<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(int len1 , int len2 , string &word1, string &word2 , vector<vector<int>> &dp){

        if (len1 == 0) return len2; // Need to insert all characters of word2
        if (len2 == 0) return len1; // Need to delete all characters of word1

        if(dp[len1][len2] !=-1 ) return dp[len1][len2];
        
        if(word1[len1-1]==word2[len2-1]){
            return dp[len1][len2] =  find(len1-1,len2-1,word1,word2,dp);
        }
        else{
            int del = 1 + find(len1-1,len2,word1,word2 , dp);
            int rep = 1 + find(len1-1,len2-1,word1,word2 , dp);
            int ins = 1 + find(len1,len2-1,word1,word2 , dp);
            return dp[len1][len2] = min(del,min(rep,ins));
        }
    }
    int minDistance(string word1, string word2) {
        
        int n1 = word1.length();
        int n2 = word2.length();

        vector<vector<int>> dp(n1+1,vector<int>(n2+1,-1));

        // for(int i = 0; i<=n1; i++){
        //     dp[i][0] = i;
        // }
        // for(int i = 0; i<=n2; i++){
        //     dp[0][i] = i;
        // }

        // for(int len1 = 1; len1<=n1; len1++){
        //     for(int len2 = 1; len2<=n2; len2++){

        //         if(word1[len1-1]==word2[len2-1]){
        //          find(len1-1,len2-1,word1,word2,dp);
        //         }
        //         else{
        //         int del = 1 + find(len1-1,len2,word1,word2 , dp);
        //         int rep = 1 + find(len1-1,len2-1,word1,word2 , dp);
        //         int ins = 1 + find(len1,len2-1,word1,word2 , dp);
        //         return dp[len1][len2] = min(del,min(rep,ins));
        //         }  

        //     }
        // }
        return find(n1,n2,word1,word2 , dp);
    }
};
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