<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:
    unordered_map<int,int> memo;
    int minStickers(vector<string>& stickers, string target) {
        int state = (1<<target.size())-1;

        vector<vector<int>> fs(stickers.size(),vector<int>(26,0));
        for(int i=0;i<stickers.size();i++)
        {
            for(char c : stickers[i])
                fs[i][c-'a']++;
        }

        int res = gen(state,fs,target);
        return (res==INT_MAX) ? -1 : res;
    }
    int gen(int state, vector<vector<int>>& fs, string& target)
    {
        if(!state)
            return 0;
        if(memo.count(state))
            return memo[state];
        int res = INT_MAX;
        
        for(vector<int>& f : fs)
        {
            // check if the current word is useful
            bool useful = false;
            for(int i=0;i<target.size();i++)
            {
                if(f[target[i]-'a']>0 && ((state>>i)&1))
                {
                    useful = true;
                    break;
                }
            }
            if(!useful) continue;

            vector<int> used(26,0);
            bool word_used = false;
            int newState = state;
            for(int i=0;i<target.size();i++)
            {
                char c = target[i];

                if(!( (state>>i) & 1)) // if the ith bit is 0 that means its been filled
                    continue;

                if(used[c-'a']<f[c-'a'])
                {
                    used[c-'a']++;
                    newState ^= (1<<i);
                    word_used = true;
                }
            }
            
            if(word_used)
            {   
                int newRes = gen(newState,fs,target);
                if(newRes!=INT_MAX)
                    res=min(res,newRes+1);
            }
        }
        memo[state]=res;
        return res;
    }
};
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