Ashish Gupta, Data JUET, Guna
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2 Categories of data structures Data structures are categories in two classes 1. Linear data structure: - organized into sequential fashion - elements are attached one after another - easy to implement because follow the computer memory organization - Traversing is very easy - Examples array, linked list, stack, queue etc. 2. Non - Linear data structure: - data elements are not organized in a sequential fashion - Implementation is difficult - Examples tree, graph and 2D array etc.
3 Lists Implementation Linear Arrays Collection of similar elements stored at contiguous memory locations Linked List Collection of similar data elements stored at discrete memory locations and connected by pointer (link). Hence size can grow or shrink at any point of time. Abstract data type so we will implement only operations Data elements are called nodes Types 1. Linear linked list or one way list 2. Doubly linked list or two way list 3. Circular linked list 4. Header linked list
4 Linear Linked list Each node have two fields 1. Information 2. Pointer to next node Representation of node struct Node{ int INFO; struct Node *NEXT; }; For head Node *head data data data data NULL head
5 Operations on linear linked list 1. Creating empty linked list 2. Appending nodes to linked list 3. Traversing 4. Insertion 5. Deletion 6. Searching 7. Sorting
6 Creating a linked list Algorithm Create_List() This function creates an empty linked list and START is a pointer pointing to created list. 1. Node START 2. START= NULL
7 Appending node to linked list Algorithm Append_List(START, info) This function add the node at the end of linked list. Temp and Temp1 are temporary pointers. START is the pointer pointing to starting of list and info is the information of node. 1. Node Temp, Temp 1 2. If (START == NULL) \\ if there is no node in list 3. Temp = Allocate memory 4. Temp -> INFO =info 5. Temp -> NEXT = NULL 6. START = Temp 7. Else 8. Temp = START 9. While (Temp -> NEXT!= NULL) 10. Temp = Temp ->NEXT 11. Temp1 = Allocate memory 12. Temp1 -> INFO =info 13. Temp1 -> NEXT = NULL 14. Temp -> NEXT = Temp1
8 Traversing of linked list Algorithm Traverse_List(START) This function visits each node of linked list only once. Temp is a temporary pointer to node. START is the pointer pointing to starting of list. 1. Node Temp 2. Temp = START 3. While (Temp!= NULL) 4. Print Temp -> INFO 5. Temp = Temp -> NEXT
9 Insertion Three ways to insert a node into linked list 1. Insert at beginning 2. Insert after specified location 3. Insert at the end
10 Insertion at beginning of linked list Algorithm InsertBeg_List(START, info) This function add the node at the starting of linked list. Temp is temporary pointer to node to be inserted into list. START is the pointer pointing to starting of list and info is the information of node. 1. Node Temp 2. Temp = Allocate memory 3. Temp -> INFO =info 4. Temp -> NEXT = START 5. START = Temp
11 Insertion at after specified location of linked list Algorithm InsertAfter_List(START, info, Loc) This function add the node after the specified location of linked list. Temp and Temp1 are temporary pointers. START is the pointer pointing to starting of list and info is the information of node. Loc is the numbered location after which node is to be inserted. i is a loop variable. 1. Node Temp, Temp1 2. Temp = START 3. For i=1 to Loc-1 4. Temp = Temp -> NEXT 5. If (Temp == NULL) 6. Exit 7. Temp1 = Allocate memory 8. Temp1 -> INFO = info 9. Temp1 -> NEXT = Temp -> NEXT 10. Temp -> NEXT = Temp1
12 Insertion at End of linked list Algorithm InsertEnd_List(START, info) This function add the node at the end of linked list. Temp and Temp1 are temporary pointers. START is the pointer pointing to starting of list and info is the information of node. 1. Node Temp, Temp1 2. Temp = START 3. While (Temp -> NEXT!= NULL) 4. Temp = Temp ->NEXT 5. Temp1 = Allocate memory 6. Temp1 -> INFO =info 7. Temp1 -> NEXT = NULL 8. Temp -> Temp1
13 Deletion Three ways to insert a node into linked list 1. Delete from beginning 2. Delete after specified location 3. Delete from the end NOTE: Deletion could be done on the base information (to be deleted) available at any node or not. Here, first find that node and then delete it.
14 Deletion at beginning of linked list Algorithm DeleteBeg_List(START) This function delete the node at the starting of linked list. Temp is temporary pointer. START is the pointer pointing to starting of list. 1. Temp = START 2. If Temp ==NULL 3. Exit 4. START = Temp -> NEXT 5. Free Temp
15 Deletion after specified location of linked list Algorithm DeleteAfter_List(START, Loc) This function delete the node after the specified location of linked list. Temp and Temp1 are temporary pointers. START is the pointer pointing to starting of list and info is the information of node. Loc is the numbered location from where next node is to be deleted. i is a loop variable. 1. Node Temp, Temp1 2. Temp = START 3. For i=1 to Loc-1 4. Temp = Temp -> NEXT 5. If (Temp == NULL) 6. Exit 7. Temp1 = Temp ->NEXT 8. Temp -> NEXT = Temp1 -> NEXT 9. Free Temp1
16 Deletion at End of linked list Algorithm DeleteEnd_List(START) This function delete the node at the end of linked list. Temp and Temp1 are temporary pointers. START is the pointer pointing to starting of list. 1. Node Temp, Temp1 2. Temp1 = START 3. If Temp1==NULL 4. Exit 5. While (Temp1 -> NEXT!= NULL) 6. Temp =Temp1 7. Temp1 = Temp -> NEXT 8. Temp -> NEXT = NULL 9. Free Temp1
17 Searching Only linear search As there is no way to find out the middle of linked list. Algorithm SearchUnsorted_List(START,info) This function search the node in linked list. Temp is temporary pointer. START is the pointer pointing to starting of list and info is the information of node to be searched. If element is found then Loc is used to returned the location of node in list. 1. Node Temp 2. Initialize Loc = 0 3. Temp = START 4. If Temp==NULL 5. Exit 6. While (Temp -> NEXT!= NULL) 7. Loc = Loc If (Temp->INFO == info) 9. Return Loc OR Temp 10. Temp = Temp -> NEXT 11. If (Temp->INFO == info) 12. Return Loc+1 OR Temp 13. Return NULL
18 Algorithm SearchSorted_List(START,info) This function search the node in linked list. Temp is temporary pointer. START is the pointer pointing to starting of list and info is the information of node to be searched. If element is found then Loc is used to returned the location of node in list. 1. Node Temp 2. Initialize Loc = 0 3. Temp = START 4. If Temp==NULL 5. Exit 6. While (Temp -> NEXT!= NULL) 7. Loc = Loc+1 8. If (Temp->INFO == info) 9. Return Loc OR Temp 10. Else If (Temp->INFO > info) 11. Return NULL 12. Else 13. Temp = Temp ->NEXT 14. If (Temp->INFO == info) 15. Return Loc+1 OR Temp 16. Return NULL
19 Reverse Algorithm Reverse_List(START) This function reverse the linked list. Pnode, Cnode and Nnode are temporary pointers. START is the pointer pointing to starting of list. 1. Node Cnode, Pnode, Nnode 2. Cnode =START 3. Nnode = Cnode ->NEXT 4. Pnode = NULL 5. Cnode -> NEXT =NULL 6. While (Nnode!= NULL) 7. Pnode = Cnode 8. Cnode = Nnode 9. Nnode = Cnode ->NEXT 10. Cnode -> NEXT = Pnode 11. START = Cnode
20 Arrays Vs. Linked List Array Elements stored at contiguous memory locations Size of array is static and can not be changed at later stage if need arise. Traversing takes O(n) Time Searching Unsorted list Linear O(n) Sorted list Binary O(log 2 n) Insertion Shift all element one position right, Less efficient than in linked list Deletion Shift all element one position left, Less efficient than in linked list Linked List Elements stored at discrete memory locations No fixed size, can grow and shrink very efficiently Traversing takes O(n) Time Searching Only Linear O(n) Insertion Only some pointers need to be managed, more efficient than in array Deletion Only some pointers need to be managed, more efficient than in array
21 Doubly Linked list Each node have two fields 1. Information 2. Pointer to next node Representation of node struct Node{ struct Node *PREV; int INFO; struct Node *NEXT; }; For head Node *head, *tail 3. Pointer to previous node head tail
22 Creating a doubly linked list Algorithm Create_DList() This function creates an empty linked list and START is a pointer pointing to created list. 1. Node START, LAST 2. START= NULL 3. LAST = NULL
23 Appending node to Doubly linked list Algorithm Append_DList(START, END, info) This function add the node at the end of linked list. Temp and Temp1 are temporary pointers. START and END are the pointers pointing to starting of list and end of list respectively. info is the information of node. 1. Node Temp, Temp 1 2. If (START == NULL OR END == NULL) \\ if there is no node in list 3. Temp = Allocate memory 4. Temp -> INFO =info 5. Temp -> NEXT = NULL 6. Temp -> PREV = NULL 7. START = Temp 8. END = Temp 9. Else 10. Temp = START 11. While (Temp -> NEXT!= NULL) 12. Temp = Temp ->NEXT 13. Temp1 = Allocate memory 14. Temp1 -> INFO =info 15. Temp1 -> NEXT = NULL 16. Temp1 -> PREV = Temp 17. Temp -> NEXT = Temp1 18. END = Temp1
24 Traversing of Doubly linked list Algorithm Traverse_DList(START, END) This function visits each node of linked list only once. Temp is a temporary pointer to node. START and END are the pointers pointing to starting of list and end of list respectively. 1. Node Temp 2. Temp = START 3. While (Temp!= NULL) 4. Print Temp -> INFO 5. Temp = Temp -> NEXT OR (from last to first) 1. Node Temp 2. Temp = END 3. While (Temp!= NULL) 4. Print Temp -> INFO 5. Temp = Temp -> PREV
25 Insertion Three ways to insert a node into doubly linked list 1. Insert at beginning 2. Insert after specified location 3. Insert before specified location 4. Insert at the end
26 Insertion at beginning of Doubly linked list Algorithm InsertBeg_DList(START, info) This function add the node at the starting of linked list. Temp is temporary pointer to node to be inserted into list. START is the pointer pointing to starting of list and info is the information of node. 1. Node Temp 2. Temp = Allocate memory 3. Temp -> INFO =info 4. Temp -> NEXT = START 5. Temp ->PREV = NULL 6. START -> PREV= Temp 7. START = Temp
27 Insertion after specified location of doubly linked list Algorithm InsertAfter_DList(START, info, Loc) This function add the node after the specified location of linked list. Temp and Temp1 are temporary pointers. START is the pointer pointing to starting of list and info is the information of node. Loc is the numbered location after which node is to be inserted. i is a loop variable. 1. Node Temp, Temp1 2. Temp = START 3. For i=1 to Loc-1 4. Temp = Temp -> NEXT 5. If (Temp == NULL) 6. Exit 7. Temp1 = Allocate memory 8. Temp1 -> INFO = info 9. Temp1 -> NEXT = Temp -> NEXT 10. Temp1 ->PREV = Temp 11. (Temp -> NEXT) -> PREV = Temp1 12. Temp -> NEXT = Temp1
28 Insertion before specified location of D linked list Algorithm InsertBefore_DList(START, info, Loc) This function add the node before the specified location of linked list. Temp and Temp1 are temporary pointers. START is the pointer pointing to starting of list and info is the information of node. Loc is the numbered location before which node is to be inserted. i is a loop variable. 1. Node Temp, Temp1 2. Temp = START 3. For i=1 to Loc-1 4. Temp = Temp -> NEXT 5. If (Temp == NULL) 6. Exit 7. Temp1 = Allocate memory 8. Temp1 -> INFO = info 9. Temp1 -> NEXT = Temp 10. Temp1 ->PREV = Temp ->PREV 11. (Temp -> PREV) -> NEXT = Temp1 12. Temp -> PREV= Temp1
29 Insertion at End of Doubly linked list Algorithm InsertEnd_DList(END, info) This function add the node at the end of linked list. Temp and Temp1 are temporary pointers. END is the pointer pointing to end of list. info is the information of node. 1. Node Temp, Temp1 2. Temp = END 3. Temp1 = Allocate memory 4. Temp1 -> INFO =info 5. Temp1-> NEXT = NULL 6. Temp1->PREV = END 7. Temp ->NEXT = Temp1 8. END = Temp1
30 Deletion Three ways to insert a node into linked list 1. Delete from beginning 2. Delete after specified location 3. Delete before specified location 4. Delete from the end NOTE: Deletion could be done on the base information (to be deleted) available at any node or not. Here, first find that node and then delete it.
31 Deletion at beginning of linked list Algorithm DeleteBeg_DList(START,END) This function delete the node at the starting of linked list. Temp is temporary pointer. START and are the pointers pointing to starting of list and end of list. 1. Temp = START 2. If Temp ==NULL 3. Exit 4. If (START == END) 5. START = END =NULL 6. ELSE 7. (Temp ->NEXT) -> PREV =NULL 8. START = Temp -> NEXT 9. Free Temp
32 Deletion after specified location of linked list Algorithm DeleteAfter_DList(START, Loc) This function delete the node after the specified location of linked list. Temp and Temp1 are temporary pointers. START is the pointer pointing to starting of list and info is the information of node. Loc is the numbered location from where next node is to be deleted. i is a loop variable. 1. Node Temp, Temp1 2. Temp = START 3. For i=1 to Loc-1 4. Temp = Temp -> NEXT 5. If (Temp == NULL) 6. Exit 7. Temp1 = Temp ->NEXT 8. Temp -> NEXT = Temp1 -> NEXT 9. (Temp1->NEXT) ->PREV = Temp 10. Free Temp1
33 Deletion before specified location of linked list Algorithm DeleteBefore_DList(START, Loc) This function delete the node after the specified location of linked list. Temp and Temp1 are temporary pointers. START is the pointer pointing to starting of list and info is the information of node. Loc is the numbered location from where previous node is to be deleted. i is a loop variable. 1. Node Temp, Temp1 2. Temp = START 3. For i=1 to Loc-1 4. Temp = Temp -> NEXT 5. If (Temp == NULL) 6. Exit 7. Temp1 = Temp ->PREV 8. Temp1 -> NEXT = Temp -> NEXT 9. (Temp->NEXT) ->PREV = Temp1 10. Free Temp
34 Deletion at End of linked list Algorithm DeleteEnd_List(END) This function delete the node at the end of linked list. Temp and Temp1 are temporary pointers. END is the pointer pointing to end of list. 1. Node Temp, Temp1 2. Temp = END 3. If Temp==NULL 4. Exit 5. Temp1 = Temp -> PREV 6. Temp1 -> NEXT = NULL 7. END = Temp1 8. Free Temp
35 Singly Vs. Doubly Linked List Singly Linked List Doubly Linked List Node has two fields. Node has three fields. Reverse traversing is not possible. Reverse traversing is possible. Insertion at the end of linked list takes O(n) time and insertion before specified location is not possible. Insertion at the end of linked list take constant time and insertion before specified location is also possible. Deletion at the end of linked list take O(n) time and deletion before specified location is not possible. Deletion at the end of linked list take constant time and deletion before specified location is also possible.
36 Exercises 1. Write an algorithm for searching in doubly linked list. 2. Write an algorithm for sorting in singly linked list. 3. Why reverse algorithm is not needed in doubly linked list. Justify your answer comparing with singly linked list. 4. Write an algorithm to delete the entire singly linked list or doubly linked list.
37 Circular Linked list It could be singly or doubly linked list. Each node have two fields 1. Information 2. Pointer to next node Representation of node struct Node{ int INFO; struct Node *NEXT; }; For head Node *head data data data data head
38 Supported operations All operation which can be performed on singly or doubly linked list can be extended to circular by maintaining last node next pointer to first node. 1. Creating empty linked list 2. Appending nodes to linked list 3. Traversing 4. Insertion 5. Deletion 6. Searching 7. Sorting How do we know end of list? Compare next pointer field with address of first node or head
39 Circular Linked list Advantages: We can go to any node, in linear linked list it is not possible to go to previous node. It saves time when we have to go to the first node from the last node. It can be done in single step because there is no need to traverse the in between nodes. But in double linked list, we will have to go through in between nodes. Disadvantages: 1. It is not easy to reverse the linked list. If proper care is not taken, then the problem of infinite loop can occur. 2. If we want to go back to the previous node, then we can not do it in single step. Entire circle to be covered.
40 Header Linked list It contains a special node called Header at the beginning of list. Header node keeps information about list like number of nodes, sorted or not sorted etc. Header linear linked list: head Header Node Header doubly linked list: head Header Node
41 Application of Linked list To maintain directory To represent sparse matrices To implement other data structures like stack, queue, tree etc. To manipulate polynomials
42 Sparse matrix representation Header Node
43 Polynomial representation Let polynomial is 7x 3 + 5x 2 + 7x head Representation of node struct Node{ int coef; int pow; struct Node *NEXT; }; For head Node *head
44 Addition of polynomials Algorithm Add_Poly(poly1, poly2,poly3) This algorithm adds two given polynomial poly1 and poly2 and resultant polynomial is poly3. This algorithms calls append_node algorithm which is being used to add the resultant node into poly3. 1. While (poly1!=null and poly2!=null) 2. If (poly1->pow > poly2->pow) 3. coeff = poly1->coef 4. powe = poly1->pow 5. poly1 = poly1-> NEXT 6. Else If (poly1->pow < poly2->pow) 7. coeff = poly2->coef 8. powe = poly2->pow 9. poly2 = poly2-> NEXT 10. Else 11. coeff = poly1->coef + poly2 ->coef 12. powe = poly1 ->pow 13. poly1 = poly1->next 14. poly2 = poly2->next 15. If (coeff!=0) 16. append_node(poly3, coef, powe)
45 17. If(poly1 == NULL) 18. While (poly2!=null) 19. append_node(poly3,poly2->coef,poly2->pow) 20. poly2 = poly2->next 21. If(poly2 == NULL) 22. While (poly1!=null) 23. append_node(poly3,poly1->coef,poly1->pow) 24. poly1 = poly1->next Algorithm append_node is same as Append_List. But here we have three fields instead of two fields. Exercise Write an algorithm for appending polynomial node into list.
46 Summary Linear Linked List Overview Operations : Traversing, insertion, deletion, Searching and reverse etc. Doubly Linked List Overview Operations: Traversing, insertion, deletion etc. Circular Linked List Overview Header Linked List Applications of linked list
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