<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:
        # Memoization dictionary
        memo = {}
        def helper(i: int, j: int) -> int:
            # Base cases
            if i == 0:  # If source string is exhausted, insert remaining target characters
                return j
            if j == 0:  # If target string is exhausted, remove remaining source characters
                return i

            # Check if result is already computed
            if (i, j) in memo:
                return memo[(i, j)]

            if word1[i - 1] == word2[j - 1]:
                # Characters match, no operation needed
                memo[(i, j)] = helper(i - 1, j - 1)
            else:
                # Characters don't match, consider operations
                # 1. Insert target[j-1] into source (equivalent to moving `j` back)
                insert = helper(i, j - 1) + 1
                # 2. Replace source[i-1] with target[j-1] (equivalent to moving both `i` and `j` back)
                replace = helper(i - 1, j - 1) + 1
                # 3. Remove source[i-1] (equivalent to moving `i` back)
                delete = helper(i - 1, j) + 1

                # Take the minimum of the three possible operations
                memo[(i, j)] = min(insert, replace, delete)
            return memo[(i, j)]
        return helper(len(word1), len(word2))
18137