LeetCode72 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:

Insert a character
Delete a character
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’)

public int minDistance(String word1, String word2) {
        int m = word1.length();
        int n = word2.length();
        
        int[][] cost = new int[m + 1][n + 1];
        for(int i = 0; i <= m; i++)
            cost[i][0] = i;
        for(int i = 1; i <= n; i++)
            cost[0][i] = i;
        
        for(int i = 0; i < m; i++) {
            for(int j = 0; j < n; j++) {
                if(word1.charAt(i) == word2.charAt(j))
                    cost[i + 1][j + 1] = cost[i][j];
                else {
                    int a = cost[i][j];
                    int b = cost[i][j + 1];
                    int c = cost[i + 1][j];
                    cost[i + 1][j + 1] = a < b ? (a < c ? a : c) : (b < c ? b : c);
                    cost[i + 1][j + 1]++;
                }
            }
        }
        return cost[m][n];
    }