Question

USING C++:

Consider the precedence levels of the relational, logical, and arithmetic operators of the PySub language to be as follows (NOTE: 5 has highest precedence and 0 lowest):

5	*, /, %
4	+, -
3	<, <=, >, >=, !=, ==
2	not
1	and
0	or

1.  Infix-Postfix Conversion and Evaluation with Logical and Relational operators – Convert the following infix expression to a postfix expression and evaluate the result (assume that true=1 and false=0). Provide both the postfix expression and the result.

• (19 + 4) * 2 < (32 * 2 + 1) and (16 / 4) == 4

Answer 1

The Given Infix expression is:

(19 + 4) * 2 < (32 * 2 + 1) AND (16 / 4) == 4

To convert Infix to Postfix expression, we use stack, called 'Operator stack'. For coversion, we use precedence and associatiativity rules of operators.

Infix Expression is: A operand B

Potfix Expresion is: A B operand

As precedence is already given in quetion, following is generally followed associativity:

Precedence	Operator	Associativity
5	*, /, %	Left to right
4	+, -	Left to right
3	<, <=, >, >=, !=, ==	Left to right
2	not	Left to right
1	and	Left to right
0	or	Left to right

Rules:

1. scan infix expession left to right.
2. whenever you see the operand, add it to postfix expression.
3. whenever you see the operator, push it into the stack.
4. if priority of operator is higher than operator present on top of stack, then push operator on the stack. If priority is low, pop the top of stack and it to prefix expression and add the low priority operator on to the stack.
5. If operator is of same precedence to the operator on the top of stack, then there are two cases according to associativity: if associativity is Left to right then pop top of stack and add to postfix expression; if associativity is right to left then push operator on top of stack.
6. if closing bracket is seen, pop operators one by one from top of the stack until you see opening bracket on the stack, and add to postfix expression.

now, for conversion: see the image

The postfix expression is:

19 4 + 2 * 32 2 * 1 + < 16 4 / 4 == AND

Postfix Evaluation

For evaluation, we use stack called, operand stack.

Rules:

1. scan postfix expression left to right.
2. whenever you se operand, push it into stack.
3. whenever you see operator, pop 1 top operand, it is B; pop 2nd top operator, it is A. Then perform: A operator B
4. push the result into top of stack

Now, for evaluation: see image