1. Reverse Polish Notation Written by J.J. Shepherd

2. Reverse Polish Notation Most math expressions you have seen were written in “in-fix” notation Example: 3 + 5 However there is another notation called “post- fix” or “Revere Polish Notation” where the operator is at the end Example 3 5 +

3. Big Idea Use a stack to solve reverse polish notation You push onto the stack when there’s a number When there’s an operator (+, -, *, /) then – Pop off two items from the stack – Evaluate the two numbers with that operation – Push the result back to the stack Once it has completed the expression there should only be one item left on the stack

5. Reverse Polish Example Here the user has inputted the string 3 2 + Head Tail 3 2 +

6. Reverse Polish Example 3 is a number so push it on the stack Head Tail 3 2 + 3

7. Reverse Polish Example 2 is a number so push it on the stack Head Tail 3 2 + 32

8. Reverse Polish Example + is an operator so pop of two Head Tail 3 2 + 32

9. Reverse Polish Example + is an operator so pop of two Head Tail 3 2 + 32 POP + 2

10. Reverse Polish Example + is an operator so pop of two Head Tail 3 2 + 3 POP 3 + 2

11. Reverse Polish Example Evaluate Head Tail 3 2 + 5

12. Reverse Polish Example Push the value back Head Tail 3 2 + 5 5

13. Reverse Polish Example DONE! Head Tail 3 2 + 5

15. Reverse Polish Example Here the user has inputted the string 8 2 – 3 * Head Tail 8 2 – 3 *

16. Reverse Polish Example 8 is a number so push it on the stack Head Tail 8 2 – 3 * 8

17. Reverse Polish Example 2 is a number so push it on the stack Head Tail 8 2 – 3 * 82

18. Reverse Polish Example - is an operator so pop of two Head Tail 8 2 – 3 * 82

19. Reverse Polish Example + is an operator so pop of two Head Tail 8 2 – 3 * 82 POP - 2

20. Reverse Polish Example + is an operator so pop of two Head Tail 8 2 – 3 * 3 POP 8 - 2

21. Reverse Polish Example Evaluate Head Tail 8 2 – 3 * 6

22. Reverse Polish Example Push the value back Head Tail 8 2 – 3 * 6 6

23. Reverse Polish Example 3 is a number so push it onto the stack Head Tail 8 2 – 3 * 63

24. Reverse Polish Example * is an operator so pop of two Head Tail 8 2 – 3 * 62 POP * 3

25. Reverse Polish Example * is an operator so pop of two Head Tail 8 2 – 3 * 6 POP 6 * 3

26. Reverse Polish Example Evaluate Head Tail 8 2 – 3 * 18

27. Reverse Polish Example Push the value back Head Tail 8 2 – 3 * 18

28. Reverse Polish Example DONE! Head Tail 8 2 – 3 * 18