<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 f(int i,int j,string word1,string word2,vector<vector<int>>&dp)
    {
        if(i<0)
        {
            return j+1;
        }
        if(j<0)
        {
            return i+1;
        }
        if(dp[i][j]!=-1)
        {
            return dp[i][j];
        }
        if(word1[i]==word2[j])
        {
            return dp[i][j]=f(i-1,j-1,word1,word2,dp);
        }
        int a=f(i,j-1,word1,word2,dp);
        int b=f(i-1,j,word1,word2,dp);
        int c=f(i-1,j-1,word1,word2,dp);
        return dp[i][j]=min(a,min(b,c))+1;
    }
    int minDistance(string word1, string word2) {
        int n1=word1.size();
        int n2=word2.size();
        vector<vector<int>>dp(n1,vector<int>(n2,-1));
        // for(int i=0;i<n1;i++)
        // {
        //     dp[i][0]=i+1;
        // }
        // for(int i=0;i<n2;i++)
        // {
        //     dp[0][i]=i+1;
        // }

        return f(n1-1,n2-1,word1,word2,dp);
    }
};
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