1. EC-211 DATA STRUCTURES LECTURE 8

2. STACK APPLICATIONS Infix, Prefix, and Postfix Expressions Example – Infix: A+B – Prefix: +AB – Postfix: AB+

3. Postfix Example: Infix: A+(B*C) Convert to Postfix A+(B*C) =A+(BC*) =ABC*+ which is the required postfix form

4. Postfix Example: Infix: (A+B)*(C-D) Convert to Postfix (A+B)*(C-D) =(AB+)*(CD-) =AB+CD-* which is the required postfix form

5. Evaluating a Postfix Expression Each operator in a postfix expression refers to the previous two operands in the expression. Each time we reach an operand we push it onto a stack. When we reach an operator, its operands will be the top two elements on the stack. We then pop these two elements, perform the indicated operation on them, and push the result on the stack. In the end, the result of the expression is left as the only element in the stack, which is popped and returned as the result of evaluation

6. Algorithm for Evaluating a Postfix Expression opndstk=the empty stack; //scan the input string one element a time into symb while (not end of input) { symb=next input character; if (symb is an operand) push(opndstk, symb); else { //symb is an operator opnd2=pop(opndstk); opnd1=pop(opndstk); value=result of applying symb to opnd1 and opnd2; push(opndstk, value); }//end else }//end while return (pop(opndstk));

7. Example symbopnd1opnd2valueopndstk 66 26,2 36,2,3 +2356,5 -6511 31,3 81,3,8 21,3,8,2 /8241,3,4 +3471,7 *1777 6 2 3 + - 3 8 2 / + *

8. Converting an Expression from Infix to Postfix 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) && (operator at top of the stack has precedence greater than or equal symb)){ topsymb=pop(opstk); add topsymb to the postfix string; } push(opstk, symb); }//end else }//end while //output any remaining operator while (!empty(opstk){ topsymb=pop(opstk); add topsymb to the postfix string; }//end while

9. Example SymbPostfix stringopstk AA +A+ BAB+ * +* CABC+* ABC*+ ABC*+ Convert to Postfix:A+B*C

10. Example SymbPostfix stringopstk AA *A* BAB* +AB*+ CAB*C+ * +* DAB*CD+* AB*CD*+ AB*CD*+ Convert to Postfix:A*B+C*D

11. CLASS WORK Suppose S is a non-empty stack of integers. Write a main() function that appropriately utilizes calls to push, pop, and empty to remove the bottom element from the stack. Rest of the stack stays the same. Remember, you do not know the number of elements currently present in stack Prototypes of stack functions: – void push( int) – int pop(); – bool empty();

12. Solution void main() { stack T; int element; while (!S.empty()) { element=S.pop(); T.push( element); } element=T.pop(T); while (!T.empty(){ element=T.pop(); S.push( element); }