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Reverse Polish Notation
Written by J.J. Shepherd
Reverse Polish Notation
• Most math expressions you have seen were
written in “in-fix” notation
• Example:
3+5
• However there is another notation called “postfix” or “Revere Polish Notation” where the
operator is at the end
• Example
35+
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
Reverse Polish Example
• Here the user has inputted the string 3 2 +
3 2 +
Head
Tail
Reverse Polish Example
• 3 is a number so push it on the stack
3 2 +
3
Head
Tail
Reverse Polish Example
• 2 is a number so push it on the stack
3 2 +
2
Head
3
Tail
Reverse Polish Example
• + is an operator so pop of two
3 2 +
2
Head
3
Tail
Reverse Polish Example
• + is an operator so pop of two
3 2 +
+2
POP
2
Head
3
Tail
Reverse Polish Example
• + is an operator so pop of two
3 2 +
3+2
3POP
Head
Tail
Reverse Polish Example
• Evaluate
3 2 +
5
Head
Tail
Reverse Polish Example
• Push the value back
3 2 +
5
5
Head
Tail
Reverse Polish Example
• DONE!
3 2 +
5
Head
Tail
Reverse Polish Example
• Here the user has inputted the string 8 2 – 3 *
8 2 – 3 *
Head
Tail
Reverse Polish Example
• 8 is a number so push it on the stack
8 2 – 3 *
8
Head
Tail
Reverse Polish Example
• 2 is a number so push it on the stack
8 2 – 3 *
2
Head
8
Tail
Reverse Polish Example
• - is an operator so pop of two
8 2 – 3 *
2
Head
8
Tail
Reverse Polish Example
• + is an operator so pop of two
8 2 – 3 *
-2
POP
2
Head
8
Tail
Reverse Polish Example
• + is an operator so pop of two
8 2 – 3 *
8-2
3POP
Head
Tail
Reverse Polish Example
• Evaluate
8 2 – 3 *
6
Head
Tail
Reverse Polish Example
• Push the value back
8 2 – 3 *
6
6
Head
Tail
Reverse Polish Example
• 3 is a number so push it onto the stack
8 2 – 3 *
3
Head
6
Tail
Reverse Polish Example
• * is an operator so pop of two
8 2 – 3 *
*3
POP
2
Head
6
Tail
Reverse Polish Example
• * is an operator so pop of two
8 2 – 3 *
6*3
POP
6
Head
Tail
Reverse Polish Example
• Evaluate
8 2 – 3 *
18
Head
Tail
Reverse Polish Example
• Push the value back
8 2 – 3 *
18
18
Head
Tail
Reverse Polish Example
• DONE!
8 2 – 3 *
18
Head
Tail