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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.
In pigeonhole sort (often called bucket sort), pointers to the data items are distributed to a table of buckets, represented as collection data types such as linked lists, using the keys as indices into the table. Then, all of the buckets are concatenated together to form the output list. [12]
Bucket sort is a divide-and-conquer sorting algorithm that generalizes counting sort by partitioning an array into a finite number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm or by recursively applying the bucket sorting algorithm.
Bucket sort may be used in lieu of counting sort, and entails a similar time analysis. However, compared to counting sort, bucket sort requires linked lists, dynamic arrays, or a large amount of pre-allocated memory to hold the sets of items within each bucket, whereas counting sort stores a single number (the count of items) per bucket. [4]
The bucket queue is the priority-queue analogue of pigeonhole sort (also called bucket sort), a sorting algorithm that places elements into buckets indexed by their priorities and then concatenates the buckets. Using a bucket queue as the priority queue in a selection sort gives a form of the pigeonhole sort algorithm. [2]
A doubly linked list whose nodes contain three fields: an integer value, the link forward to the next node, and the link backward to the previous node. A technique known as XOR-linking allows a doubly linked list to be implemented using a single link field in each node. However, this technique requires the ability to do bit operations on ...
Bucket sort can be mixed with other sorting methods to complete sorting. If it is sorted by bucket sort and insert sort, also is a fairly efficient sorting method. But when the series appears a large deviation from the value: For example, when the maximum value of the series is greater than N times the next largest value.
Sort each bucket using insertion sort. Steps 1–3 and 6 are common to any bucket sort, and can be improved using techniques generic to bucket sorts. In particular, the goal is for the buckets to be of approximately equal size (n/m elements each), [1] with the ideal being division into m quantiles.