Question

Evaluate the postfix expression (i) 75*34*+ (ii) 456*+

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Answer 1

Answer:

Let the given expression be “2 3 1 * + 9 -“. We scan all elements one by one.

1) Scan ‘2’, it’s a number, so push it to stack. Stack contains ‘2’

2) Scan ‘3’, again a number, push it to stack, stack now contains ‘2 3’ (from bottom to top)

3) Scan ‘1’, again a number, push it to stack, stack now contains ‘2 3 1’

4) Scan ‘*’, it’s an operator, pop two operands from stack, apply the * operator on operands, we get 3*1 which results in 3. We push the result ‘3’ to stack. Stack now becomes ‘2 3’.

5) Scan ‘+’, it’s an operator, pop two operands from stack, apply the + operator on operands, we get 3 + 2 which results in 5. We push the result ‘5’ to stack. Stack now becomes ‘5’.

6) Scan ‘9’, it’s a number, we push it to the stack. Stack now becomes ‘5 9’.

7) Scan ‘-‘, it’s an operator, pop two operands from stack, apply the – operator on operands, we get 5 – 9 which results in -4. We push the result ‘-4’ to stack. Stack now becomes ‘-4’.

8) There are no more elements to scan, we return the top element from stack (which is the only element left in stack).