# postfix Postfix Demo The Equation Infix

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```					                        Postfix Demo: The Equation

Infix: (1 + (2 * ((3 + (4 * 5)) * 6))) = 277
Postfix: 1 2 3 4 5 * + 6 * * +                                           = 277

(   1   +   (       2    *   (   (       3   +   (   4       *       5   )   )       *       6   )   )   )

(   1   (   2       (    (   3   (       4   5   )   *       )   +       6   )       *       )   *   )   +

23 531 138
20 * + = ==23
4 * +*62 20276
138
276         277

1        2   3       4       5   *       +       6       *       *       +

1
Postfix Demo: The Stack

What is a ‘STACK’?
At the grocery store, on the canned goods aisle, the cans
are STACKED on top of each other.
Which one do we take to make sure the stack doesn’t
fall over?
How did the store worker put the cans into the
stack? Where did he or she place the new can?
We take the top item and we place new items on the top.
So does the computer.
To evaluate the problem (1 + (2 * ((3 + (4 * 5)) * 6))), the
computer uses a stack and postfix notation.
1   2   3   4   5   *   +   6   *   *   +

2
Postfix Demo: The Evaluation
1   2     3    4     5       *    +    6   *     *   +

The Stack

5
4          *        5    =       20
4
6
20
3          +       20    =       23
3
138
23

2
276             23         *        6    =       138

1
2          *       138   =       276

1          +       276   =       277

3

```
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