Parsing - leftmost and rightmost derivation

Question

process after Left most derivation i think, im not totally convinced. I am just intrigued of how to create a parser in C#. I've been studying the theory for the past couple of days and I have come into something I don't fully understand which is rightmost and leftmost derivations for example:

Input  - aa+a* 

and the grammar is S -> SS + | SS * | a S -> SS + | SS * | a

My Solution: S | S+S | S S+S | a+S S | AA+S A | AA + A obviously my paper solution had interior leaves and what not.

I have a solution for this just not convinced its right in the parser tree. Any solutions would be very much appreciated. anybody know the right solution including the parse tree?

Answer 1

Parse Tree

|  |==| a
|  |   
|==|==| a  
|  |
|  | +  
|   
|==| a
|   
| *

How do I build this tree?

given a -> shift (a)
given a -> shift (a)
given + -> reduce ((a) (a) +)
given a -> shift (a)
given * -> reduce (((a) (a) +) (a) *)

Answer 2

This parse tree

- S
-
  - S
  -
    - S
    - a
  -
    - S
    - a
  - +
-
  - S
  - a
- '*'

is produced by this Perl script using a general BNF parser . Hope this will help you test various grammar/input combinations you may have.