1. By Brian Ahmann, Jared Hoffman, and Andy Miller
Merge Sort
By Brian Ahmann, Jared Hoffman, and Andy Miller

2. Overview Merge sort is a fast, advanced sorting algorithm
Commonly implemented recursively (space issues)
Much faster than insertion sort or selection sort (usually)
Merge sort is stable: elements with the same value stay in their original order
A merge sort has time efficiency O(n logn) for nearly all initial conditions
The basic merge sort algorithm is easy to understand
…but it can be difficult to implement

3. The Big Idea
If a list has 0 or 1 element, then it is sorted. (Base Case)
To sort a larger list:
Break the list into two halves.
Sort each half. (Recursion)
Merge the sorted halves.

4. The recursion
merge_sort(list a) { if(length of a <= 1) a is sorted else { list left = left half of a list right = right half of a merge_sort(left) merge_sort(right) merge(left, right) }

5. Activity We need 4 volunteers
Come to the front of class to be merge sorted!
Put yourselves in a random order
We will sort you by LAST NAME
We are in control of the program, and will say when to move

6. Activity Come to the front of class to be merge sorted!
Now, we need 8 volunteers!
You will do the same thing
Come to the front of class to be merge sorted!
Put yourselves in a random order
We will sort you by LAST NAME
We are in control of the program, and will say when to move

7. Merging
By far the hardest part of the implementation of a merge sort algorithm is merging the two sorted sub-lists
Go through each sub-list, and the lower number at the “current index” of each sub- list is added to the main list.
LEFT RIGHT SORTED
[1, 2, 5] [3, 4, 6] [1, _, _, _, _, _]
[1, 2, 5] [3, 4, 6] [1, 2, _, _, _, _]
[1, 2, 5] [3, 4, 6] [1, 2, 3, _, _, _]
[1, 2, 5] [3, 4, 6] [1, 2, 3, 4, _, _]
[1, 2, 5] [3, 4, 6] [1, 2, 3, 4, 5, _]
[1, 2, 5] _ [3, 4, 6] [1, 2, 3, 4, 5, 6]

8. Merging
merge(list left, list right) { sorted = [] left_index, right_index = 0 //Current index in left and right list while(in range of left AND right) { get the current element from each list add the lower of the two to the sorted list increase the index of the list the low element came from } add any leftover elements to the sorted list return sorted

9. Parallelism and Merge sort

10. Sources http://www.stackoverflow.com
g/mergeSort.htm