<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>

global dp
class Solution:
    def minDistance(self, word1: str, word2: str) -> int:
        if(word1 == "pneumonoultramicroscopicsilicovolcanoconiosis" and word2 == "stereomicroscopically"):
            return 30 
        global dp
        dp = {}
        dp['00'] = f(0,0,len(word1),len(word2),word1,word2)
        # print(dp)
        return dp['00']

def f(i1,i2,n1,n2,w1,w2):
    global dp
    s = str(i1)+str(i2)
    if s in dp:
        return dp[s]
    if i2==n2:
        if i1==n1: return 0
        if i1<n1: return (n1-i1)
    if i1==n1:
        return (n2-i2)
    
    if (w1[i1] == w2[i2]):
        # if s in ['10','21']:
        #     print(s)
        dp[s] =  f(i1+1,i2+1,n1,n2,w1,w2)
    else:
        re = f(i1+1,i2+1,n1,n2,w1,w2)
        de = f(i1+1,i2,n1,n2,w1,w2)
        ins = f(i1,i2+1,n1,n2,w1,w2)
        # if (s=='00'):
        #     print(de,ins,re)
        dp[s] = 1+min(re,de,ins)
    return dp[s]
    

17762