<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 {
    vector<vector<int>> freq;
    unordered_map<string, int> memo; 
    
public:
    string getIndex(string &target, vector<int>& sticker,int idx) {
        vector<int>tar(26,0);
        for(int i = 0;i<target.size();i++){
            tar[target[i]-'a']++;
        }
        vector<int>helper = freq[idx];
        for(int i = 0;i<26;i++){
            tar[i] -= min(tar[i],helper[i]);
        }
        string remaining = "";
        for(int i = 0;i<26;i++){
            for(int j = 0;j<tar[i];j++){
                remaining += ('a'+i);
            }
        }
        return remaining;
    }

    int solve(vector<string>& stickers, string target, int size) {
        if (target == "") return 0;
        if (memo.find(target) != memo.end()) return memo[target]; 
        
        int ans = 1e8;
        
        for (int i = 0; i < size; i++) {
            if (freq[i][target[0] - 'a'] > 0) {  
                string remaining = getIndex(target, freq[i],i);
                if (remaining.size() < target.size()) { 
                    ans = min(ans, 1 + solve(stickers, remaining, size));
                }
            }
        }
        
        memo[target] = ans;
        return ans;
    }

    int minStickers(vector<string>& stickers, string target) {
        int size = stickers.size();
        freq.resize(size, vector<int>(26, 0));
        for (int i = 0; i < size; i++) {
            string s = stickers[i];
            for (char &ch : s) {
                freq[i][ch - 'a']++;
            }
        }
        
        int ans = solve(stickers, target, size);
        return ans == 1e8 ? -1 : ans;
    }
};

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