- Asked 2/14
- 2068 Bhadra · 6 marks
Convert and evaluate A/B-(C+D)*E
Short answer
Postfix: AB/CD+E*-. Evaluating with A=8, B=2, C=3, D=1, E=1 yields 0.
Convert the given infix expression A/B-(C+D)*E into equivalent postfix expression showing each step in tabular form and evaluate the obtained postfix expression showing STACK status each time when A=8, B=2, C=3, D=1 and E=1.
Conversion of A / B − (C + D) * E
| Step | Symbol | Stack (bottom → top) | Postfix output |
|---|---|---|---|
| 1 | A | (empty) | A |
| 2 | / | / | A |
| 3 | B | / | AB |
| 4 | - | - | AB/ |
| 5 | ( | -( | AB/ |
| 6 | C | -( | AB/C |
| 7 | + | -(+ | AB/C |
| 8 | D | -(+ | AB/CD |
| 9 | ) | - | AB/CD+ |
| 10 | * | -* | AB/CD+ |
| 11 | E | -* | AB/CD+E |
| end | (pop all) | (empty) | AB/CD+E*- |
Postfix: AB/CD+E*-
Evaluation with A = 8, B = 2, C = 3, D = 1, E = 1
| Step | Symbol | Action | Stack (bottom → top) |
|---|---|---|---|
| 1 | A | push 8 | 8 |
| 2 | B | push 2 | 8, 2 |
| 3 | / | pop 2 (right), 8 (left); 8 / 2 = 4; push | 4 |
| 4 | C | push 3 | 4, 3 |
| 5 | D | push 1 | 4, 3, 1 |
| 6 | + | pop 1 (right), 3 (left); 3 + 1 = 4; push | 4, 4 |
| 7 | E | push 1 | 4, 4, 1 |
| 8 | * | pop 1 (right), 4 (left); 4 * 1 = 4; push | 4, 4 |
| 9 | - | pop 4 (right), 4 (left); 4 - 4 = 0; push | 0 |
Answer: 0. Check: 8/2 − (3+1)*1 = 4 − 4 = 0.
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- Convert and evaluate (A+B)*(C-D) · Data Structure and Algorithm, chapter 2 · asked 2×
- Convert expression to prefix and postfix · Data Structure and Algorithm, chapter 2
- Importance of postfix; convert expression · Data Structure and Algorithm, chapter 2
- Evaluate postfix expression 574-*8/4+ · Data Structure and Algorithm, chapter 2
- Infix to postfix and evaluation · Data Structure and Algorithm, chapter 2
- Convert expression to prefix and postfix · Data Structure and Algorithm, chapter 2
- Algorithm for infix to postfix conversion · Data Structure and Algorithm, chapter 2 · asked 3×