<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>

def makeTrie(words):
    trie = {}
    def makeTrieWord(trie, word):
        if len(word) == 1:
            trie[word[0]] = trie.get(word[0], dict())
        else:
            trie[word[0]] = makeTrieWord(trie.get(word[0], dict()), word[1:])
        return trie
    for word in words:
        trie = makeTrieWord(trie, word)
    return trie

def checkInTrieLength(trie, word):
    if len(word) == 0:
        return 0, True

    elif len(word) == 1:
        return int(word[0] in trie), word[0] in trie
    else:
        if word[0] in trie:
            length, optimal = checkInTrieLength(trie[word[0]], word[1:])
            return 1 + length, optimal and True
        else:
            return 0, False

class Solution:
    def minValidStrings(self, words: List[str], target: str) -> int:
        trie = makeTrie(words)
        substring = target
        dp = [float(inf) for _ in range(len(target)+1)]
        dp[0] = 0
        idx = 0
        while idx < len(target):
            inTrieLen, optimal = checkInTrieLength(trie, substring)
            for innerIdx in range(1, inTrieLen+1):
                dp[idx+innerIdx] = min(dp[idx] + 1, dp[idx+innerIdx])
            if not optimal:
                idx = idx + 1
                substring = substring[1:]
            else:
                idx += inTrieLen
                substring = substring[inTrieLen:]

        return dp[-1] if  dp[-1] != float(inf) else -1

37571