Question

For the postfix expressions, 32 5 3 + / 5 *, trace the algorithm for evaluating postfix expressions by showing the contents of the stack immediately before each of the tokens marked with a caret is read. Also, give the value of the postfix expression.

Answer 1

Postfix Expression:

The postorder scan is used to convert an expression into a postfix expression. In this scan, first of all, we will scan the left subtree, then the right subtree, and at the last root node.

Postfix expression evaluation:

In postfix expression evaluation, the stack data structure is used and we need the expression from left to right.

If it is operand then it is pushed on to the stack and if it is operator then two operands are popped from the stack and then evaluated. The result is pushed back onto the stack and the same process is repeated until the end fo the expression.

The given postfix expression is:

32 5 3 + / 5 *

The step by step evaluation of the given postfix expression is given below:

The expression scan process is highlighted in bold from left to right.

32 5 3 + / 5 *

32 5 3 + / 5 *

32 5 3 + / 5 *

32 5 3 + / 5 *

Now we will pop the two items from the stack and happy + operation.

32 5 3 + / 5 *

Now we will pop the two two item from the stack and happy / operation.

32 5 3 + / 5 *

32 5 3 + / 5 *

Now we will pop the two two item from the stack and happy * operation.

The final value in stack is 20.

The value of the postfix expression = 20