The Shunting Yard algorithm was developed by Edsger Dijkstra as a means to parse an infix mathematical expression into Reverse Polish notation (postfix).

Here is an step-by-step image for A+B*C-D from wiki.

A simplified version of the Shunting-yard algorithm (complete version) |

- For all the input tokens
^{[S1]}:- Read the next token
^{[S2]}; - If token is an operator
**(x)**^{[S3]}:- While there is an operator
**(y)**at the top of the operators stack and either**(x)**is left-associative and its precedence is less or equal to that of**(y),**or**(x)**is right-associative and its precedence is less than**(y)**^{[S4]}:- Pop
**(y)**from the stack^{[S5]}; - Add
**(y)**output buffer^{[S6]};
- Pop
- Push (x) on the stack
^{[S7]};
- While there is an operator
- Else If token is left parenthesis, then push it on the stack
^{[S8]}; - Else If token is a right parenthesis
^{[S9]}:- Until the top token (from the stack) is left parenthesis, pop from the stack to the output buffer
^{[S10]}; - Also pop the left parenthesis but don’t include it in the output buffer
^{[S11]};
- Until the top token (from the stack) is left parenthesis, pop from the stack to the output buffer
- Else add token to output buffer
^{[S12]}.
- Read the next token
- While there are still operator tokens in the stack, pop them to output
^{ [S13]}
Note: |

Here is a simple implementaion in Java :

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