Learning Goals
==============
* Understand recursion
* Use transitivity to reduce redundant computation
* Sort numbers using the merge sort algorithm
Merge Sort
==========
Merge Sort is a Divide and Conquer algorithm. You can read more about [the algorithm](https://medium.com/basecs/making-sense-of-merge-sort-part-1-49649a143478).
The function has three phases:
* If the input array has only one or no element, it is already sorted
and do nothing. This is the terminating condition.
* If the input array has two or more elements, divide the array into two non-overlapping arrays and these two arrays include all elements in the input array. Send the two arrays to the sort function.
* After the two arrays are individually sorted, merge them into one
array. Here, *transitivity* is used. Consider the two arrays [x1, x2,
..., xn] and [y1, y2, ..., ym]. Each array is already sorted: x1 <=
x2 <= ... <= xn and y1 <= y2 <= ... <= ym. If x1 < y1, then x1 < y2,
x1 < y3 ... It is unnecessary to compare x1 with y2, or y3, ...,
ym. Transitivity is important avoiding unnecessary comparisons.
WARNINGS
========
Be very very careful about the indexes. Read your programs very
carefully to ensure that you programs do not miss any element or have
an index beyond an array's size. Create a lot of test cases to help
you catch different scenarios.
WHAT TO SUBMIT
==============
```
zip hw09.zip main.c hw09.c
```
Upload `hw09.zip`.
