<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) -> int:
        # Let md[a][b] be the min distance of the result if we only need to go until indices a and b in word1 and word2
        if min(len(word1), len(word2)) == 0:
            return max(len(word1), len(word2))

        md = [[1000 for _ in range(len(word2))] for _ in range(len(word1))]

        for i in range(len(word1)):
            if word2[0] in word1[:i+1]:
                md[i][0] = i
            else:
                md[i][0] = i + 1
        
        for j in range(len(word2)):
            if word1[0] in word2[:j+1]:
                md[0][j] = j
            else:
                md[0][j] = j + 1
 
        for i in range(1, len(word1)):
            for j in range(1, len(word2)):
                print(i, j, word1[i], word2[j])
                if word1[i] == word2[j]:
                    print('ihuh')
                    md[i][j] = md[i-1][j-1]
                else:
                    md[i][j] = min(md[i-1][j-1], md[i][j-1], md[i-1][j]) + 1
        
        print(md)
        return md[-1][-1]
22762