<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(string word1, string word2) {
      std::unordered_map<int,int> dp;
      std::function<int(int,int)> lcs;
      lcs = [&dp, &lcs,
             word1 = std::as_const(word1),
             word2 = std::as_const(word2)](int i1, int i2)->int{
        if(i1<0 && i2<0){ return 0;}
        else if(i1<0 || i2<0){ return max(i1,i2)+1; }
        int h = i1*600 + i2;
        if(dp.count(h)){ return dp[h]; }
        int retv=std::numeric_limits<int>::max();
        if(word1[i1]==word2[i2]){  retv = lcs(i1-1,i2-1);  }
        retv = min(retv,lcs(i1-1,i2)+1);// remove from w1 (or add to w1)
        retv = min(retv,lcs(i1,i2-1)+1);// remove from w2 (or add to w1)
        retv = min(retv,lcs(i1-1,i2-1)+1);// change
        dp[h] = retv;
        return retv;
      };
      return lcs(word1.size()-1, word2.size()-1);
    }
};
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