int m = word1.length();
        int n = word2.length();
        
        if(n*m ==0) return n+m;
        if(word1.equals(word2)) return 0;
        
        int [][] d = new int[m+1][n+1];
        
        // init boundaries
        for (int i = 0; i < m + 1; i++) {
          d[i][0] = i;  
        }
        for (int j = 0; j < n + 1; j++) {
          d[0][j] = j;
        }
        
        for(int i =1;i<m+1;i++){
            for(int j=1;j<n+1;j++){
                int left = d[i-1][j]+1;
                int below = d[i][j-1]+1;
                int diagonal = d[i-1][j-1];
                
                if(word1.charAt(i-1) != word2.charAt(j-1)){
                    diagonal += 2;   // changing this to 2 helped solve it.
                }
                d[i][j] = Math.min(left,Math.min(below,diagonal));
            }
        }
        return d[m][n];