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

用一个二维数组，map[i][j]  代表从word1(0,i)变化到word2(0,j)需要的次数。

public class Solution {
    //Time: O(m*n)  Space: O(m*n)
    public int minDistance(String word1, String word2) {
        if (word1.length() == 0) {
            return word2.length();
        }
        
        if (word2.length() == 0) {
            return word1.length();
        }
        
        int m = word1.length() + 1;
        int n = word2.length() + 1;
        int[][] map = new int[m][n];
        for (int i = 1; i < m; i++) {
            map[i][0] = i;
        }
        for (int i = 1; i < n; i++) {
            map[0][i] = i;
        }
        
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                if (word1.charAt(i - 1) == word2.charAt(j - 1)) {
                    map[i][j] = map[i - 1][j - 1];
                } else {
                    int delete = map[i - 1][j] + 1;
                    int insert = map[i][j - 1] + 1;
                    int replace = map[i - 1][j - 1] + 1;
                    map[i][j] = Math.min(delete, Math.min(insert, replace));
                }
            }
        }
        return map[m - 1][n - 1];
    }
}