<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 solveRec(string &word1, string &word2, int i, int j){
        if(i>= word1.length()){
            return word2.length() - j;
        }

        if(j>= word2.length()){
            return word1.length() - i;
        }
        int ans  = 0;
        if(word1[i] == word2[j]) ans = solveRec(word1,word2, i+1, j+1);

        else{
            int insert  = 1 + solveRec(word1,word2,i,j+1);
            int del = 1 + solveRec(word1,word2,i+1,j);
            int replace  = 1 + solveRec(word1,word2,i+1,j+1);

            ans = min(insert, min(del,replace));
        }
        return ans;
    }
    int topDown(string&s1, string s2, int i, int j, vector<vector<int>>& dp){
        if(i >= s1.length())
         return s2.length() - j;

        if(j >= s2.length())
        return s1.length() - i;

        if(dp[i][j]!= -1) return dp[i][j];

        int ans = 0;
        if(s1[i] == s2[j]) ans = topDown(s1,s2,i+1,j+1,dp);

        else{
            int ins = 1 + topDown(s1,s2,i,j+1,dp);
            int del  = 1 + topDown(s1,s2,i+1,j,dp);
            int rep = 1 + topDown(s1,s2,i+1,j+1,dp);

            ans = min(ins,min(del,rep));
        }
        dp[i][j] = ans;

        return dp[i][j];

    }
    int minDistance(string word1, string word2) {
        int i = 0;
        int j = 0;

        if(word1.length() == 0){
            return word2.length();
        }

        if(word2.length() == 0)
           return word1.length();
        
        // return solveRec(word1,word2,i,j);

        vector<vector<int>> dp(word1.length()+1, vector<int>(word2.length()+1, -1));

        return  topDown(word1,word2,i,j,dp);
    }
};
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