<p>Given two strings <code>word1</code> and <code>word2</code>, return <em>the minimum number of operations required to convert <code>word1</code> to <code>word2</code></em>.</p>

<p>You have the following three operations permitted on a word:</p>

<ul>
	<li>Insert a character</li>
	<li>Delete a character</li>
	<li>Replace a character</li>
</ul>

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

<pre>
<strong>Input:</strong> word1 = &quot;horse&quot;, word2 = &quot;ros&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> 
horse -&gt; rorse (replace &#39;h&#39; with &#39;r&#39;)
rorse -&gt; rose (remove &#39;r&#39;)
rose -&gt; ros (remove &#39;e&#39;)
</pre>

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

<pre>
<strong>Input:</strong> word1 = &quot;intention&quot;, word2 = &quot;execution&quot;
<strong>Output:</strong> 5
<strong>Explanation:</strong> 
intention -&gt; inention (remove &#39;t&#39;)
inention -&gt; enention (replace &#39;i&#39; with &#39;e&#39;)
enention -&gt; exention (replace &#39;n&#39; with &#39;x&#39;)
exention -&gt; exection (replace &#39;n&#39; with &#39;c&#39;)
exection -&gt; execution (insert &#39;u&#39;)
</pre>

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

<ul>
	<li><code>0 &lt;= word1.length, word2.length &lt;= 500</code></li>
	<li><code>word1</code> and <code>word2</code> consist of lowercase English letters.</li>
</ul>

class Solution:
    def minDistance(self, word1: str, word2: str, new_word=True) -> int:
        if word1 == word2:
            return 0

        if new_word:
            self.visited = {}

        if word2 in self.visited:
            return self.visited[word2]
        # print(word2, self.visited)

        n1 = len(word1)
        n2 = len(word2)

        i = 0
        while (i < n1 and i < n2 and word1[i] == word2[i]):
            i += 1
        
        if i == n1 or i == n2:
            self.visited[word2] = abs(n1 - n2)
        else:
            replace_dist = self.minDistance(word1,
                                            word1[:i+1] + word2[i+1:],
                                            False)
            insert_dist = self.minDistance(word1,
                                           word1[:i+1] + word2[i:],
                                           False)
            remove_dist = self.minDistance(word1,
                                           word2[:i] + word2[i+1:],
                                           False)
            self.visited[word2] = min(replace_dist, insert_dist, remove_dist) + 1
        return self.visited[word2]

23137