<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 m,n;
   int solve(int i,int j,string ans,string &s1,string &s2,vector<vector<int>>&dp)
   { 
      if(i==m && j==n)
        {
            if(s2==ans)
             return 0;
            else
              return 1e8;
        }
      if(i==m)
      {
        return n-j;
      }
      if(j==n)
        return m-i;
      if(dp[i][j]!=-1)
        return dp[i][j];
      if(s1[i]==s2[j])
      { 
        return dp[i][j]=0+solve(i+1,j+1,ans+s1[i],s1,s2,dp);

      }
      int del=1e8;
      int insert=1e8;
      int replace=1e8;
      del=1+solve(i+1,j,ans,s1,s2,dp);
      insert=1+solve(i,j+1,ans+s2[j],s1,s2,dp);
      replace=1+solve(i+1,j+1,ans+s2[j],s1,s2,dp);
      return dp[i][j]=min(del,min(insert,replace));
         
   }
    int minDistance(string word1, string word2) {
        m=word1.length();
        n=word2.length();
        string ans="";
        vector<vector<int>>dp(m,vector<int>(n,-1));
        return solve(0,0,ans,word1,word2,dp);

    }
};
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