Big-O Notation for Searching and Sorting Algorithms Quiz
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Questions and Answers

What is the time complexity of Merge Sort for all cases?

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

    • Which sorting algorithm is known for dividing the array into a sorted and an unsorted region?

  • Bubble Sort
  • Insertion Sort
  • Selection Sort (correct)
  • Merge Sort

    • In the Tower of Hanoi algorithm, what is the minimum number of moves required to solve a tower with 64 disks?

  • $2^{16} - 1$
  • $2^{32} - 1$
  • $2^{8} - 1$
  • $2^{64} - 1$ (correct)

    • What is the key characteristic of Bubble Sort among the sorting algorithms mentioned?

    <p>Performs poorly on large datasets</p> Signup and view all the answers

    Which algorithm involves dividing the array into two halves, recursively sorting each half, and then merging them?

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

    What is the primary difference between iterative and recursive algorithms?

    <p>Iterative algorithms use loops for repetition, recursive algorithms use function calls.</p> Signup and view all the answers

    What is the time complexity of the Tower of Hanoi algorithm?

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

    In a recursive algorithm, what is the space complexity as the recursion depth increases?

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

    What is the time complexity of the Binary Search algorithm?

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

    Which searching algorithm examines elements from the right side of the list?

    <p>RLSearch (Right-to-Left) Algorithm</p> Signup and view all the answers

    In terms of time complexity, which algorithm has the best-case scenario of O(1)?

    <p>LRSearch (Left-to-Right) Algorithm</p> Signup and view all the answers

    What is the primary role of searching algorithms in computer science?

    <p>Locating specific elements within a dataset</p> Signup and view all the answers

    What is the time complexity of Binary Search in the worst case scenario?

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

    Which algorithm is efficient for small datasets or partially sorted data?

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

    In which algorithm does the sorted array build one element at a time?

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

    What is the worst case time complexity of Linear Search?

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

    Which sorting algorithm enhances the efficiency of searching, organizing, and retrieving information by arranging elements in a desired sequence?

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

    What is the characteristic of Binary Search that makes it efficient for sorted lists?

    <p>Requires a pre-sorted dataset</p> Signup and view all the answers

    Study Notes

    Recursive Algorithms

    • Factorial algorithm has a time complexity of O(n)
    • Fibonacci Sequence algorithm has a time complexity of O(2^n)
    • Tower of Hanoi algorithm has a time complexity of O(2^n)

    Searching Algorithms

    • LRSearch (Left-to-Right) Algorithm: examines elements from the left side of the list until a match is found or the end of the list is reached
      • Best case: O(1)
      • Worst and average cases: O(n)
    • RLSearch (Right-to-Left) Algorithm: examines elements from the right side of the list until a match is found or the beginning of the list is reached
      • Best case: O(1)
      • Worst and average cases: O(n)
    • Binary Search Algorithm: divides the sorted list in half repeatedly, discarding half of the remaining elements based on the comparison with the target value
      • Best case: O(1)
      • Worst and average cases: O(log n)
    • Linear Search Algorithm: sequentially checks each element in the list until a match is found or the entire list is traversed
      • Best case: O(1)
      • Worst and average cases: O(n)

    Sorting Algorithms

    • Merge Sort: divides the array into two halves, recursively sorts each half, and then merges the two sorted arrays
      • Time complexity: O(n log n)
      • Stable and suitable for large datasets
    • Selection Sort: divides the array into a sorted and an unsorted region, and selects the smallest element from the unsorted region to swap with the first element of the unsorted region
      • Time complexity: O(n^2)
      • Simple, but performs poorly on large datasets
    • Bubble Sort: repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order
      • Time complexity: O(log n) for pre-sorted datasets
      • Efficient for sorted lists, but requires a pre-sorted dataset
    • Insertion Sort: builds the sorted array one element at a time by repeatedly taking elements from the unsorted part and inserting them into their correct position in the sorted part
      • Time complexity: O(n^2)
      • Simple, efficient for small datasets or partially sorted data

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    Description

    Test your knowledge on the time complexities of various searching and sorting algorithms, including Factorial, Fibonacci Sequence, and Tower of Hanoi. Learn about the importance of searching algorithms in computer science and how they help in efficient information retrieval.

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