<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>

from collections import Counter
class Solution:
    def minStickers(self, stickers: List[str], target: str) -> int:

        def use(sticker_word, target_word):
            sticker_word = Counter(sticker_word)
            target_word = Counter(target_word)
            
            for w, freq in sticker_word.items():
                target_word[w] -= freq
            
            ans = ""
            for k, v in target_word.items():
                if v > 0:
                    ans += k*v
            return ans

        
        dp = {}
        def helper(sticker_index, remaining_target):
            if len(remaining_target) == 0:
                return 0
            # base cases
            if sticker_index >= len(stickers):
                return float('inf')
            
            if (sticker_index, remaining_target) in dp:
                return dp[(sticker_index, remaining_target)]
            
            used_word = use(stickers[sticker_index], remaining_target)
            if used_word != remaining_target:
                dp[(sticker_index, remaining_target)] =  min(1 + helper(sticker_index, used_word), helper(sticker_index + 1, remaining_target))
            else:
                dp[(sticker_index, remaining_target)] = helper(sticker_index + 1, remaining_target)
            
            return dp[(sticker_index, remaining_target)]
        
        ans = helper(0, target)
        return ans if ans != float('inf') else -1






        
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