[LC] 72. Edit Distance

Given two words word1 and word2, find the minimum number of operations required to convert word1 to word2.

You have the following 3 operations permitted on a word:

1. Insert a character
2. Delete a character
3. Replace a character

Example 1:

Input: word1 = "horse", word2 = "ros"
Output: 3
Explanation: 
horse -> rorse (replace 'h' with 'r')
rorse -> rose (remove 'r')
rose -> ros (remove 'e')

Example 2:

Input: word1 = "intention", word2 = "execution"
Output: 5
Explanation: 
intention -> inention (remove 't')
inention -> enention (replace 'i' with 'e')
enention -> exention (replace 'n' with 'x')
exention -> exection (replace 'n' with 'c')
exection -> execution (insert 'u')

class Solution {
    public int minDistance(String word1, String word2) {
        int[][] steps = new int[word1.length() + 1][word2.length() + 1];
        for (int i = 0; i <= word1.length(); i++) {
            for (int j = 0; j <= word2.length(); j++) {
                if (i == 0) {
                    steps[i][j] = j;
                } else if (j == 0) {
                    steps[i][j] = i;
                } else if (word1.charAt(i - 1) == word2.charAt(j - 1)) {
                    steps[i][j] = steps[i - 1][j - 1];
                } else {
                    steps[i][j] = Math.min(steps[i - 1][j - 1], Math.min(steps[i - 1][j], steps[i][j - 1])) + 1;
                }
            }
        }
        return steps[word1.length()][word2.length()];
    }
}