1. Fundamentals of Programming II Bucket Sort: An O(N) Sort Algorithm
Computer Science 112
Fundamentals of Programming II
Bucket Sort: An O(N) Sort Algorithm

2. N2 and Nlog2N Sort Algorithms
Selection sort and bubble sort are O(N2), because they run nested loops over the entire list
Quicksort and heap sort are O(Nlog2N), because one executes a linear process log2N times and the other executes a log2N process N times

3. An O(N) Sort Algorithm
Consider a sorted list of unique integers, ranging from 0 to N - 1: 1 2 3 4

4. An O(N) Sort Algorithm
Consider a sorted list of unique integers, ranging from 0 to N - 1: 1 2 3 4
Shuffle the list to randomize the numbers: 2 1 4 3

5. An O(N) Sort Algorithm
Consider a sorted list of unique integers, ranging from 0 to N - 1: 1 2 3 4
Shuffle the list to randomize the numbers: 2 1 4 3
How can we sort this randomly ordered list in linear time?

6. An O(N) Sort Algorithm Create a temporary array of length N: 0 1 2 3 4 2 1 4 3
How can we sort this randomly ordered list in linear time?

7. An O(N) Sort Algorithm For each integer in the unsorted list:
Copy the integer to the array at that position 2 2 1 4 3
How can we sort this randomly ordered list in linear time?

8. An O(N) Sort Algorithm For each integer in the unsorted list:
Copy the integer to the array at that position 1 2 2 1 4 3
How can we sort this randomly ordered list in linear time?

9. An O(N) Sort Algorithm For each integer in the unsorted list:
Copy the integer to the array at that position 1 2 2 1 4 3
How can we sort this randomly ordered list in linear time?

10. An O(N) Sort Algorithm For each integer in the unsorted list:
Copy the integer to the array at that position 1 2 4 2 1 4 3
How can we sort this randomly ordered list in linear time?

11. An O(N) Sort Algorithm For each integer in the unsorted list:
Copy the integer to the array at that position 1 2 3 4 2 1 4 3
How can we sort this randomly ordered list in linear time?

12. An O(N) Sort Algorithm For each integer in the unsorted list:
Copy the integer to the array at that position
Copy ‘em back to the list 1 2 3 4 1 2 3 4
How can we sort this randomly ordered list in linear time?

13. Complexity Analysis For each integer in the unsorted list:
Copy the integer to the array at that position
Copy ‘em back to the list
No comparisons!
2 * N assignments
O(N) memory 1 2 3 4 1 2 3 4
How can we sort this randomly ordered list in linear time?

14. Lists with Duplicate Items
Create a temporary array of linked lists of length K, for the integers in the list ranging from 0 to K - 1:
Each linked list will serve as a bucket to receive items from the original list 2 1 4 3 1 1

15. Lists with Duplicate Items
Copy items from the original list to the corresponding buckets in the array 1 2 3 4 1 1 2 1 4 3 1 1

16. Lists with Duplicate Items
Copy ‘em back to the original list
No comparisons!
2 * N assignments
O(N + K) memory 1 2 3 4 1 1 1 1 1 2 3 4

17. Generalize to a Keyed List
Each item in the list must have an integer key
The keys can be repeated, but must be integers from 0 through a positive upper bound
The keys can be stored with the items, or computed as needed

18. Bucket Sort of a Keyed List
from arrays import Array
from node import Node
def bucketSort(keyedList):
# Create an array to accommodate the keys
array = Array(keyedList.getMaxKey())
# Copy items from the list to the buckets
for item in keyedList:
key = item.getKey()
array[key] = Node(item, array[key])
# Copy items from buckets back to the list
index = 0
for node in array:
while node != None:
keyedList[index] = node.data
node = node.next
index += 1
Computer Science 112

19. Some Buckets Can Be Empty 1 3 4 1 3 1 3 1 4 3 1 1

20. Hashing and O(k) Sets and Dictionaries
For Wednesday
Hashing and O(k) Sets and Dictionaries