![Operations done:
1. Insertion
2. Deletion
3. Display/traversing
4. Searching
5. Sorting
Bubble sort:
Compare 2 adjacent elements, adjust by swapping & compare next 2 elements.
Insertion sort:
1st
element will be considered as a total array & the rest would be considered as a 2nd
array & the adjustment is made by swapping.
2nd
step: take 1st
2 elements as the 1st
array & rest as 2nd
array.
Continue till the 2nd
array becomes null.
Selection sort:
Take the smallest element & place it in the 1st
position.
Then start from the 2nd
block & take the 2nd
smallest element
In each pass we store 2 variables.
Binary search:
Last index will be in high. 1st
index will be in low.
Middle index will be stored in mid=(low + high)/2 for low<=high
Merge sort:
Last index will be in high. 1st
index will be in low.
Middle index will be stored in mid=(low + high)/2 for low<=high
Quick sort:
Mid= a[(high +low)/2] =p0
We will start checking from the left side & we will compare with p0 element.
Towers of Hanoi](https://image.slidesharecdn.com/datastructuresmynotes-180612132401/85/Data-structures-notes-5-320.jpg)
Data structures notes
- 1. DATA STRUCTURES The logical and mathematical model of a particular organization of data is called data structure. PRIMITIVE Array: Array is an ordered collection of items. It contains same data type. Array is a static object i.e. no of item is fixed and is assigned by the declaration of the array Stack: Stack is a ordered collection of items It is a list of dynamic objects/ elements in which an element may be inserted or deleted only at one end called top of the stack. DS PRIMITIVE NON PRIMITIVE LINEAR NON LINEAR ARRAYS STRUCTURE LIST STACKS QUEUES TREE GRAPH
- 2. Elements are removed from a stack in the reverse order of that in which they are inserted in the stack. “Push”- to insert into the stack “pop”- to delete an element from a stack. Stacks are used to indicate the order of processing of data when certain steps of the processing must be postponed until other conditions are fulfilled. Follows LIFO Elements are removed from a stack (pop) in the reverse order of that in which they were inserted into the stack (push). It may contain different data types Integer to indicate the current stack top within the array. Operations: push, pop. Queue: An ordered collection of items from which items may be deleted at one end (front end) & items inserted at the other end (rear end). It follows FIFO. Priority Queue: priority queue is a data structure in which the intrinsic ordering of the elements (numeric or alphabetic) Linked list: A linked list is a linear collection of data elements, called nodes, where the linear order is given by pointers. Each node has two parts 1st part contain the information of the element 2nd part contains the address of the next node in the list. double linked list: It is a collection of data elements called nodes, where each node is divided into three parts i) An info field that contains the information stored in the node
- 3. ii) Left field that contain pointer to node on left side iii) Right field that contain pointer to node on right side Tree: It is used to represent data which has a hierarical relationship. It can have any no. of children per node. Binary tree: it can have max. 2 children per node. LEFT SUCCESSOR RIGHT SUCCESSOR A spanning tree is a tree associated with a network. All the nodes of the graph appear on the tree once. A minimum spanning tree is a spanning tree organized so that the total edge weight between nodes is minimized Binary search tree: The values in all nodes in the right subtree of a node are greater than the node values. AVL tree: An empty binary tree, is an AVL tree, a non empty binary T tree is a AVL tree. If given, TL & TR to be the left & right subtrees of T & H(TL) & H(TR) to be the height of the subtrees TL & TR respectively. TL & TR are AVL trees & | H(TL)- H(TR)| <=1 where { H(TL)- H(TR } is known as the balance factor. The balance factor of a node can be either 0,1, or -1 B=-1 B=0 B=-1 50 40 60 () 70 R T1 T2
- 4. B=0 Graph: A+B ::: INFIX +AB ::: PREFIX AB+ ::: POSTFIX Precedence order: 1. Exponential 2. Multiplication 3. Divison 4. Addition 5. Substraction
- 5. Operations done: 1. Insertion 2. Deletion 3. Display/traversing 4. Searching 5. Sorting Bubble sort: Compare 2 adjacent elements, adjust by swapping & compare next 2 elements. Insertion sort: 1st element will be considered as a total array & the rest would be considered as a 2nd array & the adjustment is made by swapping. 2nd step: take 1st 2 elements as the 1st array & rest as 2nd array. Continue till the 2nd array becomes null. Selection sort: Take the smallest element & place it in the 1st position. Then start from the 2nd block & take the 2nd smallest element In each pass we store 2 variables. Binary search: Last index will be in high. 1st index will be in low. Middle index will be stored in mid=(low + high)/2 for low<=high Merge sort: Last index will be in high. 1st index will be in low. Middle index will be stored in mid=(low + high)/2 for low<=high Quick sort: Mid= a[(high +low)/2] =p0 We will start checking from the left side & we will compare with p0 element. Towers of Hanoi
- 6. A B C Moving the blocks, from peg A to peg C, the condition is that only one block can be moved at a time. TREE: It is used in networking. Binary tree: A set of elements that is either empty or is portioned into 3 disjoint subset. The 1st subset contains a single element called “root of the tree”. Each element is called “node of the tree” ROOT LEFT SUB TREE A B C RIGHT SUB TREE D F PREDEESSOR SIBBLINGS S E
- 7. D,E,F – LEAVE NODE, because they don’t have successor. Different type of binary tree: 1. Strictly binary tree: A non leave node has non empty left & right sub tree. A node can contain max. 2 child. 2. Complete binary tree: Each node will contain maximum no. of child. A B C D E F G H I J K L M N O MAX. 1 2 3 4 LEVEL 0 1 2 3
- 8. 3. Almost binary tree: All nodes are at its max. level except possibly the last level & all nodes at the last level appear as far left as possible A B C E F G