<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:
    map<pair<int,int>,int>dp;
    int compute(int i,int j,string &word1, string& word2){
        if(i==word1.size()&&j==word2.size())return 0; //if end together, word has been edited properly
        if(i>word1.size()||j>word2.size())return 1e6; //if dissimar, wrong answer
        if(dp.find({i,j})!=dp.end())return dp[{i,j}];
        if(word1[i]==word2[j])return compute(i+1,j+1,word1,word2);
        int x = 1+compute(i+1,j+1,word1,word2); //Replace;
        int y = 1+compute(i+1,j,word1,word2) ;//Delete;
        int z = 1+compute(i,j+1,word1,word2); //Insert
        return dp[{i,j}] = min(min(x,y),z);
    }
    int minDistance(string word1, string word2) {
        return compute(0,0,word1,word2);
    }
};
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