# CS 371: Module 15: Exercise 1 (2 Points)

Developed by Professor Tralie and Professor Mongan.

# Exercise Goals

The goals of this exercise are:- Implement merge sort
- Implement a divide and conquer algorithm

Finish the code below to complete merge sort.

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### Merge

def swap(arr, i, j):
temp = arr[i]
arr[i] = arr[j]
arr[j] = temp
def merge(x, y, i1, mid, i2):
"""
Perform a merge of two contiguous sorted sub-chunks of
the array x, using y as a staging area
Parameters
----------
x: list
The main array
y: list
The array to copy into as the two chunks are being merged
i1: int
Left of first chunk
mid: int
Right of first chunk
i2: int
End of second chunk
"""
i = i1
j = mid+1
idx = 0
while i != mid+1 and j != i2+1:
if x[i] < x[j]:
y[idx] = x[i]
i += 1
else:
y[idx] = x[j]
j += 1
idx += 1
## TODO: Copy over any elements that are left in
## the first chunk
## TODO: Copy over any elements that are left in
## the second chunk
# Copy our merged sorted chunk from the staging area
# back into the chunk from i1 to i2
for idx in range(i2-i1+1):
x[i1+idx] = y[idx]
def mergesort_rec(x, y, i1, i2):
"""
A recursive call to sort a subset of the array
Parameters
----------
x: list
Array to sort
y: list
A temporary array / staging area to store intermediate results
i1: int
First index of chunk to sort, inclusive
i2: int
Second index of chunk to sort, inclusive (i2 >= i1)
"""
if (i1 == i2):
# Base case: A single number
return
elif (i2 - i1 == 1):
# Base case: A pair of numbers right next to each other
if (x[i2] < x[i1]):
swap(x, i1, i2)
else:
# More than two; need to "divide and conquer"
mid = (i1 + i2)//2
mergesort_rec(x, y, i1, mid)
mergesort_rec(x, y, mid+1, i2)
merge(x, y, i1, mid, i2)
def mergesort(x):
"""
An entry point for merge sort on the entire array
Parameters
----------
x: list
Array to sort
"""
y = [0]*len(x)
mergesort_rec(x, y, 0, len(x)-1)

### Test Code Block

arr = [51, 21, 66, 69, 56, 13, 44, 6]
mergesort(arr)
print(arr, end='.')
arr = [23, 1, 15, 24, 47, 29]
mergesort(arr)
print(arr)