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On average (assuming the rank of the (k + 1)-st element rank is random), insertion sort will require comparing and shifting half of the previous k elements, meaning that insertion sort will perform about half as many comparisons as selection sort on average. In the worst case for insertion sort (when the input array is reverse-sorted ...
Average case is the function which performs an average number of steps on input data of n elements. ... Insertion sort: Array: O(n) O(n 2) O(n 2) O(1) Selection sort ...
Faster than bubble sort on average. Insertion sort: n: 1: Yes Yes Insertion O(n + d), in the worst case over sequences that have d inversions. Bubble sort: n: 1: Yes Yes Exchanging Tiny code size. Cocktail shaker sort: n: 1: Yes
Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expressed as a function of the size of the input.
For example, since the run-time of insertion sort grows quadratically as its input size increases, insertion sort can be said to be of order O(n 2). Big O notation is a convenient way to express the worst-case scenario for a given algorithm, although it can also be used to express the average-case — for example, the worst-case scenario for ...
Performing a Fast Fourier transform; heapsort, quicksort (best and average case), or merge sort quadratic: Multiplying two n-digit numbers by a simple algorithm; bubble sort (worst case or naive implementation), Shell sort, quicksort , selection sort or insertion sort (), >
Among quadratic sorting algorithms (sorting algorithms with a simple average-case of Θ(n 2)), selection sort almost always outperforms bubble sort and gnome sort. Insertion sort is very similar in that after the kth iteration, the first elements in the array are in sorted order.
Third, average-case complexity allows discriminating the most efficient algorithm in practice among algorithms of equivalent best case complexity (for instance Quicksort). Average-case analysis requires a notion of an "average" input to an algorithm, which leads to the problem of devising a probability distribution over inputs.