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In computer science, radix sort is a non-comparative sorting algorithm.It avoids comparison by creating and distributing elements into buckets according to their radix.For elements with more than one significant digit, this bucketing process is repeated for each digit, while preserving the ordering of the prior step, until all digits have been considered.
Here input is the input array to be sorted, key returns the numeric key of each item in the input array, count is an auxiliary array used first to store the numbers of items with each key, and then (after the second loop) to store the positions where items with each key should be placed, k is the maximum value of the non-negative key values and ...
Counting sort is applicable when each input is known to belong to a particular set, S, of possibilities. The algorithm runs in O(|S| + n) time and O(|S|) memory where n is the length of the input. It works by creating an integer array of size |S| and using the ith bin to count the occurrences of the ith member of S in the input. Each input is ...
Radix sort is a sorting algorithm that works for larger keys than pigeonhole sort or counting sort by performing multiple passes over the data. Each pass sorts the input using only part of the keys, by using a different sorting algorithm (such as pigeonhole sort or counting sort) that is suited only for small keys.
Bucket sort can be seen as a generalization of counting sort; in fact, if each bucket has size 1 then bucket sort degenerates to counting sort. The variable bucket size of bucket sort allows it to use O(n) memory instead of O(M) memory, where M is the number of distinct values; in exchange, it gives up counting sort's O(n + M) worst-case behavior.
procedure heapsort(a, count) is input: an unordered array a of length count (Build the heap in array a so that largest value is at the root) heapify(a, count) (The following loop maintains the invariants that a[0:end−1] is a heap, and every element a[end:count−1] beyond end is greater than everything before it, i.e. a[end:count−1] is in ...
The difference between pigeonhole sort and counting sort is that in counting sort, the auxiliary array does not contain lists of input elements, only counts: 3: 1; 4: 0; 5: 2; 6: 0; 7: 0; 8: 1; For arrays where N is much larger than n, bucket sort is a generalization that is more efficient in space and time.
American flag sort is most efficient with a radix that is a power of 2, because bit-shifting operations can be used instead of expensive exponentiations to compute the value of each digit. When sorting strings using 8- or 7-bit encodings such as ASCII, it is typical to use a radix of 256 or 128, which amounts to sorting character-by-character. [1]