1. Concept and need of Data Structure, abstract data type.
Data structures are ways of organizing and storing data to perform operations efficiently. Abstract Data Types (ADTs) are high-level descriptions of data structures that focus on operations, not implementation details.
2. Types of data structure.
Data structures can be categorized into linear and non-linear types. Linear structures include arrays, linked lists, stacks, and queues. Non-linear structures include trees and graphs.
3. Linear data structure.
Linear data structures store data elements in a linear sequence. Examples include arrays, linked lists, stacks, and queues.
4. Non-linear data structures.
Non-linear data structures do not store data in a sequential manner. Examples include trees and graphs, where nodes can have multiple connections.
5. Algorithm complexity of DSA on the basis of Time and Space.
Algorithm complexity is analyzed in terms of time complexity (how long it takes to run) and space complexity (how much memory it uses).
6. Operations on data structure.
Data structures support various operations such as insertion, deletion, searching, and traversal.
7. Traversing.
Traversing a data structure means visiting all its elements. This is often done using techniques like iteration or recursion.
8. Searching.
Searching involves finding a specific element within a data structure. Common searching algorithms include linear search and binary search.
9. Insertion.
Insertion is the process of adding an element to a data structure at a specified location or position.
10. Deletion.
Deletion removes an element from a data structure, often based on a specified criterion.
11. Sorting.
Sorting arranges the elements of a data structure in a particular order, such as ascending or descending.
12. Searching an item in data set using linear search.
Linear search involves scanning each element in the data structure until the target element is found.
13. Searching an item in data set using binary search.
Binary search is an efficient search algorithm for sorted data structures, dividing the search space in half at each step.
14. Sorting a data set using bubble sort.
Bubble sort repeatedly compares and swaps adjacent elements if they are in the wrong order until the entire data set is sorted.
15. Sorting a data set using selection sort.
Selection sort repeatedly selects the minimum element and places it at the beginning of the data set until the entire set is sorted.
16. Sorting a data set using insertion sort.
Insertion sort builds the sorted portion of the data set one element at a time by inserting each element into its correct position.
17. Sorting a data set using quick sort.
Quick sort is a divide-and-conquer sorting algorithm that partitions the data set and sorts each partition recursively.
18. Sorting a data set using radix sort.
Radix sort is a non-comparative sorting algorithm that works on integer keys by grouping digits from the least significant to the most significant.
19. Introduction to stack.
A stack is a linear data structure that follows the Last-In-First-Out (LIFO) principle.
20. Stack representation in memory using an array.
Stacks can be implemented using arrays, with operations like push and pop to manipulate the stack.
21. Stack as an ADT.
A stack can be described as an Abstract Data Type (ADT) with operations like push, pop, and isEmpty.
22. Stack operations PUSH AND POP.
Push adds an element to the top of the stack, and pop removes the top element from the stack.
23. Stack operation conditions.
Stack operations may have conditions like stack full and stack empty, which need to be handled.
24. Stack full.
A stack is considered full when it cannot accommodate more elements due to limited capacity.
25. Stack overflow.
A stack overflow occurs when you try to push an element onto a full stack.
26. Stack empty.
A stack is considered empty when it has no elements.
27. Stack underflow.
A stack underflow occurs when you try to pop an element from an empty stack.
28. Application of stack.
Stacks are used in various applications, including expression evaluation, function calls, and backtracking algorithms.
29. Reversing a list.
Reversing a list can be accomplished using a stack to reverse the order of elements.
30. Polish notations.
Polish notations, also known as prefix notations, are a way to represent mathematical expressions without parentheses.
31. Conversion of postfix to prefix expression.
Converting a postfix (Reverse Polish) expression to a prefix (Polish) expression involves using a stack to rearrange operators and operands.
32. Evaluation of postfix expression.
Evaluating a postfix expression involves using a stack to perform the arithmetic operations in the correct order.
33. Converting an infix into prefix expression.
Converting an infix expression (standard mathematical notation) into a prefix expression involves using a stack to handle operators and parentheses.
34. Evaluation of prefix expression.
Evaluating a prefix expression involves using a stack to perform arithmetic operations in the correct order.
35. Recursion.
Recursion is a programming technique where a function calls itself to solve a problem.
36. Tower of Hanoi.
The Tower of Hanoi is a classic problem in computer science that involves moving disks from one peg to another, following certain rules.
37. Introduction to queue.
A queue is a linear data structure that follows the First-In-First-Out (FIFO) principle.
38. Queue representation in memory using an array.
Queues can be implemented using arrays, with operations like enqueue and dequeue to manipulate the queue.
39. Queue as an ADT.
A queue can be described as an Abstract Data Type (ADT) with operations like enqueue, dequeue, and isEmpty.
40. Types of queue.
Types of queues include linear queues, circular queues, and priority queues.
41. Linear queue.
A linear queue is a simple queue with a front and a rear, where elements are removed from the front and added to the rear.
42. Circular queue.
A circular queue is a type of queue where the rear points back to the front, allowing for efficient use of space.
43. Concept of priority queue.
A priority queue assigns a priority to each element and allows higher-priority elements to be dequeued first.
44. Queue operations.
Queue operations include insert (enqueue) and delete (dequeue) operations.
45. Queue operation INSERT.
The insert operation, also known as enqueue, adds an element to the rear of the queue.
46. Queue operation DELETE.
The delete operation, also known as dequeue, removes an element from the front of the queue.
47. Queue operation conditions: Queue full and Queue empty.
Queue operations may have conditions like queue full and queue empty, which need to be handled.
48. Application of queue.
Queues are used in various applications, including scheduling, breadth-first search, and task management.
49. Introduction to linked list terminologies.
Linked list terminologies include nodes, addresses, pointers, data fields, next pointers, null pointers, and empty lists.
50. Node.
A node is a fundamental element of a linked list, containing data and a pointer to the next node.
51. Address.
An address is a reference to the location of a node in memory.
52. Pointer.
A pointer is a variable that stores the address of a node or data.
53. Information field/ Data field.
The information field, also called the data field, holds the actual data in a node.
54. Next pointer.
The next pointer in a node points to the next node in the linked list.
55. Null pointer.
A null pointer indicates the end of a linked list and points to nothing.
56. Empty list.
An empty list is a linked list with no nodes, represented by a null pointer at the head.
57. Types of lists.
Types of lists include linear lists and circular lists.
58. Linear list.
A linear list is a list where elements are connected sequentially, with a distinct first and last element.
59. Circular list.
A circular list is a list where the last element points back to the first, forming a closed loop.
60. Operations on singly linked lists.
Operations on singly linked lists include searching, inserting, and deleting nodes.
61. Searching a key in a linked list.
Searching for a specific key in a linked list involves traversing the list and comparing key values.
62. Inserting a new node in a linked list.
Insertion in a linked list involves creating a new node and adjusting pointers to include it in the list.
63. Deleting a node from a linked list.
Deletion in a linked list involves adjusting pointers to bypass the node to be deleted.
64. Introduction to tree.
A tree is a hierarchical data structure with nodes connected by edges. It has a root node, parent-child relationships, and levels.
65. Tree.
A tree is a data structure made up of nodes connected by edges, with a hierarchical structure.
66. Degree of a node.
The degree of a node is the number of children it has in a tree.
67. Degree of a tree.
The degree of a tree is the maximum degree among all its nodes.
68. Level of a node.
The level of a node in a tree is its distance from the root, with the root node at level 0.
69. Leaf node.
A leaf node is a node in a tree that has no children, i.e., it's at the end of a branch.
70. Depth/Height of a tree.
The depth or height of a tree is the length of the longest path from the root to a leaf node.
71. In-degree and out-degree.
In-degree is the number of incoming edges to a node in a directed graph, while out-degree is the number of outgoing edges.
72. Path.
A path in a tree or graph is a sequence of nodes connected by edges.
73. Ancestor and descendant nodes.
In a tree, a node's ancestors are the nodes on the path from the root to that node, while its descendants are all nodes reachable from it.
74. Tree types and traversal methods.
Trees can be categorized into general trees, binary trees, and binary search trees (BST). Traversal methods include in-order, pre-order, and post-order.
75. Types of trees: General tree, binary tree, binary search tree (BST).
A general tree allows nodes to have any number of children. A binary tree has at most two children per node. A BST is a binary tree with a specific order property.
76. Binary tree traversal.
Binary tree traversal methods include in-order, pre-order, and post-order traversal to visit nodes in a specific order.
77. In-order traversal.
In-order traversal visits nodes in a binary tree in ascending order based on their values.
78. Pre-order traversal.
Pre-order traversal visits the root node first, then its left subtree, and finally its right subtree.
79. Post-order traversal.
Post-order traversal visits the left and right subtrees of a node before visiting the node itself.
80. Expression tree.
An expression tree is a binary tree used to represent mathematical expressions in a way that allows for efficient evaluation.
81. Introduction to graph terminologies.
Graph terminologies include nodes (vertices), arcs (edges), directed and undirected graphs, in-degree, out-degree, adjacency, successors, predecessors, relations, paths, sinks, and articulation points.
82. Graph.
A graph is a collection of nodes (vertices) and edges (arcs) that connect them, representing relationships between objects.
83. Node (vertices).
Nodes, also called vertices, are the fundamental units in a graph.
84. Arcs (edges).
Arcs, or edges, are the connections between nodes in a graph.
85. Directed graph.
A directed graph, or digraph, has edges with directions, indicating one-way relationships between nodes.
86. Undirected graph.
An undirected graph has edges without directions, indicating two-way relationships between nodes.
87. In-degree.
In-degree in a directed graph is the number of incoming edges to a node.
88. Out-degree.
Out-degree in a directed graph is the number of outgoing edges from a node.
89. Adjacent.
Nodes in a graph are adjacent if there is a direct edge between them.
90. Successor.
In a directed graph, a node's successors are the nodes it has outgoing edges to.
91. Predecessor.
In a directed graph, a node's predecessors are the nodes with incoming edges from it.
92. Relation.
A relation in a graph represents a specific type of connection or association between nodes.
93. Path.
A path in a graph is a sequence of nodes connected by edges, allowing traversal from one node to another.
94. Sink.
A sink is a node in a directed graph with no outgoing edges, making it a dead end.
95. Articulation point.
An articulation point is a node in an undirected graph whose removal would disconnect the graph.
96. Adjacency list.
An adjacency list is a common way to represent a graph, where each node stores a list of its adjacent nodes.
97. Adjacency matrix of directed/undirected graph.
An adjacency matrix is a two-dimensional array that represents the connections between nodes in a graph, indicating whether there is an edge between each pair of nodes.
