<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 minDistance(std::string word1, std::string word2) {
        memo.clear();  // Clear memoization table before each call
        return editDistance(word1, word2, word1.length(), word2.length());
    }

private:
    std::unordered_map<std::string, int> memo;  // Memoization table

    int editDistance(const std::string& word1, const std::string& word2, int m, int n) {
        // Check memoization table
        std::string key = std::to_string(m) + "," + std::to_string(n);
        if (memo.find(key) != memo.end()) {
            return memo[key];
        }

        // Base cases
        if (m == 0) {
            return n;
        }
        if (n == 0) {
            return m;
        }
        if (word1[m - 1] == word2[n - 1]) {
            return editDistance(word1, word2, m - 1, n - 1);
        }

        // Recursive calls
        int insertCost = 1 + editDistance(word1, word2, m, n - 1);
        int deleteCost = 1 + editDistance(word1, word2, m - 1, n);
        int replaceCost = 1 + editDistance(word1, word2, m - 1, n - 1);

        // Minimum of insert, delete, and replace
        int result = std::min({insertCost, deleteCost, replaceCost});

        // Memoize the result
        memo[key] = result;

        return result;
    }
};

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