#XSORT ALGORITHM UPDATE#

Insertion sort, merge sort, and bubble sort are stable. Unstable sorting algorithms do not maintain the order of equal values, and the output array may be. Stable sorting algorithms will maintain the order of 2a and 2b, meaning the output array will be.

#XSORT ALGORITHM UPDATE#

And to help differentiate between the two equal values, 2, let's update them to 2a and 2b, making the input array. Unstable sorting algorithms do not maintain the relative order of elements with equal values / keys.įor example, imagine you have the input array. Whether they are stable or unstable: Stable sorting algorithms maintain the relative order of elements with equal values, or keys.Finally, some sorting algorithms, such as merge sort, make use of both recursive as well as non-recursive techniques to sort the input. Other sorting algorithms, such as selection sort or insertion sort, use non-recursive techniques. Whether or not they use recursion: Some sorting algorithms, such as quick sort, use recursive techniques to sort the input.Using Big-O notation, the sorting algorithm examples listed above require at least O(nlogn) comparisons in the best case, and O(n^2) comparisons in the worst case for most of the outputs. The number of comparisons: This is the number of times the algorithm compares elements to sort the input.Selection sort requires the minimum number of swaps. The number of swaps or inversions required: This is the number of times the algorithm swaps elements to sort the input.Sorting algorithms can be categorized based on the following parameters: Some of the most common sorting algorithms are:īut before we get into each of these, let's learn a bit more about what classifies a sorting algorithm. You should determine what your requirements are, and consider the limitations of your system before deciding which sorting algorithm to use. Some algorithms like merge sort may need a lot of space or memory to run, while insertion sort is not always the fastest, but doesn't require many resources to run. The answers to these questions may determine which algorithm is going to work best for each situation. When choosing a sorting algorithm, some questions have to be asked – How big is the collection being sorted? How much memory is available? Does the collection need to grow? These algorithms have direct applications in searching algorithms, database algorithms, divide and conquer methods, data structure algorithms, and many more. Since they can often reduce the complexity of a problem, sorting algorithms are very important in computer science. Sorts are most commonly in numerical or a form of alphabetical (or lexicographical) order, and can be in ascending (A-Z, 0-9) or descending (Z-A, 9-0) order. Here's a table showing the stablilty of different sorting algorithm.Sorting algorithms are a set of instructions that take an array or list as an input and arrange the items into a particular order. Stable sorting with the positions preserved However, after a stable sorting algorithm, there is always one possibility where the positions are maintained as in the original array. Unstable sorting with two possible outcomes An unstable sorting algorithm allows two possibilities where the two positions of 3 may or may not be maintained. Usually, auxiliary memory is considered for calculating the space complexity of an algorithm.Ī sorting algorithm is considered stable if the two or more items with the same value maintain the same relative positions even after sorting.įor example, in the image below, there are two items with the same value 3. The auxiliary memory is the additional space occupied by the algorithm apart from the input data. It includes both the auxiliary memory and the input. Space Complexity: Space complexity refers to the total amount of memory used by the algorithm for a complete execution. It can be represented in different forms:Ģ. Time Complexity: Time complexity refers to the time taken by an algorithm to complete its execution with respect to the size of the input. The efficiency of any sorting algorithm is determined by the time complexity and space complexity of the algorithm.ġ. And, we can use any algorithm based on the requirement. There are various sorting algorithms that can be used to complete this operation. Here, we are sorting the array in ascending order. Decrease Key and Delete Node Operations on a Fibonacci HeapĪ sorting algorithm is used to arrange elements of an array/list in a specific order.

Xsort algorithm