When preparing for technical interviews in the past, I found myself spending hours crawling the internet putting together the best, average, and worst case complexities for search and sorting algorithms so that I wouldn't be stumped when asked about them. The sorted part is empty at the beginning: We search for the smallest element in the right, unsorted part. An example can be constructed very simply. Thanks and happy as you find it useful. The minimum element is not known until the end of the array is not reached. includes the Java source code for Selection Sort, shows how to derive its time complexity (without complicated math). Selection Sort kind of works the other way around: We select the smallest card from the unsorted cards and then – one after the other – append it to the already sorted cards. We put it in the correct position by swapping it with the element in the first place. Selection sort is the in-place sorting algorithm. Note: We have assigned elements to the array in the program itself. In each step, the number of comparisons is one less than the number of unsorted elements. It will get live soon. 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. Selection Sort has significantly fewer write operations, so Selection Sort can be faster when writing operations are expensive. Selection Sort Algorithm Time Complexity is O(n2). With unsorted elements, we have – as assumed – almost as many swap operations as elements: for example, with 4,096 unsorted elements, there are 4,084 swap operations. This time it is the 3; we swap it with the element in the second position: Again we search for the smallest element in the right section. The outer loop iterates over the elements to be sorted, and it ends after the second-last element. 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. Then you look for the next larger card and place it to the right of the smallest card, and so on until you finally pick up the largest card to the far right. and checks whether the performance of the Java implementation matches the expected runtime behavior. We walk over the rest of the array, looking for an even smaller element. Selection Sort is an easy-to-implement, and in its typical implementation unstable, sorting algorithm with an average, best-case, and worst-case time complexity of O(n²). Insertion sort is a simple sorting algorithm with quadratic worst-case time complexity, but in some cases it’s still the algorithm of choice.. It’s efficient for small data sets.It typically outperforms other simple quadratic algorithms, such as selection sort or bubble sort. Selection sort Time Complexity. But to find out the smallest element, we need to iterate and check for all the elements in the array. With Insertion Sort, the best case time complexity is O(n) and took less than a millisecond for up to 524,288 elements. Let’s now look at the swapping of the elements. It takes a constant amount of space and does not require any auxiliary data structure for sorting. You look for the smallest card and take it to the left of your hand. Hi Patrik, Increment ‘i’ to point it to next element in the array. First, you lay all your cards face-up on the table in front of you. It is good to improve my knowledge. At every step, you have to find the minimum element and put it in the right place. 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. (COA) Computer Organization & Architecture. Bubble sort is a stable algorithm, in contrast, selection sort is unstable. Replace the smallest element with the array element placed at position ‘i’. If you have any doubt feel free to write in a comment. Selection Sort can also be illustrated with playing cards. Suppose we have two different elements with key 2 and one with key 1, arranged as follows, and then sort them with Selection Sort: In the first step, the first and last elements are swapped. Time complexity is a way to describe how much time an algorithm needs to finish executing relative to the size of the input. Selection sort is easiest to implement and to code than other sorting algorithms. I am working on writing about other sorting algorithms. Save my name, email, and website in this browser for the next time I comment. Thus, we have, in sum, a maximum of n-1 swapping operations, i.e., the time complexity of O(n) – also called “linear time”. In each loop cycle, the first element of the right part is initially assumed as the smallest element min; its position is stored in minPos. We swap it with the 9: The last element is automatically the largest and, therefore, in the correct position. This is the reason why these minPos/min assignments are of little significance in unsorted arrays. It takes the complexity of O(n). Selection sort Time Complexity Analysis Selecting the lowest element requires scanning all n elements (this takes n - 1 comparisons) and then swapping it into the first position. With a linked list, cutting and pasting the element to be sorted could be done without any significant performance loss. I have written a test program that measures the runtime of Selection Sort (and all other sorting algorithms covered in this series) as follows: After each iteration, the program prints out the median of all previous measurement results. This is not the case with sequential writes to arrays, as these are mostly done in the CPU cache. We denote with n the number of elements, in our example n = 6. That would not only go beyond the scope of this article, but of the entire blog. So the total complexity of the Selection sort algorithm is O(n)* O(n)  i.e. when the array is previously sorted. You can also check if the array is already sorted before applying selection sort. 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