Sorting Algorithms Overview
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What is the first step in the selection sort algorithm?

  • Sort the array in ascending order.
  • Find the largest item in the range of the array. (correct)
  • Swap the largest item with the last item in the array.
  • Reduce the size of the array by one.

    • Which of the following is not an application of sorting?

  • Finding a target pair x, y such that x+y = z
  • Deleting duplicates
  • Searching for the maximum value (correct)
  • Reconstructing the original order

    • What characterizes selection sort compared to bubble sort?

  • It always results in a sorted array after one pass.
  • It outperforms bubble sort in all cases.
  • It requires fewer comparisons than bubble sort.
  • It selects the largest item in each pass. (correct)

    • Which sorting algorithm is based on the divide-and-conquer approach?

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

    Which of the following statements about iterative and recursive sorting algorithms is true?

    <p>Both types can be comparison-based.</p> Signup and view all the answers

    What is the running time of the Bubble Sort algorithm in the worst-case scenario?

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

    What is the crucial step of the Divide-and-Conquer method in solving problems?

    <p>Dividing the problem into smaller parts and combining results</p> Signup and view all the answers

    During which step of Merge Sort do we combine two halves to create a sorted array?

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

    How does Merge Sort handle the sorting of the initial pairs of elements?

    <p>It merges pairs into sets of 2</p> Signup and view all the answers

    In the best-case scenario, what is the running time of the Merge Sort algorithm?

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

    What is the time complexity of the traditional bubble sort algorithm?

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

    Which of the following is a key feature of bubble sort?

    <p>It compares adjacent pairs of elements.</p> Signup and view all the answers

    In the bubble sort algorithm, under what condition can the algorithm terminate early?

    <p>If no swaps occur during an iteration.</p> Signup and view all the answers

    How many iterations does the outer loop execute in bubble sort when sorting an array of size n?

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

    What initial assumption does the optimized version of bubble sort rely on?

    <p>The array is sorted before running the inner loop.</p> Signup and view all the answers

    Which of the following statements about bubble sort is true?

    <p>It swaps elements based on their values to achieve sorting.</p> Signup and view all the answers

    What mechanism is used in bubble sort to track whether the array is already sorted?

    <p>Sorting Flag</p> Signup and view all the answers

    How does the implementation of bubble sort ensure pairs of numbers are compared only once in each iteration?

    <p>By decreasing the range of j in each iteration.</p> Signup and view all the answers

    What is the primary goal of the selection sort algorithm?

    <p>To build a sorted array by repeatedly placing the smallest or largest items</p> Signup and view all the answers

    In the given implementation of selection sort, how many times does the inner loop execute in total?

    <p>n(n-1)/2</p> Signup and view all the answers

    What does the 'swap' routine do in the selection sort algorithm?

    <p>It swaps the maximum element with the last item of the unsorted section</p> Signup and view all the answers

    How does bubble sort ensure that the largest item floats to the end of the array?

    <p>By comparing adjacent items and swapping when necessary</p> Signup and view all the answers

    Which of the following describes the time complexity of selection sort?

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

    In bubble sort, what should happen after each complete pass through the array?

    <p>The largest item will have been moved to its final position</p> Signup and view all the answers

    What is the fundamental process by which bubble sort operates?

    <p>Moving elements to their sorted position through adjacent comparisons</p> Signup and view all the answers

    What characterizes the 'bubbles' in bubble sort?

    <p>They denote the largest items rising to the top of the array</p> Signup and view all the answers

    What is the base case for the mergeSort function?

    <p>When low = high</p> Signup and view all the answers

    Which part of the mergeSort function is responsible for dividing the array into halves?

    <p>Calculating the mid index</p> Signup and view all the answers

    What does the merge function do?

    <p>It combines two sorted halves into a single sorted array</p> Signup and view all the answers

    Which lines in the mergeSort function are responsible for the recursive sorting of the two halves?

    <p>mergeSort(a, low, mid);</p> Signup and view all the answers

    In mergeSort, what condition is checked to ensure recursion stops?

    <p>When low equals high</p> Signup and view all the answers

    When merging two sorted halves, what is the role of the temporary array?

    <p>To hold the merged result before updating the original array</p> Signup and view all the answers

    What is the result of calling merge(a, low, mid, high)?

    <p>Combines and sorts the elements from a[low...mid] and a[mid+1...high]</p> Signup and view all the answers

    What is the time complexity of the mergeSort algorithm in the average and worst cases?

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

    Study Notes

    Sorting Algorithms

    • Sorting algorithms arrange elements in a specific order (ascending or descending).
    • Different algorithms have different efficiencies (time complexity).

    Sorting Algorithm Types

    • Iterative Algorithms:
      • Selection Sort: Finds the largest element and places it at the end, repeating for remaining elements.
        • Time complexity: O(n²).
        • Simple to understand but inefficient for large datasets.
      • Bubble Sort: Compares adjacent elements and swaps if out of order. Repeats until no swaps are needed.
        • Time complexity: O(n²).
        • Efficient for small datasets, but becomes inefficient for large datasets.
        • Has a property to stop early if the array is sorted. This can improve efficiency in some cases.
    • Recursive Algorithms:
      • Merge Sort: Divides the array into two halves, recursively sorts them, and then merges the sorted halves.
        • Time complexity: O(n log n).
        • This is an optimal comparison-based sorting algorithm.
        • Uses extra memory for merging.
    • Divide-and-Conquer Method:
      • Divides a large problem into smaller, solvable subproblems, recursively solves these subproblems, and then combines the results to get the final solution.
      • This methodology is used in various algorithms, not just for sorting.

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    Description

    This quiz explores different sorting algorithms, including both iterative and recursive methods. You will learn about selection sort, bubble sort, and merge sort, along with their efficiencies and time complexities. Test your knowledge on how these algorithms work and their applications!

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