The goal of this project is reinforce the work on sorting arrays by implementing the quicksort algorithm.
Recall the difference between insertion and selection sorts. Although they share the same basic pattern (repeatedly move an element from the unsorted section to the sorted section), we have
Insertion
Selection
Now, consider the basic pattern of merge sort:
More specifically, merge sort splits the array simplistically (it's the "easy" part). The reuniting is complicated. What if there were a sorting algorithm that had the same basic pattern as merge sort, but stood in analogy to merge sort as selection stands towards insertion? In other words, could there be a recursive, divide-and-conquer, sorting algorithm for which the splitting is the hard part, but leaves an easy or trivial reuniting at the end?
To design such an algorithm, let's take another look at what merge sort does. Since the splitting is trivial, the interesting parts are the recursive sorting and the reuniting. The recursive call sorts the subarrays internally, that is, each subarray is turned into a sorted subarray. The reuniting sorts the subarrays with respect to each other, that is, it moves elements between subarrays, so the entire range is sorted.
To rephrase our earlier question, the analogue to mergesort would be an algorithm that sorts the subarrays with respect to each other before sorting each subarray. Then reuniting them is trivial. The algorithm is called "quicksort," and as its name suggests, it is a very good sorting algorithm.
Here's a big picture view of it. Suppose we have an array, as pictured below. We pick one element, x, and delegate it as the "pivot." In many formulations of array-based quicksort, the last element is used as the pivot (though it doesn't need to be the last).
Then we separate the other elements based on whether they are greater than or less than the pivot, placing the pivot in the middle.
In a closer look, while we do this partitioning of the array, we maintain three portions of the array: the (processed) elements that are less than the pivot, the (processed) elements that are greater than the pivot, and the unprocessed elements. (In a way, the pivot itself constitutes a fourth portion.) The indices i and j mark the boundaries between portions: i is the last position of the portion less than the pivot and j is the first position in the unprocessed portion. Initially, the "less than" and "greater than" portions are empty.
During each step in the partitioning, the element at position j is examined. It is either brought into the "greater than" portion (simply by incrementing j) or brought into the "less than" portion (by doing a swap and incrementing both i and j).
(Think about that very carefully; it's the core and most difficult part of this project.)
At the end, the unprocessed portion is empty.
All that's left is to move the pivot in between the two portions, using a swap. We're then set to do the recursive calls on each portion.
Make a directory for this class (if you haven't already). Make a new directory for this project. Then copy into it some starter code, which will be similar to the code you started with in lab.
cd 245 mkdir proj1 cd proj1 cp /homes/tvandrun/Public/cs245/proj1/* .
Notice there are two functions with quickSort
in their name.
The second function corresponds to the
prototype for quick sort found in sorts.h
and used in the driver sDriver.c
It is finished.
It starts the recursive process by calling
quickSortR(), which is the one you need to finish.
Notice that quickSortR() takes not only
an array but also a starting point and a stopping
point in the array.
It is only sorting a given range in the array.
Both functions return an int to be consistent with the
other functions, all of which return the number
of comparisons.
As we will be talking about in class while you work on this project, merge sort and quick sort are in different "complexity classes" in terms of the their worst case performance. Merge sort is O(n lg n), whereas quicksort is O(n^2). (O(n lg n) is faster). However, these are worst cases; we might find that experimentally one of the algorithms may behave better on average.
Write a program or programs to automate experiments to compare the running time and number of comparisons for quicksort, mergesort, shell sort, and one of the other sorts (selection, insertion, or one of the bubbles)
This time, instead of counting comparisons,
we'll take actual time measurements.
arrayUtil has a function getTimeMillis().
It returns the number of milliseconds that have elapsed since
midnight, Jan 1, 1970---the standard way to do time keeping on
many computer platforms.
By calling this function before and after sorting and taking the
difference, we can compute how long it takes to sort.
Use several different arrays of several sizes, and compare the results for the different algorithms.
Write a few paragraphs explaining how you did your experiment and what your findings are. Present your data using a table and one or more graphs.
Print out the files you wrote.
The command to print files neatly, two to a page, is a2ps.
The flag --file-align=fill tells it not to start each file on
a new page, so less paper is wasted.
For example, to print the files sort.c and
experiment.c, use
a2ps --file-align=fill sort.c experiment.c
DUE: Monday, Jan 31, 5:00 pm.