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External sorting explains how merge sort is implemented with disk drives. A typical tape drive sort uses four tape drives. A minimal implementation can get by with just two record buffers and a few program variables. Mergesort is an asymptotically optimal compare-based sorting algorithm.

Pseudocode for top-down merge sort algorithm which recursively divides the input list into smaller sublists until the sublists are trivially sorted, and then merges the sublists while returning up the call chain. Better parallelism can be achieved by using a parallel merge algorithm. Cormen et al. present a binary variant that merges two sorted sub-sequences into one sorted output sequence.

## Java

This is mainly due to the sequential merge method, as it is the bottleneck of the parallel executions. With this version it is better to allocate the temporary space outside the merge routine, so that only one allocation is needed. The excessive copying mentioned previously is also mitigated, since the last pair of lines before the return result statement become superfluous. Variants of merge sort are primarily concerned with reducing the space complexity and the cost of copying. In the worst case, merge sort uses approximately 39% fewer comparisons than quicksort does in its average case, and in terms of moves, merge sort’s worst case complexity is O – the same complexity as quicksort’s best case. Most code you find online has been written to explain how bottom-up merge sort works.

- Merge sort’s most common implementation does not sort in place; therefore, the memory size of the input must be allocated for the sorted output to be stored in (see below for variations that need only n/2 extra spaces).
- Its prime disadvantage is that it uses extra space proportional to N.
- Merge-sort can only sort data that takes up at most half of memory .
- Parts and assigned to the appropriate processor groups.
- // Either left or right may have elements left; consume them.
- Use of a static array like aux[] is inadvisable in library software because multiple clients might use the class concurrently.

// A more efficient implementation would swap the roles of A and B. // Copy array B to array A for the next iteration.

## Top-down implementation

However, it saves the auxiliary space required by the call stack. Merge two-record sublists from C and D into four-record sublists; writing these alternately to A and B. Merge pairs of records from A; writing two-record sublists alternately to C and D. A list of zero or one elements is sorted, by definition. // Make successively longer sorted runs of length 2, 4, 8, 16… Merge-sort can only sort data that takes up at most half of memory . Use of a static array like aux[] is inadvisable in library software because multiple clients might use the class concurrently.

### Which data structure is fastest search?

With a hash table, you can access objects by the key, so this structure is high-speed for lookups. Hash tables are faster than the arrays for lookups.

After that, the merge sort is still unstable. What you do is actually merge(, merge(, )). The order here is important as otherwise sort stability will not be held any more. When it exceeds length of array then function returns the sorted array. The above function is recursive, so uses function call stack to store intermediate values of l and h.

## Time Complexity

Give an implementation ofMerge.java that does not use a static array. Time complexity of above iterative function is same as recursive, i.e., Θ. // While there are elements in the left or right runs… // Array A[] has the items to sort; array B[] is a work array. ####Analysis This merge-sort has approximately the same performance as basic merge-sort.

### Which sorting algorithm is best in worst case?

Analysis of sorting techniques :

When order of input is not known, merge sort is preferred as it has worst case time complexity of nlogn and it is stable as well.

As suggested in the Wiki example comments, the direction of merge can be changed with each pass. The method merge inMerge.javaputs the results of merging the subarrays a[lo..mid] with a[mid+1..hi]into a single ordered array, leaving the result in a[lo..hi]. While it would be desirable to implement this method without using a significant amount of extra space, such solutions are remarkably complicated.

As of Perl 5.8, merge sort is its default sorting algorithm . In Java, the Arrays.sort() methods use merge sort or a tuned quicksort depending on the datatypes and for implementation efficiency switch to insertion sort when fewer than seven array elements are being sorted. The Linux kernel uses merge sort for its linked lists. Python uses Timsort, another tuned hybrid of merge sort and insertion sort, that has become the standard sort algorithm in Java SE 7 (for arrays of non-primitive types), on the Android platform, and in GNU Octave. Auxiliary with linked listsIn computer science, merge sort is an efficient, general-purpose, and comparison-based sorting algorithm.

The function call stack stores other bookkeeping information together with parameters. Also, function calls involve overheads like storing activation record of the caller function and then resuming execution. Unlike Iterative QuickSort, the iterative MergeSort doesn’t require explicit auxiliary stack.

## Answers

Because now the merged list is going at the start instead of at the end, and shift() is quite fast to compute, and I’ll only be using one shift Instead of 2. During each pass the array is divided into smaller sub-arrays of a pseudo-fixed size . Initially step is 1, but the value increases with every pass, as every adjacent sub-arrays are merged, thus step doubles . The main idea of the bottom-up merge sort is to sort the array in a sequence of passes . This quantity is related to the Kendall tau distance; see Section 2.5. This is responsible with the merging of two already sorted blocks (sub-arrays) from a given array . Sort the element within the range using Insertion Sort.

- // Copy array B to array A for the next iteration.
- Some parallel merge sort algorithms are strongly related to the sequential top-down merge algorithm while others have a different general structure and use the K-way merge method.
- Test whether array is already in order.We can reduce the running time to be linear for arrays that are already in order by adding a test to skip call to merge() if ais less than or equal to a[mid+1].
- For detailed information about the complexity of the parallel merge procedure, see Merge algorithm.
- One of them, the Knuth’s ‘snowplow’ (based on a binary min-heap), generates runs twice as long as a size of memory used.
- Because now the merged list is going at the start instead of at the end, and shift() is quite fast to compute, and I’ll only be using one shift Instead of 2.
- Please use our online compiler to post code in comments using C, C++, Java, Python, JavaScript, C#, PHP, and many more popular programming languages.

They specifically avoid writing compact code. An alternative implementation is the bottom-up version of the same algorithm (we don’t use recursion for this implementation). In the last article I’ve described a recursive version of the Merge Sort Algorithm . Of course every recursive algorithm can be written in an iterative manner. It will sort array until it’s range within the length of array. Give traces, in the style of the trace given in this section, showing how the keys E A S Y Q U E S T I O N are sorted with top-down mergesort and with bottom-up mergesort.Solution.