Edit Distance

题目
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:

Insert a character
Delete a character
Replace a character

答案

class Solution {
    public int minDistance(String ss1, String ss2) {
        int m = ss1.length(), n = ss2.length();
        char[] s1 = ss1.toCharArray(), s2 = ss2.toCharArray(); 
        // f[i][j]: What is the minimum edit distance between s1[i...m-1] and s2[j...n-1] ?
        int[][] f = new int[m+1][n+1];
        
        // When s[i] == s[j]:
        // f[i][j] = f[i+1][j+1] (nothing changed)
        
        // When s[i] != s[j]:
        // f[i][j] = f[i+1][j+1] + 1 (replace s[i])
        // f[i][j] = f[i + 1][j] + 1 (delete s[i])
        // f[i][j] = f[i][j+1] + 1 (insert some char before s[i])
        
        for(int i = m; i >= 0; i--) {
            for(int j = n; j >= 0; j--) {
                // Base cases
                if(i == m) {
                    f[i][j] = n - j;
                    continue;
                }
                if(j == n) {
                    f[i][j] = m - i;
                    continue;
                }

                int a = f[i + 1][j] + 1;
                int b = f[i][j + 1] + 1;
                int c = (s1[i] == s2[j])? (f[i+1][j+1]) : (f[i+1][j+1] + 1);
                f[i][j] = Math.min(a, Math.min(b, c));                
            }
        }
        return f[0][0];
    }
}