<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 {
    private:
    int f(int i,int j,string s,string t,vector<vector<int>>& dp)
    {
        if( j<0) return i+1;  //i+1 deletiions
        if(i<0) return j+1;     // j+1 insertions
        if(dp[i][j]!=-1) return dp[i][j];


        int replace=1+f(i-1,j-1,s,t,dp);

        if(s[i]==t[j]) return dp[i][j]=replace-1;
         
        int insert=1+f(i,j-1,s,t,dp);
        

        int del=1+f(i-1,j,s,t,dp);

        
        return dp[i][j]= min(del,min(replace,insert));
    }
public:
    int minDistance(string s, string t) 
    {

        int n=s.size();
        int m=t.size();
        
        vector<vector<int>> dp(n,vector<int>(m,-1));
        return f(n-1,m-1,s,t,dp);
        
    }
};
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