Introduction to data structure by anil dutt
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This document provides an introduction and overview of common data structures including linked lists, stacks, queues, trees, and graphs. It defines each structure and describes their basic operations and implementations. Linked lists allow insertions and deletions anywhere and come in singly and doubly linked varieties. Stacks and queues follow last-in, first-out and first-in, first-out rules respectively. Binary trees enable fast searching and sorting of data. Graphs represent relationships between nodes connected by edges.
![struct node
{
int x;
char c[10];
struct node *next;
}*current;
x c[10] next](https://image.slidesharecdn.com/introductiontodatastructurebyanildutt-150417000357-conversion-gate01/85/Introduction-to-data-structure-by-anil-dutt-10-320.jpg)
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{
current=(struct node *)malloc(sizeof(struct node));
current->x=10; current->c=“try”; current->next=null;
return current;
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![Create a linked list for maintaining the employee
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Steps:
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{
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Introduction to data structure by anil dutt
- 1. Introduction to Data Structures Presented By:Presented By: Anil DuttAnil Dutt
- 2. DataStructures • Outline • Introduction • Linked Lists • Stacks • Queues • Trees • Graphs
- 3. Introduction • Dynamic data structures – Data structures that grow and shrink during execution • Linked lists – Allow insertions and removals anywhere • Stacks – Allow insertions and removals only at top of stack • Queues – Allow insertions at the back and removals from the front • Binary trees – High-speed searching and sorting of data and efficient elimination of duplicate data items
- 4. Linked Lists • Linked list – 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 of the current node – 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 – You have an unpredictable number of data elements – Your list needs to be sorted quickly
- 5. Linked Lists • 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
- 6. SINGLY LINKED LIST DOUBLY LINKED LIST Previous node Data part Next node DATA ADDRESS Data 1 Data 2 . . . . . . Data n ADDRESS ADDRESS Data 1 Data 2 . . . . . Data n ADDRESS
- 7. ID Name Desig Address of Node2 ID Name Desig Address of Node 3 ID Name Desig NULL Start
- 8. NULL Data 1 Address of Node 2 Address of Data 2 Address of Node 1 Node 3 Address of Data 3 Node 2 NULL Start
- 9. CIRCULAR LINKED LIST SINGLY Node 1 Node 2 Node 3 DOUBLY Node 1 Node 2 Node 3 Start Data 1 Node 2 Data 2 Node 3 Data 3 Node1 Start Node3 Data 1 Node 2 Node 1 Data 1 Node 3 Node 2 Data 1 Node1
- 10. struct node { int x; char c[10]; struct node *next; }*current; x c[10] next
- 11. create_node() { current=(struct node *)malloc(sizeof(struct node)); current->x=10; current->c=“try”; current->next=null; return current; } Allocation Assignment x c[10] next 10 try NULL
- 12. Create a linked list for maintaining the employee details such as Ename,Eid,Edesig. Steps: 1)Identify the node structure 2)Allocate space for the node 3)Insert the node in the list EID EName EDesig struct node { int Eid; char Ename[10],Edesig[10]; struct node *next; } *current; next
- 13. The basic operations on linked lists are 1. Creation 2. Insertion 3. Deletion 4. Traversing 5. Searching 6. Concatenation 7. Display
- 14. 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
- 15. Stack A X R C push(M) A X R C M item = pop() item = M A X R C
- 16. Implementing a Stack • At least three different ways to implement a stack – array – vector – linked list • Which method to use depends on the application – what advantages and disadvantages does each implementation have?
- 17. 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 • Insert and remove operations – Enqueue (insert) and dequeue (remove)
- 18. Queues 18 A QUEUE IS A CONTAINER IN WHICH: . INSERTIONS ARE MADE ONLY AT THE BACK; . DELETIONS, RETRIEVALS, AND MODIFICATIONS ARE MADE ONLY AT THE FRONT.
- 19. Queues 19 The Queue A Queue is a FIFO (First in First Out) Data Structure. Elements are inserted in the Rear of the queue and are removed at the Front. C B C A B C A b a c k f r o n t p u s h A A B f r o n t b a c k p u s h B f r o n t b a c k p u s h C f r o n t b a c k p o p A f r o n t b a c k p o p B
- 20. Queues 20 PUSH (ALSO CALLED ENQUEUE) -- TO INSERT AN ITEM AT THE BACK POP (ALSO CALLED DEQUEUE) -- TO DELETE THE FRONT ITEM IN A QUEUE, THE FIRST ITEM INSERTED WILL BE THE FIRST ITEM DELETED: FIFO (FIRST-IN, FIRST-OUT)
- 21. 21 Printing Queue Now printing A.doc A.doc is finished. Now printing B.doc Now still printing B.docD.doc comes • A.doc B.doc C.doc arrive to printer. ABC BC BCD CD D B.doc is finished. Now printing C.doc C.doc is finished. Now printing D.doc
- 22. 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
- 23. Trees • Diagram of a binary tree B A D C
- 24. Trees • 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 47 25 77 11 43 65 93 687 17 31 44 2
- 25. Trees • Tree traversals: – Inorder traversal – prints the node values in ascending order 1. Traverse the left subtree with an inorder traversal 2. Process the value in the node (i.e., print the node value) 3. Traverse the right subtree with an inorder traversal – Preorder traversal 1. Process the value in the node 2. Traverse the left subtree with a preorder traversal 3. Traverse the right subtree with a preorder traversal – Postorder traversal 1. Traverse the left subtree with a postorder traversal 2. Traverse the right subtree with a postorder traversal 3. Process the value in the node
- 26. Trees Data Structures Tree Nodes Each node can have 0 or more children A node can have at most one parent Binary tree Tree with 0–2 children per node Tree Binary Tree
- 27. Trees Terminology Root ⇒ no parent Leaf ⇒ no child Interior ⇒ non-leaf Height ⇒ distance from root to leaf Root node Leaf nodes Interior nodes Height
- 28. Binary Search Trees Key property Value at node Smaller values in left subtree Larger values in right subtree Example X > Y X < Z Y X Z
- 29. Binary Search Trees Examples Binary search trees Not a binary search tree 5 10 30 2 25 45 5 10 45 2 25 30 5 10 30 2 25 45
- 30. Binary Tree Implementation Class Node { int data; // Could be int, a class, etc Node *left, *right; // null if empty void insert ( int data ) { … } void delete ( int data ) { … } Node *find ( int data ) { … } … }
- 31. Iterative Search of Binary Tree Node *Find( Node *n, int key) { while (n != NULL) { if (n->data == key) // Found it return n; if (n->data > key) // In left subtree n = n->left; else // In right subtree n = n->right; } return null; } Node * n = Find( root, 5);
- 32. Recursive Search of Binary Tree Node *Find( Node *n, int key) { if (n == NULL) // Not found return( n ); else if (n->data == key) // Found it return( n ); else if (n->data > key) // In left subtree return Find( n->left, key ); else // In right subtree return Find( n->right, key ); } Node * n = Find( root, 5);
- 33. Example Binary Searches Find ( root, 2 ) 5 10 30 2 25 45 5 10 30 2 25 45 10 > 2, left 5 > 2, left 2 = 2, found 5 > 2, left 2 = 2, found root
- 34. Example Binary Searches Find (root, 25 ) 5 10 30 2 25 45 5 10 30 2 25 45 10 < 25, right 30 > 25, left 25 = 25, found 5 < 25, right 45 > 25, left 30 > 25, left 10 < 25, right 25 = 25, found
- 35. Types of Binary Trees Degenerate – only one child Complete – always two children Balanced – “mostly” two children more formal definitions exist, above are intuitive ideas Degenerate binary tree Balanced binary tree Complete binary tree
- 36. Binary Trees Properties Degenerate Height = O(n) for n nodes Similar to linked list Balanced Height = O( log(n) ) for n nodes Useful for searches Degenerate binary tree Balanced binary tree
- 37. Binary Search Properties Time of search Proportional to height of tree Balanced binary tree O( log(n) ) time Degenerate tree O( n ) time Like searching linked list / unsorted array
- 38. Binary Search Tree Construction How to build & maintain binary trees? Insertion Deletion Maintain key property (invariant) Smaller values in left subtree Larger values in right subtree
- 39. Binary Search Tree – Insertion Algorithm 1. Perform search for value X 2. Search will end at node Y (if X not in tree) 3. If X < Y, insert new leaf X as new left subtree for Y 4. If X > Y, insert new leaf X as new right subtree for Y Observations O( log(n) ) operation for balanced tree Insertions may unbalance tree
- 40. Example Insertion Insert ( 20 ) 5 10 30 2 25 45 10 < 20, right 30 > 20, left 25 > 20, left Insert 20 on left 20
- 41. Binary Search Tree – Deletion Algorithm 1. Perform search for value X 2. If X is a leaf, delete X 3. Else // must delete internal node a) Replace with largest value Y on left subtree OR smallest value Z on right subtree b) Delete replacement value (Y or Z) from subtree Observation O( log(n) ) operation for balanced tree Deletions may unbalance tree
- 42. Example Deletion (Leaf) Delete ( 25 ) 5 10 30 2 25 45 10 < 25, right 30 > 25, left 25 = 25, delete 5 10 30 2 45
- 43. Example Deletion (Internal Node) Delete ( 10 ) 5 10 30 2 25 45 5 5 30 2 25 45 2 5 30 2 25 45 Replacing 10 with largest value in left subtree Replacing 5 with largest value in left subtree Deleting leaf
- 44. Example Deletion (Internal Node) Delete ( 10 ) 5 10 30 2 25 45 5 25 30 2 25 45 5 25 30 2 45 Replacing 10 with smallest value in right subtree Deleting leaf Resulting tree
- 45. Balanced Search Trees Kinds of balanced binary search trees height balanced vs. weight balanced “Tree rotations” used to maintain balance on insert/delete Non-binary search trees 2/3 trees each internal node has 2 or 3 children all leaves at same depth (height balanced) B-trees Generalization of 2/3 trees Each internal node has between k/2 and k children Each node has an array of pointers to children Widely used in databases
- 46. Other (Non-Search) Trees Parse trees Convert from textual representation to tree representation Textual program to tree Used extensively in compilers Tree representation of data E.g. HTML data can be represented as a tree called DOM (Document Object Model) tree XML Like HTML, but used to represent data Tree structured
- 47. Parse Trees Expressions, programs, etc can be represented by tree structures E.g. Arithmetic Expression Tree A-(C/5 * 2) + (D*5 % 4) + - % A * * 4 / 2 D 5 C 5
- 48. Tree Traversal Goal: visit every node of a tree in-order traversal void Node::inOrder () { if (left != NULL) { cout << “(“; left->inOrder(); cout << “)”; } cout << data << endl; if (right != NULL) right->inOrder() }Output: A – C / 5 * 2 + D * 5 % 4 To disambiguate: print brackets + - % A * * 4 / 2 D 5 C 5
- 49. Tree Traversal (contd.) pre-order and post-order: void Node::preOrder () { cout << data << endl; if (left != NULL) left->preOrder (); if (right != NULL) right->preOrder (); } void Node::postOrder () { if (left != NULL) left->preOrder (); if (right != NULL) right->preOrder (); cout << data << endl; } Output: + - A * / C 5 2 % * D 5 4 Output: A C 5 / 2 * - D 5 * 4 % + + - % A * * 4 / 2 D 5 C 5
- 50. Graph Data Structures E.g: Airline networks, road networks, electrical circuits Nodes and Edges E.g. representation: class Node Stores name stores pointers to all adjacent nodes i,e. edge == pointer To store multiple pointers: use array or linked list Ahm’bad Delhi Mumbai Calcutta Chennai Madurai