Data Structures | Stack | Question 6

The following postfix expression with single digit operands is evaluated using a stack:

              8 2 3 ^ / 2 3 * + 5 1 * - 

Note that ^ is the exponentiation operator. The top two elements of the stack after the first * is evaluated are:
(A) 6, 1
(B) 5, 7
(C) 3, 2
(D) 1, 5


Answer: (A)

Explanation: The algorithm for evaluating any postfix expression is fairly straightforward:

1. While there are input tokens left
    o Read the next token from input.
    o If the token is a value
       + Push it onto the stack.
    o Otherwise, the token is an operator 
      (operator here includes both operators, and functions).
       * It is known a priori that the operator takes n arguments.
       * If there are fewer than n values on the stack
        (Error) The user has not input sufficient values in the expression.
       * Else, Pop the top n values from the stack.
       * Evaluate the operator, with the values as arguments.
       * Push the returned results, if any, back onto the stack.
2. If there is only one value in the stack
    o That value is the result of the calculation.
3. If there are more values in the stack
    o (Error)  The user input has too many values.

Source for algorithm: http://en.wikipedia.org/wiki/Reverse_Polish_notation#The_postfix_algorithm



Let us run the above algorithm for the given expression.
First three tokens are values, so they are simply pushed. After pushing 8, 2 and 3, the stack is as follows

    8, 2, 3

When ^ is read, top two are popped and power(2^3) is calculated

    8, 8

When / is read, top two are popped and division(8/8) is performed

    1

Next two tokens are values, so they are simply pushed. After pushing 2 and 3, the stack is as follows



    1, 2, 3

When * comes, top two are popped and multiplication is performed.

    1, 6


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