Yes, bubble sort is a stable sorting algorithm.
Selection sort is more efficient for small datasets compared to bubble sort.
Yes, Quick Sort is an in-place sorting algorithm.
Yes, radix sort is an in-place sorting algorithm.
The running time of the bubble sort algorithm is O(n2), where n is the number of elements in the array being sorted.
The running time of the bubble sort algorithm is O(n2), where n is the number of elements in the array being sorted.
Use a sorting algorithm. There are a bewildering number of sorting algorithms, both stable and unstable. To sort numbers, an unstable sort suffices. The algorithm you use will depend on how many numbers need to be sorted (a small or a large set), however a hybrid algorithm (a combination of two or more algorithms) can cater for both. Introsort (unstable) and timsort (stable) are the two most common hybrid sorting algorithms.
Selection sort is more efficient for small datasets compared to bubble sort.
Yes, Quick Sort is an in-place sorting algorithm.
Yes, radix sort is an in-place sorting algorithm.
In a sorting algorithm the sort order can be changed by changing the comparison operator.
Bubble sort has no practical applications other than that it is often cited as an example of how not to write an algorithm. Insert sort is the best algorithm for sorting small lists of items and is often used in conjunction with quick sort to sort larger lists. Like insert sort, bubble sort is simple to implement and is a stable sort (equal items remain in the same order they were input). However, insert sort uses copy or move operations rather than swaps (which is actually three operations per swap) and is therefore quicker. The only time a bubble sort will work quicker than insert sort is when the array is already sorted, which renders the entire algorithm redundant. A modified algorithm that specifically tests if an array is sorted or not would be more efficient than a single-pass bubble sort.
Quick sort is not stable, but stable versions do exist. This comes at a cost in performance, however. A stable sort maintains the order of equal elements. That is, equal elements remain in the same order they were input. An unstable sort may change the order. In some cases, the order of equal elements is of no consequence, but when two elements with different values have the same sort key, then order can be important.
There are many sorting algorithms however there are only a small handful that we actually use: insertion sort (stable) is typically used for small sets while large data sets primarily use heapsort (unstable), merge sort (stable) or quicksort (unstable). Efficient implementations typically use a hybrid sort such as Timsort (stable) or introsort (unstable). The following lists all the documented algorithms currently listed in Wikipedia's "Sorting algorithm" page: Quicksort, merge sort, in-place merge sort, heapsort, insertion sort, introsort, selection sort, Timsort, cubesort, shell sort, bubble sort, binary tree sort, cycle sort, library sort, patience sorting, smoothsort, strand sort, tournament sort, cocktail sort, comb sort, gnome sort, unshuffle sort, Franceschini's sort, block sort, odd-even sort, pigeonhole sort, bucket sort (uniform keys), bucket sort (integer keys), counting sort, LSD radix sort, MSD radix sort, MSD radix sort in-place, spreadsort, burstsort, flashsort, postman sort bead sort, simple pancake sort, spaghetti sort, sorting network, bitonic sorter, bogo sort, stooge sort, Han's algorithm, Thorup's algorithm.
Every sorting algorithm has pros and cons; there is no "best" algorithm for every situation. Quick sort is generally considered to be the "best", but even a bubble sort will outperform it when there are relatively few items to consider, and optimisation is required to cater for equal items to ensure they remain in a stable sequence. The following article compares the efficiency of each of the popular algorithms, but note that the big O times reflect the standard, unoptimised algorithms.
The running time of the bubble sort algorithm is O(n2), where n is the number of elements in the array being sorted.
The running time of the bubble sort algorithm is O(n2), where n is the number of elements in the array being sorted.
The best case scenario for the Bubble Sort algorithm is when the input data is already sorted. In this case, the algorithm will only need to make one pass through the data to confirm that it is sorted, resulting in a time complexity of O(n). This makes it efficient and fast for sorting already sorted data.