1

Here are the main knowledge points covered in this PDF:

1. Introduction to recursion and its pattern

2. Recursive definition of factorial function

3. Visualizing recursion using recursion traces

4. Components of a recursive method: base case(s) and recursive calls

5. English ruler example to illustrate recursion

6. Linear recursion vs. binary recursion

7. Recursive computation of powers using repeated squaring

8. Tail recursion and converting it to iterative methods

9. Binary recursive methods like drawTicks and BinarySum

10. Recursive and iterative methods for computing Fibonacci numbers

11. Analysis of recursive algorithms (e.g. BinaryFib)

12. Multiple recursion illustrated with summation puzzles

13. Implementation of recursive and iterative methods

14. Tracing recursive calls and analyzing their efficiency

15. Exercises on:

    • Tracing recursive calls
    • Implementing recursive and iterative array reversal
    • Analyzing and implementing a recurrence relation
    • Analyzing a given recursive method
    • Tracing the drawTicks recursive method

16. Java implementation details for various recursive methods

17. Comparing performance of recursive vs iterative implementations

2

1. Inheritance in Java

   • Superclasses and subclasses
   • Extending classes
   • Method overriding

2. Polymorphism

3. Abstract classes and methods

4. Interfaces in Java

   • Implementing interfaces
   • Multiple interface implementation

5. Type conversions and casting in Java

6. Generics in Java

   • Generic classes
   • Generic methods

7. Abstract Data Types (ADTs)

8. Stack data structure

   • Stack ADT
   • Stack interface in Java
   • Array-based and linked list-based implementations

9. Singly Linked Lists

   • Node class
   • SLinkedList class
   • Operations: inserting/removing at head and tail

10. Implementation details for linked list operations

    • Inserting at head
    • Removing at head
    • Inserting at tail
    • Removing at tail (inefficiency noted)

11. Exercises on:

    • Progression classes
    • Implementing linked list methods
    • Extending linked list class

This lecture covers a review of various Java concepts and introduces linked list data structures.

3

Here are the main knowledge points covered in this PDF:

1. Analysis of Algorithms

   • Running time typically grows with input size
   • Focus on worst-case running time
   • Experimental vs theoretical analysis

2. Experimental Studies

   • Implementing and testing algorithms with various inputs
   • Measuring actual running time
   • Limitations of experimental approach

3. Theoretical Analysis

   • Uses pseudocode instead of implementation
   • Considers all possible inputs
   • Independent of hardware/software environment

4. Pseudocode

   • High-level description of algorithms
   • Conventions and notations

5. Random Access Machine (RAM) Model

   • Assumptions about computation time
   • Unit-time operations

6. Primitive Operations

   • Basic computations in algorithms
   • Assumed to take constant time

7. Counting Primitive Operations

   • To estimate running time

8. Growth Rate of Running Time

   • Independent of hardware/implementation
   • Importance of growth rate in algorithm comparison

9. Seven Important Functions in Algorithm Analysis

   • Constant, logarithmic, linear, n-log-n, quadratic, cubic, exponential

10. Constant Factors and Lower Terms

11. Not significant in growth rate analysis

12. Big-O Notation

13. Definition and examples
14. Rules for using Big-O

15. Relationship to growth rate

16. Asymptotic Algorithm Analysis

17. Determining running time in Big-O notation

18. Disregarding constant factors and lower-order terms

19. Example Algorithms

20. Array Max

21. Prefix Averages (quadratic and linear versions)

22. Arithmetic Progression

23. Sum of first n integers

24. Big-Omega (Ω) and Big-Theta (Θ) Notations

25. Definitions and relationships to Big-O

26. Exercises

27. Practice problems on asymptotic notation and algorithm analysis

This PDF covers fundamental concepts in the analysis of algorithms, focusing on theoretical analysis methods and asymptotic notation for describing algorithm efficiency.

4

Here are the key knowledge points from the PDF:

1. Abstract Data Types (ADTs)

   • Definition and components (data stored, operations, error conditions)
   • Implementation independence

2. Stack ADT

   • LIFO (Last-In-First-Out) principle
   • Main operations: push, pop
   • Additional operations: top, size, isEmpty
   • Java interface for Stack

3. Applications of Stacks

   • Web browser history, undo in text editors, method call stack in JVM
   • Auxiliary data structure for algorithms

4. Array-based Stack implementation

   • Performance and limitations
   • Java code example

5. Parentheses Matching Algorithm

   • Using stack to check balanced parentheses

6. HTML Tag Matching

   • Algorithm and Java implementation for checking matched HTML tags

7. Queue ADT

   • FIFO (First-In-First-Out) principle
   • Main operations: enqueue, dequeue
   • Additional operations: front, size, isEmpty
   • Java interface for Queue

8. Applications of Queues

   • Resource scheduling, multiprogramming
   • Round Robin schedulers

9. Array-based Queue implementation (Circular Queue)

   • Using modulo arithmetic for circular behavior
   • Handling full and empty states

10. Linked list-based Queue implementation

11. Java code for NodeQueue class

12. Exercises

13. Modifying parentheses matching algorithm
14. Optimizing array-based queue implementation
15. Maze exploration algorithm using queue

This PDF covers fundamental concepts of stacks and queues, their implementations, applications, and related algorithms.

5

Here are the key knowledge points from the PDF:

1. Lists: Definition and basic concepts

   • Linear order of elements
   • Indexing of elements
   • Comparison to stacks and queues

2. Array List ADT

   • Operations: size, isEmpty, get, set, add, remove
   • Error conditions for invalid indices

3. Array-based implementation of Array List

   • Shifting elements for insertion and deletion
   • Extending full arrays by doubling capacity
   • Performance analysis of operations

4. Interface IndexList

   • Methods defined for an indexed list

5. Class ArrayIndexList

   • Implementation of IndexList interface
   • Method add(int r, E e) implementation

6. Node List ADT and Position concept

   • Before/after relation between positions
   • Operations: first, last, prev, next, addFirst, addLast, addBefore, addAfter, remove, set

7. Doubly Linked List implementation of Node List

   • Node structure with element, prev, and next references
   • Header and trailer sentinel nodes
   • Insertion and deletion algorithms

8. Performance comparison of Array List vs Node List

9. Java interfaces and classes

   • Position interface
   • PositionList interface
   • DNode class implementing Position
   • NodePositionList class implementing PositionList

10. Implementation details

    • Checking and converting Position to DNode
    • Methods like first(), addAfter(), etc.

11. Exercises

    • Manipulating PositionList
    • Implementing remove() method
    • Extending NodePositionList
    • Performance comparison of ArrayList vs LinkedList

This PDF covers the fundamental concepts of list data structures, their ADTs, implementations, and performance characteristics, with a focus on both array-based and node-based implementations in Java.

6

Here's a list of the key knowledge points covered in the PDF:

1. General Trees

   • Definition and basic structure
   • Tree terminology (root, parent, child, internal node, external node/leaf, ancestors, descendants, siblings)
   • Depth of a node and height of a tree
   • Subtrees
   • Formal tree definition
   • Ordered trees

2. Tree ADT (Abstract Data Type)

   • Basic operations and methods
   • Accessor methods
   • Query methods
   • Generic methods

3. Linked Structure for Trees

   • Node representation

4. Tree Traversal Algorithms

   • Preorder traversal
   • Postorder traversal

5. Binary Trees

   • Definition and properties
   • Recursive definition
   • Applications (arithmetic expressions, decision processes, searching)
   • Properties of binary trees (relationship between number of nodes, external nodes, internal nodes, and height)

6. Binary Tree ADT

   • Additional methods specific to binary trees

7. Linked Structure for Binary Trees

   • Node representation for binary trees

8. Array-Based Representation of Binary Trees

   • How to store binary trees in arrays

9. Binary Tree Traversals

   • Preorder traversal for binary trees
   • Postorder traversal for binary trees
   • Inorder traversal
   • Comparison of traversal orders

10. Specialized Traversals

    • Printing arithmetic expressions
    • Evaluating arithmetic expressions

11. Euler Tour Traversal

    • Generic traversal combining preorder, inorder, and postorder

This list covers the main topics and concepts presented in the lecture slides on trees and binary trees.

7

Here's a list of the key knowledge points covered in this PDF on Priority Queues and Heaps:

1. Priority Queues

   • Definition and concepts (entry, key, value)
   • Total order relations
   • Priority Queue ADT and its methods
   • Entry ADT
   • Comparator ADT

2. Priority Queue Implementations

   • Sequence-based (unsorted and sorted list)
   • Performance comparison of different implementations

3. Priority Queue Sorting

   • General algorithm using a priority queue for sorting

4. Selection-Sort

   • Algorithm description
   • Running time analysis (O(n^2))

5. Insertion-Sort

   • Algorithm description
   • Running time analysis (O(n^2))

6. Heaps

   • Definition and properties (heap-order, complete binary tree)
   • Height of a heap (O(log n))
   • Array-based representation of complete binary trees

7. Complete Binary Tree ADT

   • Additional methods (add, remove)

8. Heap-based Priority Queue Implementation

   • Using a heap to implement a priority queue

9. Insertion into a Heap

   • Algorithm description
   • Up-heap bubbling

10. Removal from a Heap

    • Algorithm description
    • Down-heap bubbling

11. Heap-Sort

    • Algorithm overview
    • Time complexity (O(n log n))
    • Comparison with quadratic sorting algorithms

12. ADTs vs Implementations

    • Distinction between abstract data types and their implementations

This list covers the main concepts, data structures, and algorithms presented in the lecture slides on priority queues and heaps.

8

Here are the main knowledge points covered in the PDF:

1. Maps
2. Definition and basic concepts of maps
3. Map ADT and its operations (get, put, remove, size, isEmpty, etc.)

4. List-based map implementation

5. Hash Tables

6. Concept of hash tables, bucket arrays, and hash functions
7. Hash codes and compression functions
8. Collision handling techniques:
9. Separate chaining
10. Open addressing (linear probing, double hashing)
11. Performance analysis of hash tables

12. Load factor and rehashing

13. Dictionaries

14. Dictionary ADT and its operations
15. Differences between maps and dictionaries
16. List-based dictionary implementation
17. Hash table implementation of dictionaries

18. Ordered search table implementation

19. Implementation details

20. Java code snippets for various map and dictionary operations

21. Algorithms for get, put, remove operations in different implementations

22. Performance analysis

23. Time complexities of operations for different implementations

24. Tradeoffs between different implementations

25. Applications of maps and dictionaries

26. Small databases, compilers, browser caches

27. Address books, student records, credit card authorizations, DNS mappings

28. Collision handling techniques in detail

29. Linear probing
30. Double hashing

31. Separate chaining

32. Importance of load factor in hash table performance

This PDF covers the fundamental concepts, implementations, and analysis of maps, hash tables, and dictionaries as data structures.

9

Here are the main knowledge points covered in the PDF:

1. Binary Search Trees (BST)
2. Definition and basic structure
3. Property of keys in left and right subtrees

4. Inorder traversal visits keys in increasing order

5. BST operations for implementing a Map ADT

6. get(k)
7. put(k,o)

8. remove(k)

9. BST Search algorithm

10. TreeSearch function

11. BST Insertion

12. Process of adding a new key-value pair

13. BST Deletion

14. Cases for removing a node (leaf child, internal node)

15. Inorder successor replacement for internal nodes

16. Performance of Binary Search Trees

17. Time complexity related to tree height

18. Best and worst-case scenarios

19. Binary Search algorithm

20. For sorted arrays

21. Step-by-step example

22. Comparison of Linear Search vs Binary Search

23. Example with sorted and unsorted sequences
24. Number of comparisons in worst case

25. Time complexity: O(n) for linear search, O(log n) for binary search

26. Tree update operations

27. insertAtExternal

28. removeExternal

29. Importance of maintaining balance in BSTs for performance

This PDF covers the fundamental concepts, operations, and analysis of Binary Search Trees, as well as the Binary Search algorithm for sorted arrays.

10

Here are the key knowledge points covered in this PDF on sorting algorithms:

1. Introduction to sorting problem and its importance

2. Merge Sort algorithm

3. Divide-and-conquer paradigm
4. Steps: divide, recur, conquer
5. Merging process

6. Time complexity analysis: O(n log n)

7. Quick Sort algorithm

8. Randomized divide-and-conquer approach
9. Partitioning process
10. Pivot selection
11. Best, worst and average case time complexity

12. In-place implementation

13. Bucket Sort algorithm

14. Non-comparison based sorting
15. Process of distributing elements into buckets

16. Time complexity: O(n + N) where N is the range of input

17. Stability of sorting algorithms

18. Definition of stable sorting

19. Examples of stable and unstable algorithms

20. Comparison-based sorting lower bound

21. Decision tree model for comparison-based algorithms

22. Proof of Ω(n log n) lower bound

23. Summary and comparison of different sorting algorithms

24. Practical demonstrations and examples of sorting processes

25. Brief mention of Heap Sort and Selection Sort

This covers the major topics on sorting algorithms presented in the lecture slides.