<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 {
    map<pair<int, string>, int> dp;
    int minStickers(int i, string target, vector<vector<int>> &words) {

        if(target.length() == 0) return 0;
        if(i == words.size()) return 1e9;
        if(dp.find({i, target}) != dp.end()) return dp[{i, target}];

        string newTarget;
        vector<int> hash = words[i];
        for(char c: target) {
            if(hash[c - 'a'] == 0) {
                newTarget.push_back(c);
            } else {
                hash[c - 'a']--;
            }
        }

        int pick = 1e9;
        if(newTarget.length() < target.length()) {
            pick = minStickers(i, newTarget, words) + 1;
        }

        int notPick = minStickers(i+1, target, words);

        return dp[{i, target}] = min(pick, notPick);
    }
public:
    int minStickers(vector<string>& stickers, string target) {
        int n = stickers.size();
        vector<vector<int>> words(n, vector<int> (26, 0));


        for(int i=0; i<n; i++) {
            for(char c: stickers[i]) {
                words[i][c - 'a']++;
            }
        }

        int res = minStickers(0, target, words);
        return res >= 1e9 ? -1 : res;
    }
};
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