Practice running the visualizations to better understand how mostly sorted versus completely random arrays complete at different times for Bubble sort, Insertion sort, and Merge sort: http://www.sorting-algorithms.com/
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What do you notice?
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Which algorithm(s) benefit from arrays that are mostly sorted?
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Which algorithm(s) stay largely consistent?
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Why do you think this is?
Read through and practice running each algorithm in the python Jupyter notebook.
You can do this in two ways:
- You can download the python Jupyter notebook in this repo.
(For help getting started with Jupyter notebooks: https://jupyter-notebook-beginner-guide.readthedocs.io/en/latest/execute.html)
- Run the notebook on Google Colab:
https://colab.research.google.com/drive/1GjOWEjiI96PldK3lO3QhbCVPLmDw_h5c?usp=sharing
def bubble_sort(array):
n = len(array)
for i in range(n):
# Create a flag that will allow the function to
# terminate early if there's nothing left to sort
already_sorted = True
# Start looking at each item of the list one by one,
# comparing it with its adjacent value. With each
# iteration, the portion of the array that you look at
# shrinks because the remaining items have already been
# sorted.
for j in range(n - i - 1):
if array[j] > array[j + 1]:
# If the item you're looking at is greater than its
# adjacent value, then swap them
array[j], array[j + 1] = array[j + 1], array[j]
# Since you had to swap two elements,
# set the `already_sorted` flag to `False` so the
# algorithm doesn't finish prematurely
already_sorted = False
# If there were no swaps during the last iteration,
# the array is already sorted, and you can terminate
if already_sorted:
break
return array
def insertion_sort(array):
# Loop from the second element of the array until
# the last element
for i in range(1, len(array)):
# This is the element we want to position in its
# correct place
key_item = array[i]
# Initialize the variable that will be used to
# find the correct position of the element referenced
# by `key_item`
j = i - 1
# Run through the list of items (the left
# portion of the array) and find the correct position
# of the element referenced by `key_item`. Do this only
# if `key_item` is smaller than its adjacent values.
while j >= 0 and array[j] > key_item:
# Shift the value one position to the left
# and reposition j to point to the next element
# (from right to left)
array[j + 1] = array[j]
j -= 1
# When you finish shifting the elements, you can position
# `key_item` in its correct location
array[j + 1] = key_item
return array
- Recursively splits the input in half
- A function that merges both halves, producing a sorted array
def merge(left, right):
# If the first array is empty, then nothing needs
# to be merged, and you can return the second array as the result
if len(left) == 0:
return right
# If the second array is empty, then nothing needs
# to be merged, and you can return the first array as the result
if len(right) == 0:
return left
result = []
index_left = index_right = 0
# Now go through both arrays until all the elements
# make it into the resultant array
while len(result) < len(left) + len(right):
# The elements need to be sorted to add them to the
# resultant array, so you need to decide whether to get
# the next element from the first or the second array
if left[index_left] <= right[index_right]:
result.append(left[index_left])
index_left += 1
else:
result.append(right[index_right])
index_right += 1
# If you reach the end of either array, then you can
# add the remaining elements from the other array to
# the result and break the loop
if index_right == len(right):
result += left[index_left:]
break
if index_left == len(left):
result += right[index_right:]
break
return result
def merge_sort(array):
# If the input array contains fewer than two elements,
# then return it as the result of the function
if len(array) < 2:
return array
midpoint = len(array) // 2
# Sort the array by recursively splitting the input
# into two equal halves, sorting each half and merging them
# together into the final result
return merge(
left=merge_sort(array[:midpoint]),
right=merge_sort(array[midpoint:]))