<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 solve(string s1, string s2, int n, int m) {
        if (n == 0) return m;
        if (m == 0) return n;

        if (dp[n][m] != -1) return dp[n][m];

        if (s1[n-1] == s2[m-1]) {
            return dp[n][m] =  solve(s1, s2, n-1, m-1);
        }

        return dp[n][m] =  1 + min({
            solve(s1, s2, n-1, m-1),

            // insert
            solve(s1, s2, n, m-1),
            
            // delete
            solve(s1, s2, n-1, m)
        });
    }

    int minDistance(string word1, string word2) {
        int n = size(word1), m = size(word2);
        memset(dp, -1, sizeof(dp));
        return solve(word1, word2, n, m);
        
    }
};
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