Data Structures. Outline. Introduction Linked Lists Stacks Queues Trees Deitel & Associates, Inc. All rights reserved.

Transcription

1 Data Structures Outline Introduction Linked Lists Stacks Queues Trees

2 Introduction dynamic data structures - grow and shrink during execution Linked lists - insertions and removals made anywhere Stacks - insertions and removals made only at top of stack Queues - insertions made at the back and removals made from the front Binary trees - high-speed searching and sorting of data and efficient elimination of duplicate data items

3 linked list Linked Lists linear collection of self-referential class objects, called nodes, connected by pointer links accessed via a pointer to the first node of the list subsequent nodes are accessed via the link-pointer member the link pointer in the last node is set to null to mark the list s end Use a linked list instead of an array when the number of data elements is unpredictable the list needs to be sorted

4 Linked Lists (II) Types of linked lists: singly linked list begins with a pointer to the first node terminates with a null pointer only traversed in one direction circular, singly linked pointer in the last node points back to the first node doubly linked list two start pointers - first element and last element each node has a forward pointer and a backward pointer allows traversals both forwards and backwards circular, doubly linked list forward pointer of the last node points to the first node and backward pointer of the first node points to the last node

5 Linked Lists

6 Linked Lists A polynomial of degree n is the function P n (x)=a 0 +a 1 x+a 2 x 2 + +a n x n. The a i s are called the coefficients of the polynomial The polynomial can be represented by a linked list (2 data members and a link per item): a 0,0 a 1,1 a 2,2 a n,n

7 Linked Lists: Insert in the head Insert a new data A. Call new: newptr List before insertion: data data data data A After insertion to head: A data data data data The link value in the new item = old The new value of = newptr

8 Linked Lists: Insert in the tail A data data data data data data data data A The link value in the new item = NULL The link value of the old last item = newptr

9 Linked Lists: Insert in the list Insert a new data A. Call new: newptr List before insertion: data data data data data After insertion in 3 rd position: data data A data data The link-value in the new item = link-value of 2 nd item The new link-value of 2 nd item = newptr

10 Linked Lists: Delete the head List before deletion: data data data data data List after deletion of the head item: data data data data data The new value of = link-value of the old head item The old head item is deleted and its memory returned

11 Linked Lists: Delete the tail List before deletion: data data data data data List after deletion of the tail item: data data data data data New value of = link-value of the 3 rd from last item New link-value of new last item = NULL.

12 Linked Lists: Delete item inside the list List before deletion: data data data data data List after deletion of the 2 nd item: data data data data data New link-value of the item located before the deleted one = the link-value of the deleted item

13 Stacks stack new nodes can be added and removed only at the top similar to a pile of dishes last-in, first-out (LIFO) Bottom of stack indicated by a link member to null constrained version of a linked list push adds a new node to the top of the stack pop removes a node from the top stores the popped value returns true if pop was successful

14 Queues queue similar to a supermarket checkout line first-in, first-out (FIFO) nodes are removed only from the head nodes are inserted only at the tail The insert and remove operations are known as enqueue and dequeue Useful in computing Print spooling, packets in networks, file server requests

15 Trees Tree nodes contain two or more links all other data structures we have discussed only contain one Binary trees all nodes contain two links none, one, or both of which may be NULL The root node is the first node in a tree. Each link in the root node refers to a child A node with no children is called a leaf node B A D C

16 Trees (II) binary search tree values in left subtree less than parent values in right subtree greater than parent facilitates duplicate elimination fast searches - for a balanced tree, maximum of log n comparisons

17 binary search tree To search for a number b: 1. Compare b with the root; If b=root, return If b<root, go left If b>root, go right Repeat step 1, comparing b with the new node we are at. 3. Repeat until either the node is found or we reach a non-existing node

18 Insert(datatype b, Tree T): Insertion into a BST Search for the position of b as if it were in the tree. The position is the left or right child of some node x. Create a new node, and assign its address to the appropriate pointer field in x Assign b to the data field of the new node

19 Insertion into a BST Before inserting 25 After inserting 25

20 Deletion from a BST Delete(datatype b, Tree T) 1. Search for b in tree T. If not found, return. 2. Call x the first node found to contain b 3. If x is a leaf, remove x and set the appropriate pointer in the parent of x to NULL 4. If x has only one child y, remove x, and the parent of x become a direct parent of y (More on the next slide)

21 Deletion from a BST Delete(datatype b, Tree T) If x has two children, go to the left subtree, and find there in largest node, and call it y. The node y can be found by tracing the rightmost path until the end. Note that y is either a leaf or has no right child 6. Copy the data field of y onto the data field of x 7. Now delete node y in a manner similar to step 4.

22 Deletion from a BST Delete(datatype b, Tree T) From the previous example, Delete 8 & 20