Data structures1
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The document discusses various linear data structures like lists, stacks, and queues. It describes the abstract data type concept and common list operations. Stack operations like push and pop are explained along with applications such as evaluating expressions, balancing symbols, Towers of Hanoi problem, and function calls which can utilize the last-in, first-out nature of a stack.
![STACK adt
Implementation
Array
Pointers
Array Implementation
Each stack is associated with top pointer which is -1 for empty
stack
To push Element X onto the stack, Top pointer is incremented and
set stack[top]=X
To pop an element, the stack[top] value is returned and top pointer
is decremented
Pop an empty stack or push on a full stack will exceed the array
bounds](https://image.slidesharecdn.com/datastructures1-140612033658-phpapp01/85/Data-structures1-23-320.jpg)
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Data structures1
- 1. Data Structures V.PARTHIPAN AP/CSE , SAVEETHA UNIVERSITY
- 2. Unit II LINEAR DATA STRUCTURE Abstract Data Structure List ADT Stack ADT Queue ADT
- 3. Abstract data type Mathematical model for a certain class of data structures that have similar behavior Specify memory needed to store data & type of data that will be stored in that memory location Defined only by the operations that may be performed on it & by mathematical constraints of operation Often implemented as modules; declares procedure that corresponds to ADT operations
- 4. List adt List is an ordered set of elements General form of the list is A1, A2,A3…., An A1 : first element of list AN: last element of list N: size of list If elements position is Ai, successor is Ai+1 & predecessor Ai-1
- 5. List adt Various operations on the list Insert (x,5): insert element x after position 5 Delete(x): element x deleted Find(x): returns position of x Next(i): returns the position of its successor element i+1 Previous(i): returns the position of its predecessor element i-1 printlist: contents of the list is displayed Makeempty: makes the list empty
- 6. List adt Implementation Array implementation Linked List implementation Cursor implementation
- 7. List adt Array Implementation Collection of specific no. of data stored in a consecutive memory locations Insertion & deletion are expensive as it requires more data elements Find & printlist operations takes constant time Max. size of list considerably wastes the memory wastes the memory space
- 8. List adt Linked list Implementation Consists of series of nodes Singly Linked List Doubly Linked List Circular Linked List
- 9. List adt Cursor Implementation Useful where linked list concept has to be implemented without pointers Data are stored in a global array of structures. Here array index is considered as address Maintains a list of free cells called cursor space Slot 0 is considered as a header and next is equivalent to the pointer which points to the next slot
- 10. List adt Cursor Implementation
- 11. List adt Cursor Implementation
- 12. List adt Cursor Implementation Declaration
- 13. List adt Cursor Implementation
- 14. List adt Cursor Implementation
- 15. List adt Cursor Implementation
- 16. List adt Cursor Implementation
- 17. List adt Cursor Implementation
- 18. STACK adt Linear data structure which follows Last In First Out (LIFO) Both insertion and deletion occur at only one end of the list called TOP Eg: Pile of coins, stack of tray in cafeteria
- 19. STACK adt Operations on Stack Push Pop
- 20. STACK adt Push Process of inserting new element to the top of the stack For every push operation the top is incremented by 1
- 21. STACK adt Pop Process of deleting an element from the top of the stack For every push operation the top pointer is decremented by 1
- 22. STACK adt Exceptional conditions Overflow Attempt to insert an element when the stack is full Underflow Attempt to delete an element when the stack is empty
- 23. STACK adt Implementation Array Pointers Array Implementation Each stack is associated with top pointer which is -1 for empty stack To push Element X onto the stack, Top pointer is incremented and set stack[top]=X To pop an element, the stack[top] value is returned and top pointer is decremented Pop an empty stack or push on a full stack will exceed the array bounds
- 24. STACK adt Routine to Push an element into stack
- 25. STACK adt Routine to Pop an element from stack
- 26. STACK adt Routine to return top element of the stack
- 27. STACK adt Linked List Implementation of the stack • Push operation is performed by inserting an element at the front of the list • Pop operation is done by deleting an element at the front of the list • Top operation returns the element at the front of the list
- 28. STACK adt Declaration for Linked List Implementation of the stack
- 29. STACK adt Routine to check whether stack is empty
- 30. STACK adt Routine to create an empty stack
- 31. STACK adt Routine to push element onto a stack
- 32. STACK adt Routine to return top element in a stack
- 33. STACK adt Routine to pop element from a stack
- 34. STACK adt Applications of stack Evaluating arithmetic expressions Balancing the symbols Towers of Hannoi Function calls 8 Queen Problem
- 35. STACK adt Types of notations to represent arithmetic Expression Infix notation Prefix notation Postfix notation Infix notation Arithmetic operator appears between the two operands Eg. A+B/C Postfix notation Arithmetic operator appears directly after two operands Also called reverse polish notation
- 36. STACK adt Prefix notation Arithmetic operator is placed before the two operands Also called polish notation ((A/B)+C) +/ABC
- 37. STACK adt Towers of Hanoi One of the example illustrating the Recursion technique Moving collection of N disks of decreasing size from one pillar to another pillar Movement restricted by following rules Only one disk could be moved at a time No larger disk could ever reside on a pillar on top of a smaller disk A 3rd pillar can be used as an intermediate to store one or more disks, while they were being moved from
- 38. STACK adt
- 39. STACK adt Towers of Hanoi – Recursive solution N – represents the no. of disks Steps If N=1, move disk from A to C If N=2, move the 1st disk from A to B, then move the 2nd disk from A to C, then move the 1st disk from B to C If N=3, repeat the step (2) to move the first 2 disks from A to B using C as intermediate then 3rd disk is moved from A to C. then repeat the step (2) to move 2 disks from B to C using A as intermediate In general, to move N disks. Apply the recursive technique to move N-1 disks from A to B using C as an intermediate. Then move the Nth disk from A to C. Then again apply the recursive technique to move N-1 disks from B to C using A as
- 40. STACK adt Towers of Hanoi – Recursive solution
- 41. STACK adt
- 42. STACK adt Function Calls to keep track of the point to which each active subroutine should return control when it finishes executing active subroutine is one that has been called but is yet to complete execution after which control should be handed back to the point of call