# MergeSort

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# Motivation

Sorting is a problem that is well solved by divide and conquer algorithms. Merge sort is a elegant example which can be parallelized in a straight-forward manner.

Finally, parallelization of the combine step, while not trivial, is possible (and left as an optional fun exercise for those so inclined).

# Background

In computer science, merge sort refers to a sorting algorithm which splits an array of data into continuously smaller halves until the arrays reach a size of 1, after which the elements are continuously compared and merged into a sorted array.

## Visualization

If you are unclear on how merge sort works, take a look at the visualgo explanation and visualization of merge sort.

# The Core Questions

• What is the data?
• Is the data mutable?
• If so, how is it shared?

# Mistakes To Avoid

 Warning: Be sure to calculate the midpoint correctly.
 Warning: When checking the base case, remember to account for [minInclusive, maxExclusive). It is all too easy to get an off by 1 error and stack overflow.
 Warning: When transitioning to sequential, make sure to NOT sort the entire array when you are only responsible for a range [min,max).

# Code to Use

Both the sequential and parallel merge sorts will be passed a Combiner. When you are done with the divide and conquer phases, invoke combiner.combineRange(data, min, mid, maxExclusive) to merge the two sorted sub-problem results.

# Code to Implement

You will need to implement merge sort sequentially and in parallel, but you will need to do both implementations recursively. The kernel method should call itself using recursion, but each public mergesort method should only call its kernel once to do the work.

 class: MergeSort.java methods: sequentialMergeSortsequentialMergeSortKernelparallelMergeSortparallelMergeSortKernel package: sort.studio.merge source folder: src/main/java

## Sequential Implementation

The only thing you will need to edit is the kernel method. As this is a sequential implementation, there is no need to call an async or finish. Using the description of merge sort provided to you in the background, try to consider what the base case would be. Then, further consider how to call the method recursively. When the array reaches the base case, you will need to complete the “merging” aspect of merge sort. As mentioned above, there is a method in the utils class that should help with this.

method: public static void sequentialMergeSort(int[] data, Combiner combiner) (sequential implementation only)

method: private static void sequentialMergeSortKernel(int[] data, int lowInclusive, int highExclusive, Combiner combiner) (sequential implementation only)

## Parallel Implementation

This approach should behave much like the sequential implementation, but it should also include async/finish calls. Think carefully about where to place them to maximize concurrency.

Test the length of the range with isParallelPredicate to determine if you should parallelize or fall back to sequential.

method: public static void parallelMergeSort(int[] data, IntPredicate isParallelPredicate, Combiner combiner) (parallel implementation required)

method: private static void parallelMergeSortKernel(int[] data, int lowInclusive, int highExclusive, IntPredicate isParallelPredicate, Combiner combiner) (parallel implementation required)

# (Optional) Challenge Parallel Combiner

You can divide and conquer the combine step in merge sort. The work should remain $\mathcal{O}(n\lg{}n)$ while the critical path length can be cleanly improved from $\mathcal{O}(n)$ down to $\mathcal{O}(\lg^3{}n)$.

For details on how to complete this challenge, check out: MergeSort_Parallel_Combiner

## Correctness

 class: MergeSortTestSuite.java package: sort.studio.merge source folder: src/test/java

## Performance

 class: SortTiming.java package: sort source folder: src/performance/java

Note: do not be concerned if your implementations run slower than Java's highly optimized Dual Pivot Quicksort.

# Pledge, Acknowledgments, Citations

 file: studio-merge-sort-pledge-acknowledgments-citations.txt