Algorithms and Complexity: Intro to DSA
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Questions and Answers

Which of the following statements about Big-O notation is TRUE?

  • O(1) is greater than O(n)
  • O(n) indicates a constant time complexity
  • O(n^2) is greater than O(n log n) (correct)
  • O(log n) grows faster than O(n)

    • If f(n) = O(g(n)), then for any constant c > 0, cf(n) = O(g(n)).

    True (A)

    What type of complexity is associated with the running time proportional to the logarithm of the input size?

    Logarithmic Time Complexity

    The running time of bubble sort is characterized by _____ time complexity.

    <p>Quadratic</p> Signup and view all the answers

    Match the following time complexities with their characteristics:

    <p>O(1) = Constant time complexity O(n) = Linear time complexity O(n^2) = Quadratic time complexity O(n log n) = Log-linear time complexity</p> Signup and view all the answers

    Which of the following topics is covered in week 1?

    <p>Introduction and Big O (D)</p> Signup and view all the answers

    Arrays and Matrices are covered in week 2.

    <p>True (A)</p> Signup and view all the answers

    What is the primary topic of lesson 8?

    <p>Linked Lists and Hash</p> Signup and view all the answers

    The _________ topic is discussed in week 5 lesson 9.

    <p>Trees</p> Signup and view all the answers

    Match the following topics with their respective weeks:

    <p>Stack and Queue = Week 2 Divide and Conquer Algorithms = Week 3 Searching and Sorting Algorithms = Week 4 Tree Algorithms = Week 5</p> Signup and view all the answers

    Which activity is commonly assigned after each lesson?

    <p>Quiz (C)</p> Signup and view all the answers

    Week 3 includes a lab session.

    <p>True (A)</p> Signup and view all the answers

    What is the main focus of lesson 7?

    <p>Searching and Sorting Algorithms</p> Signup and view all the answers

    The total points for quizzes and tasks combined in the grading section is 30.

    <p>True (A)</p> Signup and view all the answers

    What is the main focus of Data Structures and Algorithms?

    <p>Organizing and storing data, and designing algorithms to solve problems.</p> Signup and view all the answers

    In week 6, the lab topic covered is __________.

    <p>Lab 5</p> Signup and view all the answers

    Match the types of exams to their respective total points:

    <p>Quizzes = 15 Tasks = 15 Labs = 10 Exam = 60</p> Signup and view all the answers

    How many units are there for labs according to the grading section?

    <p>7 (A)</p> Signup and view all the answers

    Time and space complexities are not important aspects of learning data structures and algorithms.

    <p>False (B)</p> Signup and view all the answers

    What is the purpose of asymptotic analysis?

    <p>To evaluate the performance of algorithms as input size increases.</p> Signup and view all the answers

    To learn about Data Structures and Algorithms, one should first choose a __________.

    <p>programming language</p> Signup and view all the answers

    What is the total point value for the exam?

    <p>60 (C)</p> Signup and view all the answers

    What does Big-O notation primarily express?

    <p>The upper bound of an algorithm’s time complexity (B)</p> Signup and view all the answers

    Worst Case Analysis is rarely used when analyzing algorithms.

    <p>False (B)</p> Signup and view all the answers

    Define the average case analysis of algorithms in one sentence.

    <p>Average case analysis considers all possible inputs and computes the average runtime over those inputs.</p> Signup and view all the answers

    Big-O Notation is denoted as O(f(n)), where f(n) represents the number of ______ performed by an algorithm.

    <p>operations</p> Signup and view all the answers

    Match the following types of algorithm analysis with their definitions:

    <p>Worst Case Analysis = Calculates the upper bound on running time Best Case Analysis = Calculates the lower bound on running time Average Case Analysis = Averages runtime over all possible inputs Big-O Notation = Expresses the upper limit of time complexity</p> Signup and view all the answers

    Which of the following properties is NOT a property of Big-O Notation?

    <p>Symmetry (C)</p> Signup and view all the answers

    The average case analysis of algorithms is utilized frequently in practice.

    <p>False (B)</p> Signup and view all the answers

    Why is Big-O Notation important in computer science?

    <p>It helps analyze the efficiency of algorithms and compare their performance.</p> Signup and view all the answers

    In the worst-case analysis, we must identify the case that produces the maximum number of ______ to be executed.

    <p>operations</p> Signup and view all the answers

    What does the function f(n) represent in Big-O notation?

    <p>The number of operations needed (D)</p> Signup and view all the answers

    Study Notes

    Algorithms and Complexity - Introduction to DSA & Complexity

    • This presentation is about algorithms and complexity in computer science, covering data structures and algorithms (DSA)
    • The presentation covers winter semester 2024/2025

    Program Week 1

    • Lesson 1: Introduction and Big O
    • Lesson 2: Complexity - time and memory
    • Lesson 3: Mathematical and Bitwise Algorithms
    • Activities: Quizzes and tasks

    Program Week 2

    • Lesson 3: Arrays and Matrices
    • Lesson 4: Stack and Queue
    • Lab 1: Lab 1
    • Activities: Quizzes and tasks

    Program Week 3

    • Lesson 5: Recursion and Backtracking Algorithms
    • Lesson 6: Divide and Conquer Algorithms
    • Lab 2: Lab 2
    • Activities: Quizzes and tasks

    Program Week 4

    • Lesson 7: Searching and Sorting Algorithms
    • Lesson 8: Linked Lists and Hash
    • Lab 3: Lab 3
    • Activities: Quizzes and tasks

    Program Week 5

    • Lesson 9: Trees
    • Lesson 10: Tree Algorithms
    • Lab 4: Lab 4
    • Activities: Quizzes and tasks

    Program Week 6

    • Lesson 11: Greedy Algorithms
    • Lesson 12: Dynamic Programming
    • Lab 5: Lab 5
    • Activities: Quizzes and tasks

    Program Week 7

    • Lesson 13: Graphs
    • Lesson 14: Graph Algorithms
    • Lab 6: Lab 6
    • Activities: Quizzes and tasks

    Grading

    • Quizzes: 20 units, 0.8 points per unit, 15 total points
    • Tasks: 20 units, 0.8 points per unit, 15 total points
    • Labs: 7 units, 1.4 points per unit, 10 total points
    • Exam: 1 unit, 60 points
    • Grading Scale: 51-60% = 6, 61-70% = 7, 71-80% = 8, 81-90% = 9, 91-100% = 10

    Data Structures and Algorithms

    • The study of data structures and algorithms involves organizing and storing data, and the design of algorithms for problems that use these structures
    • These are used in common software challenges, managing large datasets to optimize tasks

    Why This is Essential

    • Efficient data storage and retrieval is key for applications
    • This is fundamental to areas, like GPS systems and search engine optimization
    • This is vital in web applications, databases, and machine learning

    How to Learn DSA

    • Choose a programming language
    • Understand the time and space complexities of algorithms
    • Learn common data structures and algorithms
    • Focus on high-quality problem-solving
    • Participate in coding contests

    Analysis of Algorithms

    • This aspect of computer science involves evaluating the performance of algorithms
    • Measured in terms of efficiency focusing on time and space complexity

    Asymptotic Analysis

    • A mathematical technique to understand algorithm behavior under larger inputs, particularly their growth rates
    • Uses asymptotic notations to define the algorithm's performance to compare different algorithms

    Worst Case Analysis of Algorithms

    • In this analysis the upper bound of an algorithm's running time for a given input size, or the maximum amount of operations possible
    • Requires knowing the worst-case scenario for the input producing the most operations

    Best Case Analysis of Algorithms

    • The minimal running time of an algorithm for each input
    • Identifying the input that results in the fewest amount of operations is necessary

    Average Case Analysis of Algorithms

    • Analyzing the average running time from all possible inputs
    • Calculate the average value of operations

    Big-O Notation

    • A mathematical technique to express an upper bound on the time complexity, or runtime, of an algorithm
    • Used to compare different algorithms, which is a key concept in computing
    • Providing the foundation for efficiency analysis

    Properties of Big-O Notation

    • Reflexivity: A function f(n) = O(f(n))
    • Transitivity: if f(n) = O(g(n)) and g(n) = O(h(n)) then f(n) = O(h(n))
    • Constant Factor: c * f(n) = O(f(n)) given a constant c greater than zero
    • Sum Rule: f(n) = O(g(n)) and h(n) = O(g(n)) then f(n) + h(n) = O(g(n))
    • Product Rule: f(n) = O(g(n)) and h(n) = O(k(n)) then f(n) * h(n) = O(g(n) * k(n))
    • Composition Rule: f(n) = O(g(n)) and g(n) = O(h(n)) then f(g(n)) = O(h(n))

    Big-O Notation - General Rules

    • Ignore Constants: 5n = O (n)
    • Dominate Terms: O(1) < O(logn) < O(n) < O(nlogn) < O(n^2) < O(2^n) < O(n!)

    Constant Time Complexity: Big O(1)

    • The running time is independent of the input size
    • Constant time operations, like addition, subtraction, and accessing data elements are examples

    Linear Time Complexity: Big O(n)

    • The running time for each input increases linearly with the input size.
    • Iterating through a list, for instance, has a linear time complexity.

    Logarithmic Time Complexity: Big O(log n)

    • The running time for each input increases proportionally to the logarithm of the input size.
    • Binary search is an algorithm that has logarithmic time complexity.

    Quadratic Time Complexity: Big O(n^2)

    • The running time is proportional to the square of the input size.
    • Sorting algorithms like bubble sort have quadratic time complexity.

    Cubic Time Complexity: Big O(n^3)

    • The running time is proportional to the cube of the input size
    • Matrix multiplication algorithms have cubic time complexity

    Polynomial Time Complexity: Big O(n^k)

    • The running time that can be written in polynomial form of the input size n

    Exponential Time Complexity: Big O(2^n)

    • The running time doubles with each addition to the input set.

    Factorial Time Complexity: Big O(n!)

    • The running time grows factorially with the input size.
    • Generating all permutations of data has factorial time complexity

    Plot of the most common Big-O

    • A plot that illustrates the rate of growth of common Big-O notations for varying input sizes, showing the relative efficiency of algorithms.

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    Related Documents

    Algorithms and Complexity (Week 1, Lesson 1) PDF

    Description

    This quiz covers the foundational concepts of algorithms and complexity, focusing on data structures and algorithms (DSA) for the winter semester 2024/2025. Topics include Big O notation, complexity analysis, recursion, and various types of algorithms. It's designed to test your understanding of key concepts discussed in class.

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