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Lecture #8

Lecture #8. Abstract Data Type (ADT) Queues ADT Stacks ADT List ADT List ADT with Array Implementation Linked lists Basic operations of linked lists Insert, find, delete, print, etc. Variations of linked lists Circular linked lists Doubly linked lists. Agenda. Abstract Data Type.

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Lecture #8

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  1. Lecture #8

  2. Abstract Data Type (ADT) Queues ADT Stacks ADT List ADT List ADT with Array Implementation Linked lists Basic operations of linked lists Insert, find, delete, print, etc. Variations of linked lists Circular linked lists Doubly linked lists Agenda

  3. Abstract Data Type

  4. Abstract Data Types are Abstraction

  5. An Abstract Data Type is a data type that is defined by the programmer, not the language. Like any data type, it is a set of values with operations that act on those values. Working with ADTs involves three different components: The public interface, or specification, defines the ADT and how it is used. The implementation, implements the ADT in code. The client uses the ADT to perform a task. Abstract Data Type Example

  6. Several classes of operations are required in order to effectively used ADT. Constructors – used to create instances of the data type. Destructors – used to destroy an instance of the data type Accessors – used to access attributes of the data type. (Such as “get” functions) Modifiers – used to modify attributes of the data type. (Such as “set” functions) Object-oriented languages provide some of this functionality within the language. In C you must do it yourself. ADT Operations

  7. Data type a set of objects + a set of operations Example: integer set of whole numbers operations: +, -, x, / Abstract data type high-level abstractions (managing complexity through abstraction) Encapsulation Abstract Data Type (ADT)

  8. Operation on the ADT can only be done by calling the appropriate function no mention of how the set of operations is implemented The definition of the type and all operations on that type can be localized to one section of the program If we wish to change the implementation of an ADT we know where to look by revising one small section we can be sure that there is no subtlety elsewhere that will cause errors We can treat the ADT as a primitive type: we have no concern with the underlying implementation ADT  C++: class method  C++: member function Encapsulation

  9. Examples the set ADT A set of elements Operations: union, intersection, size and complement the queue ADT A set of sequences of elements Operations: create empty queue, insert, examine, delete, and destroy queue ADT…

  10. Implementation of the ADT is separate from its use Modular: one module for one ADT Easier to debug Easier for several people to work simultaneously Code for the ADT can be reused in different applications Information hiding A logical unit to do a specific job implementation details can be changed without affecting user programs Allow rapid prototying Prototype with simple ADT implementations, then tune them later when necessary Loss of efficiency Pros and Cons

  11. Examples • Queues • Stack • Linked list

  12. Queues

  13. The Queue ADT stores arbitrary objects Insertions and deletions follow the first-in first-out scheme Insertions are at the rear of the queue and removals are at the front of the queue Main queue operations: enqueue(object): inserts an element at the end of the queue object dequeue(): removes and returns the element at the front of the queue Auxiliary queue operations: object front(): returns the element at the front without removing it integer size(): returns the number of elements stored boolean isEmpty(): indicates whether no elements are stored Exceptions Attempting the execution of dequeue or front on an empty queue throws an EmptyQueueException The Queue ADT Queues

  14. Operation Output Q enqueue(5) – (5) enqueue(3) – (5, 3) dequeue() 5 (3) enqueue(7) – (3, 7) dequeue() 3 (7) front() 7 (7) dequeue() 7 () dequeue() “error” () isEmpty() true () enqueue(9) – (9) enqueue(7) – (9, 7) size() 2 (9, 7) enqueue(3) – (9, 7, 3) enqueue(5) – (9, 7, 3, 5) dequeue() 9 (7, 3, 5) Queue Example Queues

  15. Direct applications Waiting lists, bureaucracy Access to shared resources (e.g., printer) Multiprogramming Indirect applications Auxiliary data structure for algorithms Component of other data structures Applications of Queues Queues

  16. Use an array of size N in a circular fashion Two variables keep track of the front and rear f index of the front element r index immediately past the rear element Array location r is kept empty Q 0 1 2 f r Q 0 1 2 r f Array-based Queue normal configuration wrapped-around configuration Queues

  17. We use the modulo operator (remainder of division) Q 0 1 2 f r Q 0 1 2 r f Queue Operations Algorithmsize() return(N-f +r) mod N AlgorithmisEmpty() return(f=r) Queues

  18. Q 0 1 2 f r Q 0 1 2 r f Example: Algorithmsize() return (N-f + r) mod N mod is the remainder of division. In C language it is % operator 16 f = 4, r = 14 , N = 17 size = (17-4+14)%17 = 27%17 = 10 f = 11, r = 4 , N = 17 size = (17-11+4)%17 = 10%17= 10

  19. Operation enqueue throws an exception if the array is full This exception is implementation-dependent Q 0 1 2 f r Q 0 1 2 r f Queue Operations (cont.) Algorithmenqueue(o) ifsize()=N 1then throw FullQueueException else Q[r] o r(r + 1) mod N To set r to zero if r+1 reaches the end of the array

  20. Operation dequeue throws an exception if the queue is empty This exception is specified in the queue ADT Q 0 1 2 f r Q 0 1 2 r f Queue Operations (cont.) Algorithmdequeue() ifisEmpty()then throw EmptyQueueException else oQ[f] f(f + 1) mod N returno

  21. Stacks

  22. Direct applications Delimiter matching Undo sequence in a text editor Chain of method calls in the Java Virtual Machine Indirect applications Auxiliary data structure for algorithms Component of other data structures Applications of Stacks Stacks

  23. The Stack ADT stores arbitrary objects Insertions and deletions follow the last-in first-out scheme Think of a spring-loaded plate dispenser Main stack operations: push(object): inserts an element object pop(): removes and returns the last inserted element Auxiliary stack operations: object top(): returns the last inserted element without removing it integer size(): returns the number of elements stored booleanisEmpty(): indicates whether no elements are stored The Stack ADT

  24. Java interface corresponding to our Stack ADT Requires the definition of class EmptyStackException Different from the built-in Java class java.util.Stack Stack Interface in Java public interfaceStack{ public int size(); public boolean isEmpty(); public Object top()throwsEmptyStackException; public voidpush(Object o); public Object pop()throwsEmptyStackException;} Stacks

  25. Attempting the execution of an operation of ADT may sometimes cause an error condition, called an exception Exceptions are said to be “thrown” by an operation that cannot be executed In the Stack ADT, operations pop and top cannot be performed if the stack is empty Attempting the execution of pop or top on an empty stack throws an EmptyStackException Exceptions Stacks

  26. A simple way of implementing the Stack ADT uses an array We add elements from left to right A variable keeps track of the index of the top element Array-based Stack Algorithmsize() returnt +1 Algorithmpop() ifisEmpty()then throw EmptyStackException else tt 1 returnS[t +1] … S 0 1 2 t Stacks

  27. The array storing the stack elements may become full A push operation will then throw a FullStackException Limitation of the array-based implementation Not intrinsic to the Stack ADT … S 0 1 2 t Array-based Stack (cont.) Algorithmpush(o) ift=S.length 1then throw FullStackException else tt +1 S[t] o Stacks

  28. A sequence of zero or more elements A1, A2, A3, … AN N: length of the list A1: first element AN: last element Ai: position i If N=0, then empty list Linearly ordered Ai precedes Ai+1 Ai follows Ai-1 The List ADT

  29. printList: print the list makeEmpty: create an empty list find: locate the position of an object in a list list: 34,12, 52, 16, 12 find(52)  3 insert: insert an object to a list insert(x,3)  34, 12, 52, x, 16, 12 remove: delete an element from the list remove(52)  34, 12, x, 16, 12 findKth: retrieve the element at a certain position Operations

  30. A linked list is a series of connected nodes Each node contains at least A piece of data (any type) Pointer to the next node in the list Head: pointer to the first node The last node points to NULL A C B A Linked Lists  Head node data pointer

  31. We use two classes: Node and List Declare Node class for the nodes data: double-type data in this example next: a pointer to the next node in the list A Simple Linked List Class class Node { public: double data; // data Node* next; // pointer to next };

  32. Declare List, which contains head: a pointer to the first node in the list. Since the list is empty initially, head is set to NULL Operations on List A Simple Linked List Class class List { public: List(void) { head = NULL; } // constructor ~List(void); // destructor bool IsEmpty() { return head == NULL; } Node* InsertNode(int index, double x); int FindNode(double x); int DeleteNode(double x); void DisplayList(void); private: Node* head; };

  33. Operations of List IsEmpty: determine whether or not the list is empty InsertNode: insert a new node at a particular position FindNode: find a node with a given value DeleteNode: delete a node with a given value DisplayList: print all the nodes in the list A Simple Linked List Class

  34. Node* InsertNode(int index, double x) Insert a node with data equal to x after the index’thelements. (i.e., when index = 0, insert the node as the first element; when index = 1, insert the node after the first element, and so on) If the insertion is successful, return the inserted node. Otherwise, return NULL. (If index is < 0 or > length of the list, the insertion will fail.) Steps Locate index’th element Allocate memory for the new node Point the new node to its successor Point the new node’s predecessor to the new node Inserting a new node index’th element newNode

  35. Possible cases of InsertNode Insert into an empty list Insert in front Insert at back Insert in middle But, in fact, only need to handle two cases Insert as the first node (Case 1 and Case 2) Insert in the middle or at the end of the list (Case 3 and Case 4) Inserting a new node

  36. Inserting a new node Try to locate index’th node. If it doesn’t exist, return NULL. Node* List::InsertNode(int index, double x) { if (index < 0) return NULL; int currIndex = 1; Node* currNode = head; while (currNode && index > currIndex) { currNode = currNode->next; currIndex++; } if (index > 0 && currNode == NULL) return NULL; Node* newNode = new Node; newNode->data = x; if (index == 0) { newNode->next = head; head = newNode; } else { newNode->next = currNode->next; currNode->next = newNode; } return newNode; }

  37. Inserting a new node Node* List::InsertNode(int index, double x) { if (index < 0) return NULL; int currIndex = 1; Node* currNode = head; while (currNode && index > currIndex) { currNode = currNode->next; currIndex++; } if (index > 0 && currNode == NULL) return NULL; Node* newNode = new Node; newNode->data = x; if (index == 0) { newNode->next = head; head = newNode; } else { newNode->next = currNode->next; currNode->next = newNode; } return newNode; } Create a new node

  38. Inserting a new node Node* List::InsertNode(int index, double x) { if (index < 0) return NULL; int currIndex = 1; Node* currNode = head; while (currNode && index > currIndex) { currNode = currNode->next; currIndex++; } if (index > 0 && currNode == NULL) return NULL; Node* newNode = new Node; newNode->data = x; if (index == 0) { newNode->next = head; head = newNode; } else { newNode->next = currNode->next; currNode->next = newNode; } return newNode; } Insert as first element head newNode

  39. Inserting a new node Node* List::InsertNode(int index, double x) { if (index < 0) return NULL; int currIndex = 1; Node* currNode = head; while (currNode && index > currIndex) { currNode = currNode->next; currIndex++; } if (index > 0 && currNode == NULL) return NULL; Node* newNode = new Node; newNode->data = x; if (index == 0) { newNode->next = head; head = newNode; } else { newNode->next = currNode->next; currNode->next = newNode; } return newNode; } Insert after currNode currNode newNode

  40. int FindNode(double x) Search for a node with the value equal to x in the list. If such a node is found, return its position. Otherwise, return 0. Finding a node int List::FindNode(double x) { Node* currNode = head; int currIndex = 1; while (currNode && currNode->data != x) { currNode = currNode->next; currIndex++; } if (currNode) return currIndex; return 0; }

  41. int DeleteNode(double x) Delete a node with the value equal to x from the list. If such a node is found, return its position. Otherwise, return 0. Steps Find the desirable node (similar to FindNode) Release the memory occupied by the found node Set the pointer of the predecessor of the found node to the successor of the found node Like InsertNode, there are two special cases Delete first node Delete the node in middle or at the end of the list Deleting a node

  42. Deleting a node int List::DeleteNode(double x) { Node* prevNode = NULL; Node* currNode = head; int currIndex = 1; while (currNode && currNode->data != x) { prevNode = currNode; currNode = currNode->next; currIndex++; } if (currNode) { if (prevNode) { prevNode->next = currNode->next; delete currNode; } else { head = currNode->next; delete currNode; } return currIndex; } return 0; } Try to find the node with its value equal to x

  43. Deleting a node int List::DeleteNode(double x) { Node* prevNode = NULL; Node* currNode = head; int currIndex = 1; while (currNode && currNode->data != x) { prevNode = currNode; currNode = currNode->next; currIndex++; } if (currNode) { if (prevNode) { prevNode->next = currNode->next; delete currNode; } else { head = currNode->next; delete currNode; } return currIndex; } return 0; } prevNode currNode

  44. Deleting a node int List::DeleteNode(double x) { Node* prevNode = NULL; Node* currNode = head; int currIndex = 1; while (currNode && currNode->data != x) { prevNode = currNode; currNode = currNode->next; currIndex++; } if (currNode) { if (prevNode) { prevNode->next = currNode->next; delete currNode; } else { head = currNode->next; delete currNode; } return currIndex; } return 0; } head currNode

  45. void DisplayList(void) Print the data of all the elements Print the number of the nodes in the list Printing all the elements void List::DisplayList() { int num = 0; Node* currNode = head; while (currNode != NULL){ cout << currNode->data << endl; currNode = currNode->next; num++; } cout << "Number of nodes in the list: " << num << endl; }

  46. ~List(void) Use the destructor to release all the memory used by the list. Step through the list and delete each node one by one. Destroying the list List::~List(void) { Node* currNode = head, *nextNode = NULL; while (currNode != NULL) { nextNode = currNode->next; // destroy the current node delete currNode; currNode = nextNode; } }

  47. 6 7 5 Number of nodes in the list: 3 5.0 found 4.5 not found 6 5 Number of nodes in the list: 2 result Using List int main(void) { List list; list.InsertNode(0, 7.0); // successful list.InsertNode(1, 5.0); // successful list.InsertNode(-1, 5.0); // unsuccessful list.InsertNode(0, 6.0); // successful list.InsertNode(8, 4.0); // unsuccessful // print all the elements list.DisplayList(); if(list.FindNode(5.0) > 0) cout << "5.0 found" << endl; else cout << "5.0 not found" << endl; if(list.FindNode(4.5) > 0) cout << "4.5 found" << endl; else cout << "4.5 not found" << endl; list.DeleteNode(7.0); list.DisplayList(); return 0; }

  48. Circular linked lists The last node points to the first node of the list How do we know when we have finished traversing the list? (Tip: check if the pointer of the current node is equal to the head.) A C B Variations of Linked Lists Head

  49. Doubly linked lists Each node points to not only successor but the predecessor There are two NULL: at the first and last nodes in the list Advantage: given a node, it is easy to visit its predecessor. Convenient to traverse lists backwards A C B Variations of Linked Lists   Head

  50. Linked lists are more complex to code and manage than arrays, but they have some distinct advantages. Dynamic: a linked list can easily grow and shrink in size. We don’t need to know how many nodes will be in the list. They are created in memory as needed. In contrast, the size of a C++ array is fixed at compilation time. Easy and fast insertions and deletions To insert or delete an element in an array, we need to copy to temporary variables to make room for new elements or close the gap caused by deleted elements. With a linked list, no need to move other nodes. Only need to reset some pointers. Array versus Linked Lists

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