqs);
        qq.push(root);
        seen.insert(root);
        int res = 0;
        while (!qq.empty()) {
            int sz = qq.size();
            for (int i = 0; i < sz; ++i) {
                string node = qq.front();
                qq.pop();
                //cout << "node: " << node << ", res: " << res << endl; 
                if (node.empty()) return res;  // goal node
                for (int i = 0; i < stickerFreqs.size(); ++i) {
                    string child = useSticker(node, stickerFreqs[i]);
                    if (seen.contains(child)) continue;
                    seen.insert(child);
                    qq.push(child);
                }
            }
            ++res;
        }
        return -1;
    }

    string useSticker(const string& s, const vector<int>& freqs) {
        vector<int> sFreqs(26, 0);
        for (char c : s) ++sFreqs[c - 'a'];
        for (int i = 0; i < 26; ++i) sFreqs[i] -= freqs[i];
        return decode(sFreqs);
    }

    string decode(const vector<int>& freqs) {
        string res = "";
        for (int i = 0; i < freqs.size(); ++i) {
            if (freqs[i] <= 0) continue;
            res += string(freqs[i], 'a' + i);
        }
        return res;
    }
};
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