2.  STACK STACK  BASIC STACK OPERATIONS BASIC STACK OPERATIONS  PUSH ALGORITHM PUSH ALGORITHM  POP ALGORITHM POP ALGORITHM  EVALUATING A POSTFIX EXPRESSION EVALUATING A POSTFIX EXPRESSION

3.  Stores a set of elements in a particular order  Stack principle: LAST IN FIRST OUT = LIFO  It means: the last element inserted is the first one to be removed  Which is the first element to pick up? BACK

4. Basic Stack Operations The stack concept is introduced and two basic stack operations are discussed: Push Pop

7. BACK

8. STEP 1: [overflow ?] If Top = N then write “overflow” return [end of if statement] STEP 2: [increment Top] Top:=Top + 1 STEP 3: [insert new element] S[Top]:=X STEP 4: [finished] return S=name of stack X=element to be inserted Top=top pointer N=maximum size of stack BACK

9. STEP 1: [underflow ?] If Top = 0 then write “underflow” return [end of if statement] STEP 2: [delete elements] X:=S[Top] STEP 3: [decrement pointer] Top:=Top-1 STEP 4: [finished] return S=name of stack Top= top pointer X=variable used to store deleted elements BACK

10. STACK APPLICATION EVALUATING A POSTFIX EXPRESSION

11.  Whenever an operand is encountered, push onto stack.  Whenever operator is encountered, pop required number of arguments from operand stack and evaluate.  Push result back onto stack.

12. 1. Empty the operand stack 2. while there are more tokens 3. Get the next token 4. if the first character of the token is a digit 5. Push the integer onto the stack 6. else if the token is an operator 7. Pop the right operand off the stack 8. Pop the left operand off the stack 9. Evaluate the operation 10. Push the result onto the stack 11. Pop the stack and return the result

14. Another Example Expression:5 3 - 6 + 8 2 / 1 2 + - * 528 3535 Execute 5 - 3 Execute 2 + 6 8888 288288 Execute 8 / 2 4848 148148 21482148 Execute 1 + 2 348348 Execute 4 - 3 1818 Execute 8 * 1 8 3535 3535 6 2 BACK