<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:
        N1, N2 = len(word1), len(word2)

        cacheExists = [[False]*(N2+1) for i in range(N1 + 1)]
        cache = [[None]*(N2+1) for i in range(N1 + 1)]

        # Returns the min number of operations required to convert
        # word 1 to word 2 assuming that the words match so far
        # at index1 - 1, index2 - 1
        def findMin(index1, index2):
            if index1 == N1:
                return N2 - index2
            if index2 == N2:
                return N1 - index1
            
            if cacheExists[index1][index2]:
                return cache[index1][index2]

            answer = float("inf")

            if word1[index1] == word2[index2]:
                answer = min(answer, findMin(index1 + 1, index2 + 1))
            else:
                # Insert a character
                answer = min(answer, 1 + findMin(index1, index2 + 1))
                # Delete a character
                answer = min(answer, 1 + findMin(index1 + 1, index2))
                # Replace a character
                answer = min(answer, 1 + findMin(index1 + 1, index2 + 1))

            cacheExists[index1][index2] = True
            cache[index1][index2] = answer
            return answer

        return findMin(0, 0)
20762