<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) {
        if (word1.empty()) {
            return word2.size();
        } 
        if (word2.empty()) {
            return word1.size();
        }
        const int INSERT = 0;
        const int DELETE = 1;
        const int REPLACE = 2;
        const int NOTHING = 3;
        const int MAX = 505 * 505;
        int n = word1.size();
        int m = word2.size();
        vector<vector<vector<int>>> dp(n + 1, vector<vector<int>>(m + 1, vector<int>(4, MAX)));


        for (int i = 0; i < 4; ++i) {
            dp[0][0][i] = 0;
        }
        for (int i = 0; i <= m; ++i) {
            dp[0][i][INSERT] = i;
        }
        for (int i = 0; i <= n; ++i) {
            dp[i][0][DELETE] = i;
        }
        // word1[:i] == word2[:j]
        for (int i = 1; i <= n; ++i) {
            for (int j = 1; j <= m; ++j) {
                // insert
                for (int k = 0; k < 4; ++k) {
                    dp[i][j][INSERT] = min(dp[i][j][INSERT], dp[i][j - 1][k] + 1);
                }

                for (int k = 0; k < 4; ++k) {
                    dp[i][j][DELETE] = min(dp[i][j][DELETE], dp[i - 1][j][k] + 1);
                }

                if (word1[i - 1] == word2[j - 1]) {
                    for (int k = 0; k < 4; ++k) {
                        dp[i][j][NOTHING] = min(dp[i][j][NOTHING], dp[i - 1][j - 1][k]);
                    }
                } else {
                    // replace
                    for (int k = 0; k < 4; ++k) {
                        dp[i][j][REPLACE] = min(dp[i][j][REPLACE], dp[i - 1][j - 1][k] + 1);
                    }

                    // // delete
                    // if (i < n && word1[i] == word2[j - 1] || j == m) {
                    //     for (int k = 0; k < 4; ++k) {
                    //         dp[i][j][DELETE] = min(dp[i][j][DELETE], dp[i][j - 1][k] + 1);
                    //     }
                    // }
                }
                
            }
        }
        return *min_element(dp[n][m].begin(), dp[n][m].end());
    }
};
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