<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 dp[501][501];
    int helper(string word1, string word2){
        
        if(word1.length()==0) return dp[word1.length()][word2.length()]=word2.length();
        if(word2.length()==0) return dp[word1.length()][word2.length()]=word1.length();

        if(dp[word1.length()][word2.length()]!=INT_MAX) return dp[word1.length()][word2.length()];

        if(word1[0]==word2[0]) return dp[word1.length()][word2.length()]=helper(word1.substr(1),word2.substr(1));

        int x = 1 + helper(word1.substr(1),word2.substr(1)); // convert character in any string
        int y = helper(word1.substr(1),word2) + 1; // delete from word 1
        int z = helper(word1,word2.substr(1)) + 1; // insert in word 1

        return dp[word1.length()][word2.length()]=min(x,min(y,z));
    }
    
    int minDistance(string word1, string word2) {

        for(int i=0;i<=500;i++){
            for(int j=0;j<=500;j++) dp[i][j]=INT_MAX;
        }
        return helper(word1,word2);

        
        
    }
};
44708