Polish Notation - Example

Example

This uses the same expression as before and the algorithm above.


Token Action Stack Notes
1 Operand 1 Push onto stack.
1 Operand 1 1 Push onto stack.
+ Operator 2 Pop the two operands (1, 1), calculate (1 + 1 = 2) and push onto stack.
2 Operand 2 2 Push onto stack.
+ Operator 4 Pop the two operands (2, 2), calculate (2 + 2 = 4) and push onto stack.
3 Operand 3 4 Push onto stack.
1 Operand 1 3 4 Push onto stack.
1 Operand 1 1 3 4 Push onto stack.
+ Operator 2 3 4 Pop the two operands (1, 1), calculate (1 + 1 = 2) and push onto stack.
7 Operand 7 2 3 4 Push onto stack.
− Operator 5 3 4 Pop the two operands (7, 2), calculate (7 − 2 = 5) and push onto stack.
15 Operand 15 5 3 4 Push onto stack.
/ Operator 3 3 4 Pop the two operands (15, 5), calculate (15/5 = 3) and push onto stack.
* Operator 9 4 Pop the two operands (3, 3), calculate (3 * 3 = 9) and push onto stack.
− Operator 5 Pop the two operands (9, 4), calculate (9 − 4 = 5) and push onto stack.

The result is at the top of the stack.

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