<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>

struct pair_hash {
    template <class T1, class T2>
    std::size_t operator() (const std::pair<T1, T2>& p) const {
        auto hash1 = std::hash<T1>{}(p.first);
        auto hash2 = std::hash<T2>{}(p.second);
        return hash1 ^ hash2; // Combine the two hashes
    }
};

class Solution {
public:
    unordered_map<pair<int, int>, int, pair_hash> memo;
    int minDistance(string word1, string word2) {
        memo.clear();
        return calc(word1, word2, word1.length(), word2.length());
    }

    int calc(string& word1, string& word2, int pt1, int pt2) {
        if (pt1 == 0 || pt2 == 0)
            return pt1 + pt2;
        if (memo.find({pt1, pt2}) != memo.end())
            return memo[{pt1, pt2}];
        if (word1[pt1 - 1] == word2[pt2 - 1])
            return calc(word1, word2, pt1 - 1, pt2 - 1);
        int res = 1 + calc(word1, word2, pt1 - 1, pt2 - 1);
        res = min(res, 1 + calc(word1, word2, pt1 - 1, pt2));
        res = min(res, 1 + calc(word1, word2, pt1, pt2 - 1));
        memo[{pt1, pt2}] = res;
        return res;
    }
};   
19666