1. :
PROC SORT: C O O P R R S T
Jayson Shurgold, Health Canada
Ottawa Area SAS Users Society
November 17th |

2. Disclaimer
The views expressed in this presentation are the personal views of the presenting staff and do not necessarily represent the views of Health Canada or the Government of Canada. The presentation is provided for general information purposes intended only as an academic resource and does not constitute professional advice. Information has been summarized and paraphrased for presentation purposes and the examples are theoretical and have been provided for illustration purposes only.

3. About me: B.Sc in Health Sciences at Brock University (2007)
Civil Service since (PHAC ; HC 2016)
Vacationed in Vancouver between 2012 and 2015
Father of two boys, aged two and 5 months
Interests
Bass guitar
Boxing
Whiskey
Sleep

4. Introduction to Sorting
Sorting – systematic arrangement of things – is something common to us all
Natural Sort Orders – Numbers, Alphabet (simple – one class)
Logic Sort Order – Cards (more complex – multiple class)
Learned Sort Order – Social Hierarchies (most complex?)
A process often taken for granted.

5. Introduction to Sorting
Dewey Decimal Classification (DDC)
- A classification system published by Melvil Dewey in 1876
- The order in which books are sorted onto shelves
Exercise 1 : Arrange the books in the correct DDC order.
1.1
1.2
1.3
1.5
1.4

6. Introduction to Sorting
Dewey Decimal Classification (DDC)
- A classification system published by Melvil Dewey in 1876
- The order in which books are sorted onto shelves
Exercise 1 : Arrange the books in the correct DDC order.
1.1
1.2
1.3
1.5
1.4
1.1
1.2
1.3
1.4
1.5

7. Introduction to Sorting
Dewey Decimal Classification (DDC)
- A classification system published by Melvil Dewey in 1876
- The order in which books are sorted onto shelves
Exercise 1 : Arrange the books in the correct DDC order.
1.1
1.2
1.3
1.5
1.4
1.1
1.2
1.3
1.4
1.5

8. The Insertion Sort
A simple procedure that constructs an array one item at a time
Intuitive in small numbers, but inefficient in large numbers
1.1
1.2
1.3
1.5
1.4
Starting Positions
Core Logic
Ending Positions
1.1
1.2
1.3
1.4
1.5

9. The Insertion Sort
A simple procedure that constructs an array one item at a time
Intuitive in small numbers, but inefficient in large numbers
Starting Positions
Core Logic
Ending Positions
1.4
1.1
1.2
1.3
1.5
Compare reference against value
Swap reference with value if reference < value
Iterate n times
1.1
1.2
1.3
1.4
1.5

10. Automated Machine Sorting
1880 US Census – Handwritten Reports
Resident population of 50,189,209
Data processing of 8 years by hand
1890 US Census – Punch Cards / Tabulating Machine
Resident population of 62,947,714
Data processing of 6 years
The company responsible for these machines grew to become IBM

11. Automated Machine Sorting
The tabulating machine sorted by constructing an array by least significant digit, and repeating the process to most significant digit. This methodology is called a Radix Sort. 45
802
170
090
045
Core Logic
Iteration 1 90
1. Group keys based on least significant digit
2. Repeat for next least significant digit
Iteration 2
Iteration 3
Starting Order

12. Automated Machine Sorting
The tabulating machine sorted by constructing an array by least significant digit, and repeating the process to most significant digit. This methodology is called a Radix Sort. 45
802
170
090
045
Core Logic
Starting Order
Iteration 1 90
1. Group keys based on least significant digit
2. Repeat for next least significant digit
Iteration 2
Iteration 3
0 | 0 | 2 | 5
0 | 4 | 7 | 9
0 | 0 | 1 | 8

13. Automated Computer Sorting
First Place: Electronic Discrete Variable Computer (EDVAC)
Initialized in 1946
Based on a decimal system
Second Place: Electronic Numerical Integrator and Computer (ENIAC)
Initialized in 1949
Based on binary
EDVAC
ENIAC
John von Neumann

14. Automated Computer Sorting
John von Neumann: Merge-Sort Algorithm
Core Logic
1. Divide unsorted list into sub-lists
2. Sort sub-lists
3. Merge sorted sub-lists into master sub-list
Starting Order
Iteration 1
Iteration 2
Iteration 3
Iteration 4
Iteration 5
Iteration 6

15. Sorting Logic – What does it look like?
Example 1: Insertion Sort

16. Sorting Logic – What does it look like?
Example 2: Radix Sort

17. Sorting Logic – What does it look like?
Example 3: Merge Sort

19. Sorting Data in SAS Value 5 6 3 4 7 2 1
Exercise 2: Considering the following data, recommend a methodology compatible with SAS that could achieve an ascending sorted list?
Your Data
Value 5 6 3 4 7 2 1

20. Sorting Data in SAS Value 5 6 3 4 7 2 1
Exercise 2: Considering the following data, how would you manipulate the data to achieve an ascending sorted list?
Your Data
Answer 1
Value 5 6 3 4 7 2 1

21. Sorting Data in SAS Value 5 6 3 4 7 2 1
Exercise 2: Considering the following data, how would you manipulate the data to achieve an ascending sorted list?
Your Data
Answer 1
Answer 2
Value 5 6 3 4 7 2 1

22. How to use Proc Sort - Simple
SAS Code
Description
Specify the Library and Dataset Name
Specify the Variable to sort the Dataset by
Input Dataset: Library.Data
Result: Library.Data
Variable
Result 3 P . NA 1 F 2
Variable
Result . NA 1 F 2 P 3

23. How to use Proc Sort – Less Simple
SAS Code
Description
Output results to a new dataset
Only write variables a, x, and z to output dataset, and rename x to y
Output only one observation per by variable combination
Sort ascending by variable z, then sub-sort descending by variable a
Only consider observations where variable z is not missing
Input Dataset: Lib.Old
Output Dataset: Lib.New z b a x 3 T F
0.9 . M
1.1 1
5.9
4.6 2
3.9
2.2 z a y 1 M
2.2 F
5.9 2
3.9 3
0.9

24. Proc Sort- What’s Actually Happening?
Proc Sort is a powerful and commonly used tool, but not many people know exactly what’s going on behind the scenes.
My Question:
What is the specific algorithm used by SAS to sort data?
Looking back:
Example 1: Insertion Sort
Example 2: Radix Sort
Example 3: Merge Sort
Internet theories:
Proprietary Software – Unpublished
Multiple sorting algorithms depending on complexity and resources
Magic, especially since version 9
Very different approaches
Different strengths and weaknesses

25. Proc Sort- What’s Actually Happening?
Proc Sort is a powerful and commonly used tool, but not many people know exactly what’s going on behind the scenes. My Question: What is the specific algorithm used by SAS to sort data?

26. What is Heap Sort?
Invented in 1964, Heap Sort is a two step process:
Create the Heap
Arrange data into a binary tree formation
Compare daughters against parents
Swap parent with daughter if daughter is higher (recursive)
Sort the Heap
Swap the highest order of the heap with the lowest order of the heap
Remove the highest order from the heap
Update heap | Swap parent with daughter if daughter is higher (recursive)

27. Heap Sort – Visualized

28. Questions?

29. References