<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 find(string &word1,string word2,int start1,int start2,vector<vector<int>>&dp)
    {
        if(start1>=word1.length())
        {
            return word2.length()-start2;
        }
        if(start2>=word2.length())
        {
            return word1.length()-start1;
        }
        if(dp[start1][start2]!=-1)
        {
            return dp[start1][start2];
        }
        int result;
        if(word1[start1]==word2[start2])
        {
            result=find(word1,word2,start1+1,start2+1,dp);
        }
        else
        {
            int insertElement=1+find(word1,word2,start1,start2+1,dp);
            int deleteElement=1+find(word1,word2,start1+1,start2,dp);
            int replace=1+find(word1,word2,start1+1,start2+1,dp);
            result= min({insertElement,deleteElement,replace});
        }
        return dp[start1][start2]=result;
    }
    int minDistance(string word1, string word2) {
        vector<vector<int>>dp(word1.length()+1,vector<int>(word2.length()+1,-1));
        int ans=find(word1,word2,0,0,dp);
        return ans;
    }
};
49346