<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 __init__(self):
        self.cache = {}
        self.alphs = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
    def minDistance(self, word1, word2):


        if word1 == word2:
            return 0
        # uniq_word_dict={}
        # for i in range(len(word1)):
        #     if word1[i] not in uniq_word_dict:
        #         uniq_word_dict[word1[i]] = self.alphs[len(uniq_word_dict)]
        # for i in range(len(word2)):
        #     if word2[i] not in uniq_word_dict:
        #         uniq_word_dict[word2[i]] = self.alphs[len(uniq_word_dict)]
        # key = "".join([uniq_word_dict[word1[i]] for i in range(len(word1))])
        # key += ","+ "".join([uniq_word_dict[word2[i]] for i in range(len(word2))])
        key = word1+","+word2
        if key in self.cache:
            return self.cache[key]

        max_val = max(len(word1), len(word2))
        idx = -1
        for i in range(min(len(word2), len(word1))):
            if word1[i] != word2[i]:
                idx = i
                break
        if idx == -1:
            return abs(len(word1) - len(word2))
        else:
            max_val = min(max_val,
                          1 + self.minDistance(word1[idx:], word2[idx+1:]),
                          1 + self.minDistance(word1[idx+1:], word2[idx:]),
                          1 + self.minDistance(word1[idx+1:], word2[idx+1:]))
            self.cache[key] = max_val
            return max_val
23762