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A list containing a single element is, by definition, sorted. Repeatedly merge sublists to create a new sorted sublist until the single list contains all elements. The single list is the sorted list. The merge algorithm is used repeatedly in the merge sort algorithm. An example merge sort is given in the illustration.
Merge two-record sublists from C and D into four-record sublists; writing these alternately to A and B. Merge four-record sublists from A and B into eight-record sublists; writing these alternately to C and D; Repeat until you have one list containing all the data, sorted—in log 2 (n) passes.
Finding a specific element in a linked list, even if it is sorted, normally requires O(n) time (linear search). This is one of the primary disadvantages of linked lists over other data structures. In addition to the variants discussed above, below are two simple ways to improve search time.
The classic merge outputs the data item with the lowest key at each step; given some sorted lists, it produces a sorted list containing all the elements in any of the input lists, and it does so in time proportional to the sum of the lengths of the input lists. Denote by A[1..p] and B[1..q] two arrays sorted in increasing order.
Block sort, or block merge sort, is a sorting algorithm combining at least two merge operations with an insertion sort to arrive at O(n log n) (see Big O notation) in-place stable sorting time. It gets its name from the observation that merging two sorted lists, A and B , is equivalent to breaking A into evenly sized blocks , inserting each A ...
Problems of sufficient simplicity are solved directly. For example, to sort a given list of n natural numbers, split it into two lists of about n/2 numbers each, sort each of them in turn, and interleave both results appropriately to obtain the sorted version of the given list (see the picture). This approach is known as the merge sort algorithm.
A comparison sort examines the data only by comparing two elements with a comparison operator. General method: insertion, exchange, selection, merging, etc. Exchange sorts include bubble sort and quicksort. Selection sorts include cycle sort and heapsort. Whether the algorithm is serial or parallel.
External sorting algorithms generally fall into two types, distribution sorting, which resembles quicksort, and external merge sort, which resembles merge sort. External merge sort typically uses a hybrid sort-merge strategy. In the sorting phase, chunks of data small enough to fit in main memory are read, sorted, and written out to a temporary ...