<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>

/*

dp(i,j)

w1[i] != w2[i]
    if i + 1 > len(w1)
        replace
    
    else
        if w[i+1] == w2[i]
            remove
        else
    dp(i) = 1 + min(dp(i+1, remove), dp(i+1, replace), dp(i+1, insert))

*/

class Solution {
public:
    int minDistance(string word1, string word2) 
    {
        if (word1 == "")
            return word2.length();
        if (word2 == "")
            return word1.length();

        vector<vector<int>> memo = vector(word1.length(), vector(word2.length(), -1));
        return dp(word1, word2, word1.length()-1, word2.length()-1, memo);
    }

    int countSimiliar(string &word1, string& word2)
    {
        unordered_map<char, int> c2;

        for (auto c : word2)
        {
            c2[c]++;
        }

        int same_char_count = 0;
        for (auto c : word1)
        {
            if (c2.find(c) != c2.end())
            {
                same_char_count++;
                c2[c]--;
                if (c2[c] == 0)
                    c2.erase(c);
            }
        }

        return same_char_count;
    }

    int dp(string& word1, string &word2, int i, int j, vector<vector<int>> &memo)
    {
        if (word1 == word2)
            return 0;

        if (i < 0)
            return j + 1;

        if (j < 0)
            return i + 1;


        if (memo[i][j] != -1)
            return memo[i][j];

        if (word1[i] == word2[j])
        {
            memo[i][j] = dp(word1, word2, i-1,j-1, memo);
        }

        else
        {
            string replace = word1;
            replace[i] = word2[j];

            string remove = word1;
            remove.erase(remove.begin() + i);

            string insert = word1;
            insert.insert(insert.begin() + i + 1, word2[j]);
            memo[i][j] = 1 + min(dp(insert, word2, i, j-1, memo), dp(replace, word2, i-1, j-1, memo));
            memo[i][j] = min(memo[i][j], 1 + dp(remove, word2, i-1, j, memo));

        }

        return memo[i][j];
    }
};
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