<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 Node:
    def __init__(self):
        self.keys = [None for _ in range(26)]
        self.is_word = False

class Trie:
    def __init__(self):
        self.root = Node()

    def insert(self, s):
        temp = self.root
        for ch in s:
            if temp.keys[ord(ch)-97] is None:
                temp.keys[ord(ch)-97] = Node()
                temp.is_word = True
            temp = temp.keys[ord(ch)-97]

        temp.is_word = True

    def search(self, w):
        temp = self.root
        for ch in w:
            if temp.keys[ord(ch)-97] is None:
                return False
            temp = temp.keys[ord(ch)-97]

        return temp.is_word

    def searchPath(self):
        self.cur = self.root

    def searchFor(self, ch):
        if self.cur.keys[ord(ch)-97] is None:
            return False
        else:
            self.cur = self.cur.keys[ord(ch)-97]
            return True

class Solution:
    def minValidStrings(self, words: List[str], target: str) -> int:
        prefixes = Trie()

        for word in words:
            prefixes.insert(word)

        n = len(target)
        print(n)
        dp = [1e9 for _ in range(n+1)]
        dp[n] = 0

        for i in range(n-1, -1, -1):
            prefixes.searchPath()
            for j in range(i, n):
                if prefixes.searchFor(target[j]):
                    dp[i] = min(dp[i], 1 + dp[j+1])
                else:
                    break
        
        return dp[0] if dp[0] != 1e9 else -1
        
41970