Edit Distance

EditDistance.java

/*
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
*/




/* Dynamic Programming
   Example. abcee vs abddd
     0 | a | b | c | e | e
  0| 0   1   2   3   4   5
  a| 1   0   1   2   3   4 
  b| 2   1   0   1   2   3
  d| 3   2   1   1   2   3 
  d| 4   3   2   2   2   3
  d| 5   4   3   3   3   3
*/ 
public class Solution {
    public int minDistance(String word1, String word2) {
        int[][] a = new int[word1.length()+1][word2.length()+1];
        
        for(int i = 0; i < word1.length()+1; i++) {
            a[i][0] = i;
        }
        
        for(int j = 0; j < word2.length()+1; j++) {
            a[0][j] = j;
        }
        
        for(int j = 1 ; j < word2.length() + 1; j++) {
            for(int i = 1; i < word1.length() + 1; i++) {
                if(word1.charAt(i-1) == word2.charAt(j-1)){
                    a[i][j] = a[i-1][j-1];
                } else {
                    a[i][j] = Math.min(a[i-1][j-1], Math.min(a[i-1][j],a[i][j-1])) + 1;
                }
            }
        }
        
        return a[word1.length()][word2.length()];
    }
}