<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 {
    int solve(string& word1,string word2,int d,int e,vector<vector<int>>&v){
if(d<0){
    return e+1;
}
if(e<0){
    return d+1;
}
if(v[d][e]!=-1){
    return v[d][e];
}
int g=0;
int h=0;

if(word1[d]==word2[e]){
    g=solve(word1,word2,d-1,e-1,v);
}
else{
h=1+min(solve(word1,word2,d-1,e,v),min(solve(word1,word2,d,e-1,v),solve(word1,word2,d-1,e-1,v)));

}
return v[d][e]= g+h;
    }
public:
    int minDistance(string word1, string word2) {
     int d=word1.size();
     int e=word2.size();
     vector<vector<int>>v(d+1,vector<int>(e+1,-1));
     return solve(word1,word2,d-1,e-1,v);   
    }
};
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