<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:

    vector<int> getFreqVec(string s){
        vector<int> targetFreqVec(26,0);
        for(char c: s){
            targetFreqVec[c-'a']++;
        }
        return targetFreqVec;
    }

    string compareFreqVectors(vector<int>& x, vector<int>& y){

        string diff = "";
        for(int i=0 ; i<26 ; ++i){
            if(x[i]<=y[i]){
                continue;
            }

            for(int j=0 ; j<x[i]-y[i] ; ++j){
                diff.push_back('a'+i);
            }
        }
        return diff;
    } 

    int dfs(string target, vector<vector<int> >&s, unordered_map<string, int>& dp){
        if(target.size()==0){
            return 0;
        }

        if(dp.count(target)>0){
            return dp[target];
        }

        int ans = INT_MAX;
        vector<int> targetFreqVec = getFreqVec(target);

        for(auto v:s){
            string rem = compareFreqVectors(targetFreqVec, v);
            if(rem == target){
                continue;
            }
            int curans = dfs(rem, s, dp);
            if(curans == -1){
                ans = -1;
                break;
            }
            ans = min(ans, curans == INT_MAX ? INT_MAX : curans+1);
        }

        ans = ans == INT_MAX ? -1 : ans;
        dp[target] = ans;
        return ans;
    }


    int minStickers(vector<string>& stickers, string target) {
        int n = stickers.size();
        vector<vector<int> > s;

        vector<int> targetFreqVec = getFreqVec(target);
        unordered_map<string, int> dp;

        for(string sticker: stickers){
            vector<int> f(26,0);
            for(char c: sticker){
                ++f[c-'a'];
            }
            s.push_back(f);
        }

        return dfs(target, s, dp);
    }
};
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