RPN Stack Evaluation Problems

Problem 1: *3 5 + 2 **

Step Token Operation Stack After
1 3 Push 3 [3]
2 5 Push 5 [3, 5]
3 + Pop 5,3 → Push 8 [8]
4 2 Push 2 [8, 2]
5 * Pop 2,8 → Push 16 [16]

Final Answer: 16

Problem 2: 8 2 / 3 + 5 -

Step Token Operation Stack After
1 8 Push 8 [8]
2 2 Push 2 [8, 2]
3 / Pop 2,8 → Push 4 [4]
4 3 Push 3 [4, 3]
5 + Pop 3,4 → Push 7 [7]
6 5 Push 5 [7, 5]
7 - Pop 5,7 → Push 2 [2]

Final Answer: 2

Problem 3: 7 3 - 2 * 6 +

Step Token Operation Stack After
1 7 Push 7 [7]
2 3 Push 3 [7, 3]
3 - Pop 3,7 → Push 4 [4]
4 2 Push 2 [4, 2]
5 * Pop 2,4 → Push 8 [8]
6 6 Push 6 [8, 6]
7 + Pop 6,8 → Push 14 [14]

Final Answer: 14

Problem 4: 4 5 * 3 2 + / 6 -

Step Token Operation Stack After
1 4 Push 4 [4]
2 5 Push 5 [4, 5]
3 * Pop 5,4 → Push 20 [20]
4 3 Push 3 [20, 3]
5 2 Push 2 [20, 3, 2]
6 + Pop 2,3 → Push 5 [20, 5]
7 / Pop 5,20 → Push 4 [4]
8 6 Push 6 [4, 6]
9 - Pop 6,4 → Push -2 [-2]

Final Answer: -2

Problem 5: 12 3 / 2 + 5 * 1 -

Step Token Operation Stack After
1 12 Push 12 [12]
2 3 Push 3 [12, 3]
3 / Pop 3,12 → Push 4 [4]
4 2 Push 2 [4, 2]
5 + Pop 2,4 → Push 6 [6]
6 5 Push 5 [6, 5]
7 * Pop 5,6 → Push 30 [30]
8 1 Push 1 [30, 1]
9 - Pop 1,30 → Push 29 [29]

Final Answer: 29

Key Points:

  • Stack grows from left to right (rightmost element is top of stack)
  • Operators pop two values: second-to-top is left operand, top is right operand
  • For subtraction/division: be careful about operand order (a b - means a - b)
  • Final stack should contain exactly one value - that’s your answer!