<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 {
public:
    int fun(int index1,int index2, string word1, string word2,int n1,int n2,vector<vector<int>>&dp){
        if(index1==n1||index2==n2)
            return n1-index1+n2-index2;
        int operation=INT_MAX-1,noOperation=INT_MAX-1;
        if(dp[index1][index2]!=-1)
            return dp[index1][index2];

        if(word1[index1]==word2[index2]){
            noOperation=fun(index1+1,index2+1,word1,word2,n1,n2,dp);
        }
        else{
            for(int i=0;i<2;i++){
                for(int j=0;j<2;j++){
                    if(i==0&&j==0)
                    continue;
                    operation=min(operation,fun(index1+i,index2+j,word1,word2,n1,n2,dp));
                }
            }
        }
        return dp[index1][index2]=min(noOperation,1+operation);

    }
    int minDistance(string word1, string word2) {
        int n1=word1.length(),n2=word2.length();
        vector<vector<int>>dp(n1+1,vector<int>(n2+1,-1));

        return fun(0,0,word1,word2,n1,n2,dp);
        
    }
};
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