<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:
    static int minDistance(const string& word1, const string& word2) {
        short dp[5001][5001];
        // int m{}, n{};
        int m = (int)word1.size();// rows word2Target
        int n = (int)word2.size();//cols word1 WordToBeEdited
        for (int i = 0; i <= max(n, m); ++i) {
            if (i < n)
                dp[0][i] = i;
            if (i < m)
                dp[i][0] = i;
        }
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                if (word1[i - 1] == word2[j - 1]) {
                    dp[i][j] = dp[i - 1][j - 1];
                } else {
                    dp[i][j] = min({
                        dp[i - 1][j],
                        dp[i][j - 1],
                        dp[i - 1][j - 1]
                    })  + 1;
                }
            }
        }

        return dp[m][n];

        // return dfs(0, 0, word1, word2);
    }
private:
    // int dfs(int i, int j, const string& toBeEdited, const string& target) {
    //     if (j == n) {
    //         return m - i;
    //     }
    //     if (i == m) {
    //         return n - j;
    //     }
    //     if (~dp[i][j]) {
    //         return dp[i][j];
    //     }
    //     if (toBeEdited[i] == target[j]) {
    //         return dp[i][j] = dfs(i + 1, j + 1, toBeEdited, target);
    //     }

    //     return dp[i][j] = min({
    //         dfs(i , j + 1, toBeEdited, target),//insrt
    //         dfs(i + 1, j, toBeEdited, target),//remove
    //         dfs(i + 1, j + 1, toBeEdited, target)//replace
    //     }) + 1;
    // }

};
auto init = [](){
    cin.tie(nullptr);
    cout.tie(nullptr);
    ios_base::sync_with_stdio(false);

    return -1;
}();
17811