<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 H(string word1, string word2,vector<vector<int>>&dp) {
        int n=word1.size();
        int m=word2.size();
        if(word2.size()==0&&word1.size()==0){
            return 0;
        }
        if(word2.size()==0&&word1.size()!=0){
            return word1.size();
        }
        if(word2.size()!=0&&word1.size()==0){
            return word2.size();
        }
        if(dp[n][m]!=-1){
            return dp[n][m];
        }
        if(word1[0]==word2[0]){
            dp[n][m]= H(word1.substr(1),word2.substr(1),dp);
            return dp[n][m];
        }
        int choice1=H(word1,word2.substr(1),dp)+1;
        int choice2=H(word1.substr(1),word2.substr(1),dp)+1;
        int choice3=H(word1.substr(1),word2,dp)+1;
        dp[n][m]=min(choice1,min(choice2,choice3));
        return dp[n][m];
    }
    int minDistance(string s,string t){
        vector<vector<int>> dp(s.size()+1,vector<int>(t.size()+1,-1));
        return H(s,t,dp);
    }
};
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