Algorithm and recursion Quiz
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What is the worst-case time complexity of the bubble sort algorithm?

  • O(n log n)
  • O(n)
  • O(n^2) (correct)
  • O(1)

    • The best-case time complexity of selection sort is O(n).

    False (B)

    In analysis of selection sort, what mathematical formula represents the number of comparisons made?

    (n - 1) + (n - 2) + (n - 3) +...+ 1

    The time complexity of selection sort is ______ because both the upper and lower bounds are the same.

    <p>Θ(n^2)</p> Signup and view all the answers

    Which sorting algorithm is considered more efficient in practice for small datasets?

    <p>Insertion Sort (D)</p> Signup and view all the answers

    Match the sorting algorithms with their best-case time complexities:

    <p>Bubble Sort = Ω(n) Selection Sort = Ω(n^2) Insertion Sort = Ω(n) Merge Sort = Ω(n log n)</p> Signup and view all the answers

    Recursion is when a function calls itself in programming.

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

    What does the 'O' in time complexity, such as O(n^2), represent?

    <p>big O notation</p> Signup and view all the answers

    What is the primary purpose of the 'draw' function in the provided pseudocode?

    <p>To recursively print a pyramid of hashes (A)</p> Signup and view all the answers

    In the pseudocode for searching in a phone book, the number of pages has no impact on the search method used.

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

    What are the two conditions checked when searching the phone book to decide whether to open the left half or the right half?

    <p>If the person is earlier or later in the book.</p> Signup and view all the answers

    In binary search, if the number to find is less than the middle value, we will search the ______ half.

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

    Match the following algorithm types with their characteristics:

    <p>Selection Sort = Repeatedly removes the minimum element from the unsorted portion Bubble Sort = Repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order Binary Search = Divides the sorted collection in half to locate the target value Recursion = Function calls itself to solve smaller instances of the same problem</p> Signup and view all the answers

    Which of the following running times represents the fastest algorithm?

    <p>O(1) (B)</p> Signup and view all the answers

    Which of the following sorting algorithms is NOT mentioned in the content?

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

    Binary search operates with a complexity of O(n).

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

    What symbol is used to denote the best case of an algorithm?

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

    Bubble Sort is an efficient algorithm for sorting lists due to its complex swapping mechanism.

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

    What notation is used to access properties of an object in the people array?

    <p>dot notation</p> Signup and view all the answers

    Linear search has a worst-case complexity of ______.

    <p>O(n)</p> Signup and view all the answers

    The complexity of the selection sort algorithm can be simplified to O(_______).

    <p>n^2</p> Signup and view all the answers

    Match the following running times with their corresponding descriptions:

    <p>O(n2) = Quadratic time complexity O(n log n) = Log-linear time complexity O(n) = Linear time complexity O(log n) = Logarithmic time complexity</p> Signup and view all the answers

    Which of the following statements is true regarding Θ notation?

    <p>It indicates when the upper and lower bounds are the same. (B)</p> Signup and view all the answers

    Match the following sorting algorithms to their descriptions:

    <p>Selection Sort = Finds the smallest number and swaps it with the current position Bubble Sort = Swaps elements to bubble larger ones to the end Binary Search = Searches in sorted lists only Algorithm Complexity = Describes the efficiency of an algorithm</p> Signup and view all the answers

    What is the first step in the selection sort algorithm?

    <p>Find the smallest number between numbers[i] and numbers[n-1] (D)</p> Signup and view all the answers

    O(n log n) is worse than O(n2) in terms of algorithm efficiency.

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

    What is the complexity class of the selection sort algorithm in the worst case?

    <p>O(n2)</p> Signup and view all the answers

    A binary search can be effectively performed on an unsorted list.

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

    How many steps does it take the selection sort algorithm during its first iteration through a list of size n?

    <p>n - 1</p> Signup and view all the answers

    Binary search is best suited for ________ data structures.

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

    Which algorithm typically has a complexity of O(n) in terms of its average-case performance?

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

    The algorithm repeatedly swapping elements to move larger numbers to the end is called __________.

    <p>Bubble Sort</p> Signup and view all the answers

    What is the final result of the complexity calculation shown for selection sort?

    <p>O(n^2) (D)</p> Signup and view all the answers

    What is the best-case time complexity of binary search?

    <p>O(log n) (C)</p> Signup and view all the answers

    Binary search requires the array to be unsorted before it can be applied.

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

    What is the purpose of the 'middle' in the binary search algorithm?

    <p>To determine the current point of comparison in the search process.</p> Signup and view all the answers

    The pseudocode for binary search returns false if there are ______ left.

    <p>no doors</p> Signup and view all the answers

    Match the following time complexities with their descriptions:

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

    Which statement accurately describes a characteristic of bubble sort?

    <p>It repeatedly swaps adjacent elements if they are in the wrong order. (D)</p> Signup and view all the answers

    Selection sort works by repeatedly selecting the smallest (or largest) element from the unsorted part of the list.

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

    What does 'big O' notation describe?

    <p>It describes the performance or complexity of an algorithm in terms of time or space as input size grows.</p> Signup and view all the answers

    In binary search, if 50 is greater than the middle door value, the search continues in the ______ half.

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

    Which of the following algorithms has the worst average-case time complexity?

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

    Study Notes

    Sorting Algorithms

    • Bubble Sort Pseudocode: Repeats n-1 times; compares adjacent elements and swaps if out of order; quits early if no swaps occur.
    • Selection Sort Pseudocode: Iterates through list to find the smallest element from the unsorted portion; swaps it with the current position.
    • Efficiency of Selection Sort: Worst-case performance is O(n²) due to n(n-1)/2 comparisons; best-case performance is Ω(n²); overall complexity is Θ(n²).
    • Efficiency of Bubble Sort: Similar to selection sort, the worst-case is O(n²), but best-case is Ω(n) when already sorted.

    Algorithm Efficiency

    • Understanding Big O Notation: Used to analyze algorithm performance; different complexities include O(n²), O(n log n), O(n), O(log n), and O(1).
    • Performance Comparison: O(n²) is the least efficient, while O(1) is the most efficient.
    • Search Algorithms:
      • Linear Search: O(n) complexity, checking each element one by one.
      • Binary Search: O(log n) complexity, quickly reducing search space in a sorted list.

    Asymptotic Notation

    • Best Case (Ω): Denotes the optimal performance scenario for an algorithm.
    • Tight Bound (Θ): Indicates when the upper and lower bounds are identical, meaning best and worst-case scenarios are the same.

    Recursion

    • Definition: A programming technique where a function calls itself to solve smaller instances of the same problem.
    • Recursive Example: Drawing a pyramid structure through a recursive function that calls itself with an increasing size parameter.

    Additional Notes

    • Importance of Sorting: Sorting is crucial for efficient searching; binary search requires pre-sorted data.
    • Array Structure: Arrays can be utilized to store values for sorting and searching functions, often accessed via dot notation for attributes in structured data types.
    • Visualization of Algorithms: Tools are available to compare the working principles of various sorting algorithms visually, enhancing comprehension and learning.

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    Related Documents

    Lecture 3 - CS50x 2024.pdf

    Description

    Test your understanding of the bubble sort algorithm with this quiz focused on pseudocode. Evaluate your knowledge on how the sorting process works and the conditions that trigger swaps. This quiz will reinforce your understanding of sorting algorithms.

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