The algorithm maintains two subarrays in a given array. Selection Sort requires two nested for loops to complete itself, one for loop is in the function selectionSort, and inside the first loop we are making a call to another function indexOfMinimum, which has the second(inner) for loop. In total, there are 15 comparisons – regardless of whether the array is initially sorted or not. You look for the smallest card and take it to the left of your hand. If you liked the article, feel free to share it using one of the share buttons at the end. The algorithm can be explained most simply by an example. . (O(n^2) in all three cases.) Selection Sort can be made stable by not swapping the smallest element with the first in step two, but by shifting all elements between the first and the smallest element one position to the right and inserting the smallest element at the beginning. In the worst case, in every iteration, we have to traverse the entire array for finding min elements and this will continue for all n elements. The average performance insertion sort is better. Selection Sort has significantly fewer write operations, so Selection Sort can be faster when writing operations are expensive. Here is the result for Selection Sort after 50 iterations (for the sake of clarity, this is only an excerpt; the complete result can be found here): Here the measurements once again as a diagram (whereby I have displayed “unsorted” and “ascending” as one curve due to the almost identical values): Theoretically, the search for the smallest element should always take the same amount of time, regardless of the initial situation. In the third step, only one element remains; this is automatically considered sorted. You can also check if the array is already sorted before applying selection sort. You can find the source code for the entire article series in my GitHub repository. With a linked list, cutting and pasting the element to be sorted could be done without any significant performance loss. As a reminder, with Insertion Sort, we have comparisons and shifts averaging up to half of the sorted elements; with Selection Sort, we have to search for the smallest element in all unsorted elements in each step. The number of elements to be sorted doubles after each iteration from initially 1,024 elements up to 536,870,912 (= 2. that the runtime for ascending sorted elements is slightly better than for unsorted elements. © 2020 – The search for the smallest element is limited to the triangle of the orange and orange-blue boxes. In each step (except the last one), either one element is swapped or none, depending on whether the smallest element is already at the correct position or not. If you look at steps 2, 3, 4 and 5 iterates ‘n’ number of times. Your name can also be listed here. Using the CountOperations program from my GitHub repository, we can see the number of various operations. This is all about Selection Sort in C with Explanation. My focus is on optimizing complex algorithms and on advanced topics such as concurrency, the Java memory model, and garbage collection. The selection sort has a time complexity of O(n 2) where n is the total number of items in the list. No extra space is required (in-place sorting), It has very high time complexity. Selection sort is easiest to implement and to code than other sorting algorithms. This is not the case with sequential writes to arrays, as these are mostly done in the CPU cache. So the best complexity is the same a worst case complexity. In the following sections, I will discuss the space complexity, stability, and parallelizability of Selection Sort. Space Complexity: Space complexity is O(1) because an extra variable temp is used. This is all about Selection Sort in C with Explanation. Selection sort is the in-place sorting algorithm. Hence for a given input size of n, following will be the time and space complexity for selection sort algorithm: Worst Case Time Complexity [ Big-O ]: O(n 2) (Where n is a number of elements in the array (array size).) Let’s compare the measurements from my Java implementations. Hence this will perform n^2 operations in total. In the first four iterations, we have one each and in the iterations five to eight, none (nevertheless the algorithm continues to run until the end): Furthermore, we can read from the measurements: For elements sorted in descending order, the order of magnitude can be derived from the illustration just above. Even though the time complexity will remain the same due to this change, the additional shifts will lead to significant performance degradation, at least when we sort an array. Here are the average values after 100 iterations (a small excerpt; the complete results can be found here): Here as a diagram with logarithmic x-axis: The chart shows very nicely that we have logarithmic growth, i.e., with every doubling of the number of elements, the number of assignments increases only by a constant value. that the runtime for descending sorted elements is significantly worse than for unsorted elements. Selection Sort Algorithm Time Complexity is O(n2). Selection Sort’s space complexity is constant since we do not need any additional memory space apart from the loop variables i and j and the auxiliary variables length, minPos, and min.
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