<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 solve(string& word1,string& word2,vector<vector<int>>&dp,int i,int j){
        if(i==word1.length()){
            return word2.length()-j;
        }
        if(j==word2.length()){
            return word1.length()-i;
        }
        if(dp[i][j]!=-1){
            return dp[i][j];
        }
        int ans=0;
        if(word1[i]==word2[j]){
           return solve(word1,word2,dp,i+1,j+1);
        }
        else{int include=1+solve(word1,word2,dp,i,j+1);
        int Delete = 1+ solve(word1,word2,dp,i+1,j);
        int replace = 1+ solve(word1,word2,dp,i+1,j+1);
        dp[i][j]=min(include,min(Delete,replace));
        return dp[i][j]; }
    }    

    int helper(vector<vector<int>>&dp,string word1,string&word2,int i,int j){
        if(i<0){
            return j+1;
        }
        if(j<0){
            return i+1;
        }
        if(dp[i][j]!=-1)    return dp[i][j];
        int match=0;
        if(word1[i]==word2[j]){
            dp[i][j]=helper(dp,word1,word2,i-1,j-1);
            return dp[i][j];
        }
        else{
            int del=1+helper(dp,word1,word2,i-1,j);
            int replace=1+helper(dp,word1,word2,i,j-1);
            int insert=1+helper(dp,word1,word2,i-1,j-1);
            dp[i][j]=min({del,replace,insert});
        }
        return dp[i][j];
    }
public:
    int minDistance(string word1, string word2) {
        vector<vector<int>>dp(word1.length(),vector<int>(word2.length(),-1));
        return helper(dp,word1,word2,word1.length()-1,word2.length()-1);
        //return solve(word1,word2,dp,0,0);
    }
};
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