<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 editDistance(string s1, string s2, vector<vector<int>>&mem)
    {
        //Write your code here
        if(s1.size() == 0) return s2.size();
        if(s2.size() == 0) return s1.size();
        if(mem[s1.size()][s2.size()] != -1) return mem[s1.size()][s2.size()];
        if(s1[0] == s2[0]) {
            return mem[s1.size()][s2.size()] = editDistance(s1.substr(1), s2.substr(1), mem);
        }
        // Insert a char
        int a = editDistance(s1.substr(1), s2, mem);
        // delete a char
        int b = editDistance(s1, s2.substr(1), mem);
        // update a char
        int c = editDistance(s1.substr(1), s2.substr(1), mem);
        return mem[s1.size()][s2.size()] = min(a, min(b,c)) + 1;
    }
    int minDistance(string s1, string s2) {
        vector<vector<int>>mem(s1.size()+1, vector<int>(s2.size()+1, -1));
        return editDistance(s1, s2, mem);
    }
};
51201