Insertion Sort Quiz Questions And Answers

Binary search can be used in an insertion sort algorithm to reduce the number of comparisons. This is because binary search allows for efficiently finding the correct position to insert an element in a sorted array. By using binary search, the algorithm can quickly locate the correct position and minimize the number of comparisons needed to find the correct position for each element being inserted. This ultimately leads to a more efficient insertion sort algorithm.

The given answer shows the correct intermediate steps of the data set being sorted with the Insertion sort algorithm. The initial step is the given data set itself. In the first step, the algorithm compares 20 with 15 and swaps them to get 10,15,20,18. In the second step, the algorithm compares 10 with 15 and swaps them to get 10,15,18,20. In the third step, the algorithm compares 18 with 20 and leaves them as they are to get 10,15,18,20. The final step is the same as the third step since the data set is already sorted.

Insertion sort is the fastest sorting algorithm for sorting small arrays because it has a time complexity of O(n^2), which means it performs well for small input sizes. It works by iteratively inserting each element into its correct position in the sorted part of the array. This algorithm has a low overhead and performs efficiently when the array is already partially sorted or contains mostly sorted elements. On the other hand, Quick sort has an average time complexity of O(nlogn) but can have a worst-case time complexity of O(n^2), making it less efficient for small arrays.

Insertion Sort uses the operation of swapping to move numbers from the unsorted section to the sorted section of the list. In this sorting algorithm, each element is compared with the elements before it in the sorted section, and if it is smaller, it is swapped with the element before it until it reaches its correct position. This process continues until all elements are in their correct sorted positions. Therefore, the correct answer is swapping.

The correct answer is "stable, adaptive." In an insertion sort algorithm, stability refers to the preservation of the relative order of equal elements in the sorted array. Adaptive means that the algorithm's efficiency can be improved if the input is already partially sorted. Both of these features are important in an insertion sort algorithm. The other options, "dependable" and "anti-stable," do not accurately describe the features of an insertion sort algorithm.

The given list is partially sorted, with the sort marker indicating the boundary between the sorted and unsorted portions. To sort the next number (5), we need to compare it with each number in the sorted portion until we find its correct position. In this case, we need to make 3 comparisons (with 1, 3, and 4) before finding the correct position for 5. Additionally, we need to make 2 swaps to move the numbers 5 and 2 to their correct positions (5 before 8 and 2 before 5). Therefore, the correct answer is 3 comparisons, 2 swaps.

The running time of the Insertion Algorithm would be O(n) in this case because even though all the elements in the input array are equal, the algorithm still needs to iterate through each element in order to perform the necessary comparisons and insertions. The number of iterations is directly proportional to the size of the input array, hence the running time is linear.

To sort the next number, we need to compare it with each number in the partially sorted list until we find its correct position. In this case, the number 2 needs to be compared with 1, 3, 4, 5, 8, and 9, which makes a total of 6 comparisons. Additionally, since the number 2 needs to be placed before the numbers 3, 4, 5, 8, and 9, we need to perform 5 swaps to sort it correctly. Therefore, the answer is 6 comparisons and 5 swaps.

Quick sort is not a stable sorting algorithm in its typical implementation. Stability refers to the preservation of the relative order of equal elements in the sorted output. Quick sort involves partitioning the array based on a pivot element, and the order of equal elements may change during this process. Therefore, Quick sort does not guarantee the stability of the sorting algorithm. On the other hand, Merge sort and Insertion sort are stable sorting algorithms as they maintain the relative order of equal elements. Hence, the correct answer is Quick sort.

Insertion sort works by building a sorted sub-list one element at a time. It iterates through the list, comparing each element to the ones before it and inserting it into its correct position. In this case, the algorithm will require 5 passes to sort the elements completely:

Pass 1: 12, 14, 16, 6, 3, 10

Pass 2: 12, 14, 16, 6, 3, 10

Pass 3: 6, 12, 14, 16, 3, 10

Pass 4: 3, 6, 12, 14, 16, 10

Pass 5: 3, 6, 10, 12, 14, 16