QUESTION

(a) Convert each of the following expressions to prefix and postfix.

(i) (A+B)*(C+D)

(ii) A-B/(C*D^E) (^ denotes exponentiation)

(b) The following algorithm converts an infix expression into its postfix representation. We have assumed that the infix expressions contain only the operators +, -, * and /. The expressions do not contain parentheses. Examples of valid expressions are A+B*C and A/B+C/D-E.

opstk = the empty stack;

while (not end of input) {

symb = next input character;

if (symb is an operand)

add symb to the postfix string

else{

while(!empty(opstk) && prcd(stacktop(opstk),symb)){

topsymb = pop(opstk);

add topsymb to the postfix string;

}

push(opstk,symb);

}

}

while(!empty(opstk)){

topsymb = pop(opstk);

add topsymb to the postfix string;

}

(i) Write the function empty in C. The function empty must return TRUE if the stack is empty and FALSE if the stack is not empty.

(ii) Write the function pop in C. The function must perform the following three actions:

1. If the stack is empty, print a warning message and halt execution.

2. Remove the top element from the stack.

3. Return the top element of the stack to the calling function.

(iii) Write the function prcd(op1,op2) in C, where op1 and op2 are characters representing operators. The function prcd(op1,op2) must return TRUE if op1 has precedence over op2 when op1 appears to the left of op2 in an infix expression. The function prcd(op1,op2) returns FALSE otherwise.