<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(const string& word1, const string& word2) {
    vector<int> cache(word1.size() * word2.size(), -1);

    const int s1 = word1.size();
    const int s2 = word2.size();

    const function<int(const string&, int, const string&, int)> distance = [&](auto w1, int i, auto w2, int j) {
      if (i >= s1 || j >= s2) return abs((s1 - i) - (s2 - j));

      auto& cached = cache[i * w2.size() + j];
      if (cached != -1) return cached;

      if (w1[i] == w2[j]) return cached = distance(w1, i+1, w2, j+1);

      return cached = 1 + min({
        distance(w1, i+1, w2, j),
        distance(w1, i, w2, j+1),
        distance(w1, i+1, w2, j+1),
      });
    };

    return distance(word1, 0, word2, 0);
  }
};

61403