GATE | GATE-CS-2002 | Question 44
To evaluate an expression without any embedded function calls:
(A) One stack is enough
(B) Two stacks are needed
(C) As many stacks as the height of the expression tree are needed
(D) A Turing machine is needed in the general case
Any expression can be converted into Postfix or Prefix form.
Prefix and postfix evaluation can be done using a single stack.
For example : Expression ’10 2 8 * + 3 -‘ is given.
PUSH 10 in the stack.
PUSH 2 in the stack.
PUSH 8 in the stack.
When operator ‘*’ occurs, POP 2 and 8 from the stack.
PUSH 2 * 8 = 16 in the stack.
When operator ‘+’ occurs, POP 16 and 10 from the stack.
PUSH 10 * 16 = 26 in the stack.
PUSH 3 in the stack.
When operator ‘-‘ occurs, POP 26 and 3 from the stack.
PUSH 26 – 3 = 23 in the stack.
So, 23 is the answer obtained using single stack.
Thus, option (A) is correct.
Please comment below if you find anything wrong in the above post.
Quiz of this Question