<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 dp[501][501];
public:
    int solve(int n, int m, string &w1, string &w2){
        if(n==0 && m==0) return 0;
        if(n==0) return m;
        if(m==0) return n;
        if(w1.substr(0,n)==w2.substr(0,m)){
            return 0;
        }
        if(dp[n][m]!=-1) return dp[n][m];
        if(w1[n-1] == w2[m-1]) return dp[n][m] = solve(n-1,m-1,w1,w2);
        // Delete
        int del = 1+solve(n-1,m,w1,w2);
        // Insert
        int ins = 1+solve(n,m-1,w1,w2);
        // Replace
        int rep = 1 + solve(n-1,m-1,w1,w2);
        return dp[n][m] = min({del,ins,rep});
    }
    int minDistance(string word1, string word2) {
       
       int n = word1.size(), m= word2.size();
        memset(dp,-1,sizeof(dp));
       return solve(n,m,word1,word2);
        
    }
};
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