Shunting-yard algorithm

1. Shunting-yard algorithm Infix to postfix conversion Based on http://en.wikipedia.org/wiki/Shunting_yard_algorithm

2. 2 + (3 * (8 - 4)) = ? How to evaluate this (or similar) formula? • TODO: • rules should be visible and highlighted when a rule is applied • an example containing operator precedence rules

3. 2 + (3 * (8 - 4)) = ? Let’s play that the tokens are train cars and we are shunting the shunting yard. 2 + ( 3 * ( 8 - 4 ) )

4. 2 + (3 * (8 - 4)) = ? The first car is a number, it goes straight through. 2 + ( 3 * ( 8 - 4 ) )

5. 2 + (3 * (8 - 4)) = ? Next, the third track (the stack) is empty, we move the operator there. 2 + ( 3 * ( 8 - 4 ) )

6. 2 + (3 * (8 - 4)) = ? Left parenthesis goes always down. 2 ( 3 * ( 8 - 4 ) ) +

7. 2 + (3 * (8 - 4)) = ? Again, there is a number. It moves always straight to the left. 2 3 * ( 8 - 4 ) ) ( +

8. 2 + (3 * (8 - 4)) = ? Next there is an operator, it goes down because the topmost car there is an parenthesis. 2 3 * ( 8 - 4 ) ) ( +

9. 2 + (3 * (8 - 4)) = ? Again a left parenthesis, they go always to the stack. 2 3 ( 8 - 4 ) ) * ( +

10. 2 + (3 * (8 - 4)) = ? A number, straight to the left. 2 3 8 - 4 ) ) ( * ( +

11. 2 + (3 * (8 - 4)) = ? A number, straight to the left. 2 3 8 - 4 ) ) ( * ( +

12. 2 + (3 * (8 - 4)) = ? An operator, move it down. 2 3 8 - 4 ) ) ( * ( +

13. 2 + (3 * (8 - 4)) = ? A number, to the left, as always. 2 3 8 4 ) ) - ( * ( +

14. 2 + (3 * (8 - 4)) = ? A right parenthesis. Now we move the cars from the bottom until there is left parenthesis. 2 3 8 4 ) ) - ( * ( +

15. 2 + (3 * (8 - 4)) = ? The pair of the parenthesis just disappear. 2 3 8 4 - ) ) ( * ( +

16. 2 + (3 * (8 - 4)) = ? Again, we pop out the items until there is a left parenthesis. 2 3 8 4 - ) * ( +

17. 2 + (3 * (8 - 4)) = ? A pair of parenthesis disappear. 2 3 8 4 - * ) ( +

18. 2 + (3 * (8 - 4)) = ? No more cars on the right side, so we move the cars from the bottom to the left. 2 3 8 4 - * +

19. 2 + (3 * (8 - 4)) = ? Now the transformation is done, how to evaluate it? 2 3 8 4 - * +

20. 2 + (3 * (8 - 4)) = ? Move the cars back to the right side. 2 3 8 4 - * +

21. 2 + (3 * (8 - 4)) = ? Move the cars back to the right side. 2 3 8 4 - * +

22. 2 + (3 * (8 - 4)) = ? Move the numbers to the down until we find an operator. 2 3 8 4 - * +

23. 2 + (3 * (8 - 4)) = ? When operator is found, place it to the middle so that it is between two numbers. - * + 4 8 3 2

24. 2 + (3 * (8 - 4)) = ? Do the calculation and put the result back to down. 8 - 4 * + 3 2

25. 2 + (3 * (8 - 4)) = ? Do the calculation and put the result back to down. 4 * + 3 2

26. 2 + (3 * (8 - 4)) = ? Again, operator to the middle, between the two upmost numbers. * + 4 3 2

27. 2 + (3 * (8 - 4)) = ? Calculate the expression and put the result back to the down. 3 * 4 + 2

28. 2 + (3 * (8 - 4)) = ? Calculate the expression and put the result back to the down. 12 + 2

29. 2 + (3 * (8 - 4)) = ? And the last operator, it is handled in the same way. + 12 2

30. 2 + (3 * (8 - 4)) = ? Calculate the result and that’s it! 2 + 12

31. 2 + (3 * (8 - 4)) = 14 Calculate the result and that’s it! 14