<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:
        mini=float("inf")
        dp=[[-1 for _ in range(len(word2)+134)] for _ in range(len(word2)+1123)]
        def solve(a,b,ind1,ind2,dp):
            nonlocal mini
            if(ind1>=len(a)):
                return len(b)-ind2
            if(ind2>=len(b)):
                return len(a)-ind1
            if(dp[ind1][ind2]!=-1):
                return dp[ind1][ind2]
            if(a[ind1]==b[ind2]):
                dp[ind1][ind2]=solve(a,b,ind1+1,ind2+1,dp)
                return dp[ind1][ind2]
            t=1+solve(a,b,ind1,ind2+1,dp)
            nt=1+solve(a,b,ind1+1,ind2,dp)
            r=1+solve(a,b,ind1+1,ind2+1,dp)
            # Avoid Using Mini Because it sometimes might give wrong results
            # mini=min(t,nt,r])
            dp[ind1][ind2]=min(t,nt,r)
            return min(t,nt,r)
        


        return solve(word1,word2,0,0,dp)
        # return mini

# class Solution:
#     def minDistance(self, word1: str, word2: str) -> int:
#         def solve(a, b, ind1, ind2):
#             if ind1 >= len(a):
#                 return len(b) - ind2
#             if ind2 >= len(b):
#                 return len(a) - ind1
#             if a[ind1] == b[ind2]:
#                 return solve(a, b, ind1 + 1, ind2 + 1)
            
#             # Calculate minimum of insertion, deletion, and substitution
#             t = 1 + solve(a, b, ind1, ind2 + 1)  # Insert
#             nt = 1 + solve(a, b, ind1 + 1, ind2)  # Delete
#             r = 1 + solve(a, b, ind1 + 1, ind2 + 1)  # Replace
#             return min(t, nt, r)

#         return solve(word1, word2, 0, 0)


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