<p>You are given an array of strings <code>words</code> and a string <code>target</code>.</p>

<p>A string <code>x</code> is called <strong>valid</strong> if <code>x</code> is a <span data-keyword="string-prefix">prefix</span> of <strong>any</strong> string in <code>words</code>.</p>

<p>Return the <strong>minimum</strong> number of <strong>valid</strong> strings that can be <em>concatenated</em> to form <code>target</code>. If it is <strong>not</strong> possible to form <code>target</code>, return <code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">words = [&quot;abc&quot;,&quot;aaaaa&quot;,&quot;bcdef&quot;], target = &quot;aabcdabc&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">3</span></p>

<p><strong>Explanation:</strong></p>

<p>The target string can be formed by concatenating:</p>

<ul>
	<li>Prefix of length 2 of <code>words[1]</code>, i.e. <code>&quot;aa&quot;</code>.</li>
	<li>Prefix of length 3 of <code>words[2]</code>, i.e. <code>&quot;bcd&quot;</code>.</li>
	<li>Prefix of length 3 of <code>words[0]</code>, i.e. <code>&quot;abc&quot;</code>.</li>
</ul>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">words = [&quot;abababab&quot;,&quot;ab&quot;], target = &quot;ababaababa&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">2</span></p>

<p><strong>Explanation:</strong></p>

<p>The target string can be formed by concatenating:</p>

<ul>
	<li>Prefix of length 5 of <code>words[0]</code>, i.e. <code>&quot;ababa&quot;</code>.</li>
	<li>Prefix of length 5 of <code>words[0]</code>, i.e. <code>&quot;ababa&quot;</code>.</li>
</ul>
</div>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">words = [&quot;abcdef&quot;], target = &quot;xyz&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">-1</span></p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= words.length &lt;= 100</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 5 * 10<sup>3</sup></code></li>
	<li>The input is generated such that <code>sum(words[i].length) &lt;= 10<sup>5</sup></code>.</li>
	<li><code>words[i]</code> consists only of lowercase English letters.</li>
	<li><code>1 &lt;= target.length &lt;= 5 * 10<sup>3</sup></code></li>
	<li><code>target</code> consists only of lowercase English letters.</li>
</ul>

class Solution:
    def minValidStrings(self, words: List[str], target: str) -> int:
        """
        i think im spoiled by 1's solution title

        KMP?
        originally TRIE+DP O(N cahce * N per cache) = N2
        now kmp: O(N cahce * try 100 words per cache) = 100N

        worst case: match "a"*1e5 on "a"*5*1e4

        ok i watched 1's solution
        always greedy on picking longest prefix 
        """
        M=len(words)
        lpss=[]

        def kmp(s,p):   #for matching w on target
            s=p+"#"+s
            lps=[0]
            for i in range(1,len(s)):
                j=lps[i-1]
                while j>0 and s[i]!=s[j]:
                    j=lps[j-1]
                if s[i]==s[j]:
                    j+=1
                lps.append(j)
            return lps[len(p)+1:]
        
        for w in words:
            lpss.append(kmp(target,w))
        # for lps in lpss:
        #     print(lps)

        #subproblem of prefix
        INF=10**20
        N=len(target)
        dp=[INF for _ in range(N)]    #subproblem of prefix
        
        for i in range(N):
            for lps in lpss:
                """
                e.g. (w,target)= (abcabcabc, bbbabcabcabc)
                lps[i] = 9 means can match w[:9](longest)
                dp[i]= dp[i-9] +1
                """
                if lps[i]>0:
                    dp[i]=min(dp[i], 1+(dp[i-lps[i]] if i-lps[i]>=0 else 0))
        #print(dp)
        return dp[-1] if dp[-1]<INF else -1


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