Data Structure Lecture2 Prepared by Shipra Shukla Assistant

Data Structure Lecture-2 Prepared by: Shipra Shukla Assistant Professor Kaziranga University

Stack • A Stack is a linear data structure in which a data item is inserted and deleted at one record. • A stack is called a Last In First Out (LIFO) structure because the data item inserted last is the data item deleted first from the stack.

Cont. . • Stacks are used most used is system software such as compilers, operating systems, etc. In fact, many compilers store the local variables inside a function on the stack. • Stack is a specialized data storage structure (Abstract data type).

Functions in Stack 1. create. Stack function– This function takes the maximum number of elements (max. Elements) the stack can hold as an argument, creates a stack according to it and returns a pointer to the stack. It initializes Stack S 2. push function - This function takes the pointer to the top of the stack S and the item (element) to be inserted as arguments. Check for the emptiness of stack 3. pop function - This function takes the pointer to the top of the stack S as an argument. 4. top function – This function takes the pointer to the top of the stack S as an argument and returns the topmost element of the stack S.

Example: Create the stack S using create. Stack function, where S is the pointer to the structure Stack. The maximum number of elements (max. Elements) = 5. Initially S->size = 0 and S->capacity = 5. 1. push(S, 7): Since, S->size = S->capacity push 7 on the top of it and increase its size by one. Now, size = 1. 7 2. push(S, 5): Since, S->size = S->capacity push 5 on the top of it and increase its size by one. Now, size = 2. 5 7 3. push(S, 21): Since, S->size = S->capacity push 21 on the top of it and increase its size by one. Now, size = 3. 21 5 7

4. push(S, -1): Since, S->size = S->capacity push -1 on the top of it and increase its size by one. Now, size = 4. -1 21 5 7 5. top(S): Since, S->size(=4) is not equal to zero. It returns the topmost element i. e. -1. Output = ‘-1’. 6. pop(S): Since, S->size(=4) is not equal to zero. It removes the topmost element i. e. -1 by simply reducing size of the stack S by 1. Now, size = 3. 21 5 7 7. top(S): Since, S->size(=3) is not equal to zero. It returns the topmost element i. e. 21. Output = ‘ 21’.

8. pop(S): Since, S->size(=3) is not equal to zero. It removes the topmost element i. e. 21 by simply reducing size of the stack S by 1. Now, size = 2. 5 7 9. pop(S): Since, S->size(=2) is not equal to zero. It removes the topmost element i. e. 5 by simply reducing size of the stack S by 1. Now, size = 1. 7 10. pop(S): Since, S->size(=1) is not equal to zero. It removes the topmost element i. e. 7 by simply reducing size of the stack S by 1. Now, size = 0. 11. pop(S): Since, S->size(=0) is equal to zero. Output is ‘Stack is Empty’.

Al. GORITHM OF PUSH Push(stack[maxsize], item) Let stack [maxsize] is an array for implementing the stack 1. if Top=maxsize-1 then print overflow and exit 2. Set Top=Top+1 [increase by 1] 3. Set Stack[Top]=item 4. Exit

C Function void push() { int item; If (top== maxsize-1) { printf(“n stack is full”); getch(); exit(0); } else { printf(“n. Enter the element”); scanf(“%d”, &item); top=top+1; stack[top]=item; } }

Al. GORITHM OF POP(stack[maxsize], item) Let stack[maxsize] is an array for implementing the stack 1. [CHECK FOR THE STACK UNDERFLOW] If top<0 then print stack underflow and exit. else [remove the top element] Set item=stack[top] 2. Decrement the stack top Set top=top-1 3. Return the deleted item from the stack 4. exit

C Function int pop() { int item; If (top== -1) { printf(“n stack is empty”); getch(); exit(0); } else { Item=stack[top]; top=top-1; } printf(“n. The element which has been deleted is: ”); return(item); }

Polish Notations • The process of writing the operators of an expression either before their operands or after them is called Polish notation. • The notation was introduced by "Jan Lukasiewicz ". • it assumes that an arithmetic operations can be take place between two operands only. For example, A+B, C*D, D/A etc. • The computer system can understand work only on binary paradigm

• The notation refers to these complex arithmetic expressions in three forms • – If the operator symbols are placed between its operands, then the expression is in infix notation. Ex: A+B • – If the operator symbols are placed before its operands, then the expression is in prefix notation. Ex: +AB –If the operator symbols are placed after its operands, then the expression is in postfix notation Ex: AB+

Levels of precedence • The binary operations in Q may have different levels of precedence. • Highest : Exponentiation ( ↑ ) • Next highest : Multiplication ( * ) and division (/) • Lowest : Addition ( + ) and subtraction ( - )

Application of Stacks: Postfix Expression

Evaluation of a Postfix Expression Algorithm This algorithm finds the VALUE of an arithmetic expression P written in postfix notation. 1. Add a right parenthesis ")"at the end of P. [This acts as a sentinel]. 2. Scan P from left to right and repeat Steps 3 and 4 for each element of until the sentinel ")" is encountered. 3. If an operand is encountered, put it on STACK. 4. If an operator (x) is encountered, then: a) Remove the two top elements of STACK, where A is the top element and B is the next-to-top element. b) Evaluate B (x) A. c) Place the result of (b) back on STACK [End of If structure. ] [End of Step 2 loop. ] 5. Set VALUE equal to the top element on STACK. 6. Exit.

Application of Stacks: Postfix Expression Stack after pushing 6 Stack after pushing 3 Stack after retrieving the top two elements and popping twice Stack after pushing the result of op 1 + op 2, which is 9

Application of Stacks: Postfix Expression Stack after pushing 2 Stack after pushing the result of op 1 * op 2, which is 18 Stack after retrieving the top two elements Stack after popping the element and popping twice

Example • Consider the following arithmetic expression P written in postfix notation: • P: 5, 6, 2, +, *, 12, 4, /, • We evaluate P using algorithm. First we add a sentinel right parenthesis at the end of P to obtain • P: 5, 6, 2, +, *, 12, 4, /, -, ) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Questions • 1. Stacks are sometimes called FIFO lists True/False • 2. Stack allows Push and Pop from both ends True/False • 3. TOS (Top of the Stack) gives the bottom most element in the stack. True/False

Symbol Scanned STACK (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 5 5, 6, 2 5, 8 40 40, 12, 4 40, 3 37 5 6 2 + * 12 4 / )