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# GATE | GATE-CS-2002 | Question 44

To evaluate an expression without any embedded function calls :

(A)

As many stacks as the height of the expression tree are needed

(B)

One stack is enough

(C)

Two stacks are needed

(D)

A Turing machine is needed in the general case

Explanation:

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.

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