Shunting-yard algorithm Infix to postfix conversion Based on

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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