<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>

//bb: when done, push to queue and insert to hashset

class Solution {
    vector<int> str_to_freqs(const string& str)
    {
        vector<int> freqs(26,0);
        for(int i=0; i<str.length(); ++i) ++freqs[str[i]-'a'];
        return freqs;
    }
    string freqs_to_str(const vector<int>& freqs)
    {
        string str;
        for(int i=0; i<freqs.size(); ++i) str += string(freqs[i], i+'a');
        return str;
    }
    
public:
    int minStickers(vector<string>& stickers, string target) 
    {
        vector<int> target_freqs = str_to_freqs(target);
        vector<vector<int>> stickers_freqs;
        for(string str : stickers) stickers_freqs.push_back(str_to_freqs(str));
        
        queue<vector<int>> qu;
        qu.push(target_freqs);
        
        unordered_set<string> visited;
        visited.insert(target);// do it now
        
        int steps = 0;
        
        while(!qu.empty())
        {
            int K = qu.size();
            for(int k=0; k<K; ++k)
            {
                vector<int> curr_freqs = qu.front();
                qu.pop();
                string curr_str = freqs_to_str(curr_freqs);
                if(curr_str.empty()) return steps;
                
                for(vector<int> stk_freqs : stickers_freqs)
                {
                    if(stk_freqs[curr_str[0]-'a']==0) continue;
                    vector<int> child_freqs = curr_freqs;
                    for(int i=0; i<26; ++i)
                    {
                        child_freqs[i] -= stk_freqs[i];
                        child_freqs[i]  = child_freqs[i]<0 ? 0 : child_freqs[i];
                    }
                    
                    string child_str = freqs_to_str(child_freqs);
                    if(visited.count(child_str)>0) continue;
                    
                    visited.insert(child_str);
                    qu.push(child_freqs);
                }
            }
            ++steps;
        }
        return -1;
    }
};
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