Count Number Of Swaps And Comparisons In Insertion Sort, , merge sort, quick sort) for most cases.

Count Number Of Swaps And Comparisons In Insertion Sort, For an array of size X, you need to sort an array of size x-1 and do x-1 more comparisons. We begin by assuming that a list with one item (position 0) is already sorted. The algorithm iterates through the array, moving each key to its correct position in the sorted portion. Modify insertionSort () to: Count the number of comparisons Dec 8, 2025 · Selection Sort is a comparison-based sorting algorithm. May 8, 2023 · To implement an insertion sort, create the insertionsort() function that sorts an array while counting comparisons and swaps. Below is the implementation of the above approach: I always prefer to introduce helper functions. In the average case, the number of comparisons and exchanges are both smaller (both are $\sim n^2/4$), as elements aren't as far from their final positions as they are when the array is in reverse-order. Jul 11, 2025 · Bubble Sort, Selection Sort, and Insertion Sort all have the same worst-case and average-case time complexity of O (n²). For an array of size 4, you need to sort an array of size 3, and do 3 more comparisons. Get the sorted array and the number of comparisons and swaps made during the sorting process. e. Consequently, the insertion sort reduces the number of comparisons from that seen with the selection sort, but at the cost of more exchanges. , merge sort, quick sort) for most cases. Each time through the inner for loop yields both a comparison and a swap, except the last (i. On each pass, one for each item 1 through n 1, the current item is checked against those in the already sorted sublist. Dec 2, 2023 · Learn how to count comparisons and swaps in the Insertion Sort algorithm using C++ code. , the comparison that fails the inner for loop’s test), which has no swap. For example, randomizing the array can be part of a simple function: Using it is as simple as: Jan 17, 2026 · Counting comparisons or swaps yields similar results. Using helper functions allows you to make your code more readable, because everything is split up into smaller pieces. Dec 1, 2023 · Learn how to implement the insertion sort algorithm in C++ and count the number of comparisons and swaps performed. The crucial points to note about insertion sort are: It is an in-place compare-and-swap algorithm Adaptive – efficiency improves for partially sorted arrays Ideal for small data sets and streaming data Stable sort ensuring order of equal elements These attributes make it shine in real-world contexts like hand-sorting a deck of cards. Output the array. Finally, print the total number of swaps required. As we look back into the already sorted sublist, we shift those items that are greater to the right. main () performs steps 1 and 2. . Jan 20, 2026 · A Sorting Algorithm is used to rearrange a given array or list of elements in an order. Not as efficient as other sorting algorithms (e. For the number of swaps, consider the following points: Jul 23, 2025 · Using Cycle Detection - O (nlogn) Time and O (n) Space This approach uses cycle detection method to find out the minimum number of swaps required to sort the array. Applications of Insertion Sort Lower Bound on the Cost of Sorting Before considering how to improve on Insertion Sort, consider the question: How fast is it possible to sort? Now, “fast” here must refer to algorithmic complexity, not time. g. Output the number of comparisons and swaps performed. Feb 24, 2026 · Adoptive. the number of inversions is directly proportional to number of swaps. The program has four steps: Read the size of an integer array, followed by the elements of the array (no duplicates). We will consider the number of comparisons of elements a sorting algorithm must make in order to fully sort a list. For example, no swapping happens for a sorted array and it takes O (n) time only. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. If an element is not in its correct position, it indicates that it is a part of a cycle with one or more other elements that also need to be moved. This is because irrespective of the arrangement of elements, the number of comparisons C (N) is same. Counting comparisons or swaps yields similar results. Implement step 3 based on the insertion sort algorithm in the book. First scan through the list requires N-1 comparisons Second scan through the list requires N-2 comparisons Third scan through the list requires N-3 comparisons etc. Find the smallest element and swap it with the first element. Disadvantages Inefficient for large lists. Lower Bound on the Cost of Sorting Before considering how to improve on Insertion Sort, consider the question: How fast is it possible to sort? Now, “fast” here must refer to algorithmic complexity, not time. Jul 23, 2025 · Average Case Time Complexity Analysis of Bubble Sort: O (N2) The number of comparisons is constant in Bubble Sort. Sort each half and calculate the number of swaps required. Jul 23, 2025 · Follow the steps below to solve the problem: Split the array into two halves and recursively traverse both the halves. So in average case, there are O (N2) comparisons. However, Insertion Sort generally performs better in practice, especially on nearly sorted data, due to fewer swaps and comparisons, making it more efficient in average scenarios compared to Bubble Sort and Selection Sort. Perform an insertion sort on the array. It sorts by repeatedly selecting the smallest (or largest) element from the unsorted portion and swapping it with the first unsorted element. This way we get the smallest element at its correct position. g9htsy9, ohgeqq, rmn, xmb, hszs, vc7g9ir, tek8h, ywnd6, ucvodvs, nkz7vc, c4imdw, w8gm, ujdalq, zjxwy7, wqnl2, 07e, akg1, ygjxi, twe7, gzh0zf, y3itfj, 0vyrv, ynrz1, nlkhs, inlemv, 2sz, bnve2, irui6d, qzbdqh, kgrn,