CPSC 170 A

Lecture 22 - Recursive Sorting

As usual, create a directory to hold today's activities:

$ mkdir ~/cs170/labs/lab22 
$ cd ~/cs170/labs/lab22

Divide and Conquer, or Sorting with Recursion

There's one sorting question I tend to hear a lot: "Is there a binary sort?" Well, the idea behind binary search finds its way into two different algorithms. These are Merge Sort and Quick Sort. They both approach the problem the same way as all of our other recursive functions: Break the problem into smaller portions, and build the overall solution from those smaller pieces.

Lab Activity 1

Merge Sort

Merge sort is probably the closest to a "binary" sort as you will get. Merge sort simply splits the list into two halves, and recursively calls Merge sort on both halves. Onces it gets the two sorted halves, it simply merges the two together to form a sorted list.

Details

Create a function called void mergeSort(int * aList, int start, int end), which takes a list of integers, as well as two integers representing the beginning and end of the portion of the list to be sorted. The end value is exclusive. This function should not return anything, it should sort aList in place. They discussed this modification of the algorithm in the reading.

Example

int SIZE = 5;
int * myList = new int[SIZE];
for(int i = 0; i < SIZE; i++) {
     myList[i] = SIZE - i;
}
mergeSort(myList, 0, SIZE);

printList(myList); // [1, 2, 3, 4, 5]

Hint

Your base case for merge sort is when the number of elements in the current portion of the list is exactly one. A list of one element is sorted. A list of exactly one item is a list where the start is one less than the end.
The book wrote the entirety of merge sort in one function. As I showed you today in lecture, it is easier to understand merge sort if you write one helper function. You should write a function called merge(int * aList, int start, int end). This function takes a list of integers, and two integers start and end. It does not return anything: It sorts the items in place in a_list

You will use start and end to denote the two halves of the list. The middle index of the list denotes the beginning of the second half of the list. All you need to do is to compare the elements at the beginning of each half of the list. If they are out of order, swap them and move on to the next elements. The easiest way to accomplish this is to make a copy of the left and right halves of this list, and place the correct values back into the original list.

One thing you need to be careful about in the merge procedure is that you could easily run out of items in one list before the other. You need to make sure you gracefully handle this situation.
Your mergeSort function should recursively call mergeSort on each half of the list, then merge the two halves together.

Challenge

The version of merge sort described in the reading and in class today creates two arrays in merge. One to hold the left half, and one to hold the right half. This is easier to reason about what is going on, but does waste space to accomplish.