Description
# Convert Infix Expression to Postfix Expression
You should be able to reuse `list.c` and `list.h` from HW13.
If your `list.c` was incorrect, this assignment gives you a chance to obtain scores if your `list.c` is correct for HW14.
Learning Goals
==============
* Understand stack
* Implement stack using linked list
* Convert Infix to Postfix
Infix and Postfix
=================
One advantage of postfix is that the precedence of operations is already
in postfix expression. Consider the following examples:
Infix | Postfix
————|———-
6 + 3 – 5 | 6 3 + 5 –
6 + 3 * 5 | 6 3 5 * +
(6 + 3) * 5 | 6 3 + 5 *
Each input line can be one of the following
1. A number
2. An operator `+`, `-`, or `*`
3. An open parenthesis `(`
4. A close parenthesis `)`
For simplicity, you may assume that the infix inputs are always valid.
Example 1
———
A stack of operators is used to keep track of the order
Consider the input A * B + C (A, B, C are numbers).
Data Structure| Content
————–|————-
Operator Stack| `[]` (empty)
Output | `[]` (empty)
First, A is a number and it is added to the output.
Data Structure| Content
————–|————-
Operator Stack| `[]` (empty)
Output | `[A]`
Next, the operator * is seen. It is pushed to the operator stack.
Data Structure| Content
————–|————-
Operator Stack| `[*]`
Output | `[A]`
The operand B is seen. B is added to the output.
Data Structure| Content
————–|————-
Operator Stack| `[*]`
Output | `[A B]`
Data Structure| Content
————–|————-
Operator Stack| `[*]`
Output | `[A B]`
Next, read the operator +. **Since it has lower precedence, pop * and add it to the output.** Push + to the stack.
Data Structure| Content
————–|————-
Operator Stack| `[+]`
Output | `[A B *]`
The operand C is added to the output.
Data Structure| Content
————–|————-
Operator Stack| `[+]`
Output | `[A B * C]`
Nothing is left in the input. Pop the stack and append it to the end of the output.
Data Structure| Content
————–|————-
Operator Stack| `[]`
Output | `[A B * C +]`
Example 2
———
Consider the input A + B * C
Data Structure| Content
————–|————-
Operator Stack| `[]` (empty)
Output | `[]` (empty)
A is a number and it is added to the output.
Data Structure| Content
————–|————-
Operator Stack| `[]` (empty)
Output | `[A]`
Next, the operator + is seen. It is pushed to the operator stack.
Data Structure| Content
————–|————-
Operator Stack| `[+]`
Output | `[A]`
The operand B is seen. B is added to the output.
Data Structure| Content
————–|————-
Operator Stack| `[+]`
Output | `[A B]`
Next, read the operator *. **It has a higher precedence than + in the
stack and push it to the stack.**
Data Structure| Content
————–|————-
Operator Stack| `[+*]`
Output | `[A B]`
The operand C is added to the output.
Data Structure| Content
————–|————-
Operator Stack| `[+*]`
Output | `[A B C]`
Nothing is left in the input. Pop the stack and append it to the end of the output.
Data Structure| Content
————–|————-
Operator Stack| `[+]`
Output | `[A B C *]`
Keep popping and appending to the end of the output.
Data Structure| Content
————–|————-
Operator Stack| `[]`
Output | `[A B C * +]`
Example 3
———
Consider the input A * (B + C)
Data Structure| Content
————–|————-
Operator Stack| `[]` (empty)
Output | `[]` (empty)
A is a number and it is added to the output.
Data Structure| Content
————–|————-
Operator Stack| `[]` (empty)
Output | `[A]`
Next, the operator * is seen. It is pushed to the operator stack.
Data Structure| Content
————–|————-
Operator Stack| `[*]`
Output | `[A]`
An open parenthesis is seen. Push it to the stack.
Data Structure| Content
————–|————-
Operator Stack| `[* (]`
Output | `[A]`
The operand B is seen and it is added to the output.
Data Structure| Content
————–|————-
Operator Stack| `[* (]`
Output | `[A B]`
Next, read the operator + and push it to the stack.
Data Structure| Content
————–|————-
Operator Stack| `[* ( +]`
Output | `[A B]`
The operand C is added to the output.
Data Structure| Content
————–|————-
Operator Stack| `[* ( +]`
Output | `[A B C]`
Next, the close parenthesis is seen. **Pop the operator(s) in the stack until the open parenthesis is seen.**
Data Structure| Content
————–|————-
Operator Stack| `[*]`
Output | `[A B C + ]`
Nothing is left in the input. Pop the stack and append it to the end of the output.
Data Structure| Content
————–|————-
Operator Stack| `[]`
Output | `[A B C + *]`
Example 4
———
Consider the input (A + B) * (C + D) * (E + F).
Data Structure| Content | Action
————–|—————————|———————–
Operator Stack| `[]` (empty) |
Output | `[]` (empty) |
Operator Stack| `[(]` | read and push `(`
Output | `[]` |
Operator Stack| `[(]` |
Output | `[A]` | read and output `A`
Operator Stack| `[(+]` | read and push `+`
Output | `[A]` |
Operator Stack| `[(+]` |
Output | `[A B]` | read and output `B`
Operator Stack| `[]` | read `)`, pop until `(`
Output | `[A B +]` |
Operator Stack| `[*]` | read and push `*`
Output | `[A B +]` |
Operator Stack| `[* (]` | read and push `(`
Output | `[A B + ]` |
Operator Stack| `[* (]` |
Output | `[A B + C]` | read and output `C`
Operator Stack| `[* ( +]` | read and push `+`
Output | `[A B + C]` |
Operator Stack| `[* ( +]` |
Output | `[A B + C D]` | read and output `D`
Operator Stack| `[* ]` | read `)`, pop until `(`
Output | `[A B + C D +]` |
Operator Stack| `[]` | read `*`. It has the same precedence, pop `*` and add to output
Output | `[A B + C D + *]` |
Operator Stack| `[* ]` | push `*`
Output | `[A B + C D + *]` |
Operator Stack| `[* (]` | read and push `(`
Output | `[A B + C D + *]` |
Operator Stack| `[* (]` | read and output `E`
Output | `[A B + C D + * E]` |
Operator Stack| `[* ( +]` | read and push `+`
Output | `[A B + C D + * E]` |
Operator Stack| `[* ( +]` |
Output | `[A B + C D + * E F]` | read and output `F`
Operator Stack| `[* ]` | read `)`, pop until `(`
Output | `[A B + C D + * E F + ]` |
Operator Stack| `[]` | pop the stack and output
Output | `[A B + C D + * E F + *]` |
Submission
==========
“`
zip hw14.zip list.c convert.c
“`
Upload hw14.zip.
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