For the following arithmetic expression: ((2+3)*(4/2))+2 Show step-by-step process for matching parentheses using stack data structure.
The step-by-step process for matching parentheses in the expression ((2+3)*(4/2))+2 using stack is as follows:
Algorithm: Scan the expression from left to right. When an opening parenthesis '(' is encountered, PUSH it onto the stack. When a closing parenthesis ')' is encountered, POP from the stack. At the end, if the stack is empty, the parentheses are properly matched.
Step-by-Step Process:
| Step | Symbol Read | Action | Stack Status |
|---|---|---|---|
| 1 | ( | PUSH '(' | ( |
| 2 | ( | PUSH '(' | ( ( |
| 3 | 2 | Ignore | ( ( |
| 4 | + | Ignore | ( ( |
| 5 | 3 | Ignore | ( ( |
| 6 | ) | POP | ( |
| 7 | * | Ignore | ( |
| 8 | ( | PUSH '(' | ( ( |
| 9 | 4 | Ignore | ( ( |
| 10 | / | Ignore | ( ( |
| 11 | 2 | Ignore | ( ( |
| 12 | ) | POP | ( |
| 13 | ) | POP | Empty |
| 14 | + | Ignore | Empty |
| 15 | 2 | Ignore | Empty |
Conclusion: After processing all characters, the stack is empty, which indicates that all opening parentheses have been properly matched with corresponding closing parentheses. Hence, the expression has valid/matched parentheses.
Explanation
This question tests the student's understanding of using stack data structure for parentheses matching. The algorithm involves pushing opening parentheses onto the stack and popping when closing parentheses are encountered. The expression ((2+3)*(4/2))+2 has 3 opening and 3 closing parentheses, all properly nested, resulting in an empty stack at the end - indicating valid parentheses matching.
Solution Steps
Step 1: Scan expression left to right, PUSH opening parentheses onto stack
Step 2: On encountering closing parenthesis, POP from stack
Step 3: Ignore non-parenthesis characters (operands and operators)
Step 4: After processing all characters, check if stack is empty
Step 5: Empty stack = matched parentheses; Non-empty stack = unmatched parentheses