72. Edit Distance

Given two words word1 and word2, find the minimum number of steps required to convert word1 to word2. (each operation is counted as 1 step.)

You have the following 3 operations permitted on a word:

a) Insert a character
b) Delete a character
c) Replace a character

Solution:

We use f[i][j] to denote the minimum edits to convert the first i element in word1 to become the first j elements in word2.

This state depends on four conditions:

1. remove the last character of the first i characters in word1 and line up with the first j characters in word2.

2. add a character at the end of the first i characters in word1 and line up with the first j characters in word2.

3. replace the character at the end of the first i characters and line up with the first j characters in word2.

4. the last characters of the first i characters in word1 and the first j characters in word2 are the same, no edit needed.



Code:

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