<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 hasher {
public:
    long long int operator() (pair<int, int> a) const {
        long long int ans = a.first;
        ans <<= 32;
        ans += a.second;
        return ans;
    }
};

class Solution {
private:
    int recurser(string& word1, string& word2, int pos1, int pos2, unordered_map<pair<int, int>, int, hasher>& cache) {
        if (pos1 == word1.size() and pos2 == word2.size())
            return 0;
        if (pos1 == word1.size())
            return word2.size()-pos2;
        if (pos2 == word2.size())
            return word1.size()-pos1;
        
        auto search = cache.find(make_pair(pos1, pos2));
        if (search != cache.end())
            return search->second;
        
        int ans = INT_MAX;
        if (word1[pos1] == word2[pos2])
            ans = min(ans, recurser(word1, word2, pos1+1, pos2+1, cache));
        ans = min(ans, 1+recurser(word1, word2, pos1+1, pos2, cache));
        ans = min(ans, 1+recurser(word1, word2, pos1, pos2+1, cache));
        ans = min(ans, 1+recurser(word1, word2, pos1+1, pos2+1, cache));
        cache[make_pair(pos1, pos2)] = ans;
        return ans;
    }
public:
    int minDistance(string word1, string word2) {
        unordered_map<pair<int, int>, int, hasher> cache;
        return this->recurser(word1, word2, 0, 0, cache);
    }
};
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