Download presentation

Presentation is loading. Please wait.

Published byCamryn Towery Modified over 2 years ago

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

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

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. 2 + 3 * 8 - 4

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

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

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

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

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

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

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

Similar presentations

OK

Infix to postfix conversion Process the tokens from a vector infixVect of tokens (strings) of an infix expression one by one When the token is an operand.

Infix to postfix conversion Process the tokens from a vector infixVect of tokens (strings) of an infix expression one by one When the token is an operand.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on trade promotion Ppt on solar eclipse and lunar eclipse Ppt on cervical cancer vaccine Ppt on main distribution frame Ppt on c language basics Ppt on iso 9000 and 14000 Ppt on charge coupled device radiography Ppt on boilers operations manual Download ppt on acid bases and salts for class 10 Ppt on animals our friends