<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 {

    int solve(string word1,string word2,int idx1,int idx2,vector<vector<int>>&dp){
        while(idx1 <word1.length() && idx2 < word2.length() && word1[idx1]==word2[idx2]){

            idx1++;
            idx2++;
            
        }
        //base case
        if(idx2==word2.length()){

            return word1.length()-idx1;

        }

        if(idx1==word1.length()){
            return word2.length()-idx2;
        }

        if(dp[idx1][idx2]!=-1) return dp[idx1][idx2];
        int a = 1e9;
        int b = 1e9;
        int c = 1e9;

        a = 1 + solve(word1,word2,idx1+1,idx2,dp);
        b = 1 + solve(word1,word2,idx1+1,idx2+1,dp);
        c = 1 + solve(word1,word2,idx1,idx2+1,dp);

        return dp[idx1][idx2]=min({a,b,c});
    }
public:
    int minDistance(string word1, string word2) {
        vector<vector<int>>dp(word1.size(),vector<int>(word2.size(),-1));
        return solve(word1,word2,0,0,dp);        
    }
};
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