## Contents

Postfix expressions:

• expressions in which the operation being specified occurs after the two operands, in a nested way

Example: each postfix expression evaluates to 9.

```5 4 +

2 7 * 4 1 + -

1 1 + 1 1 + + 1 1 + 1 1 + + +
```

## Stacks

Postfix expressions can be evaluated by pushing the expressions onto a stack, where the stack deals with expressions. Expressions can consist of a single node (a number), or two expressions and an operator (making the expression definition recursive - like a tree).

In terms of stacks, we can push digits onto the stack UNTIL we reach a symbol, then apply the symbol to the next two expressions on the stack, turn the result into an expression, and push the result expression onto the stack.

## Trees

To represent a postfix expression with an expression tree, we can use a binary tree - particularly, we have to have a proper binary tree. (Each node can have zero or two children.)

We look at the whole expression one piece at a time, pushing the pieces onto the stack, until we reach an operator, whereupon we pop two elements off the stack, and apply the operator to them. The result becomes a new element, and gets pushed onto the stack.