Postfix Expressions: Difference between revisions
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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. | 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. | |||
Revision as of 06:00, 7 June 2017
About
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.