# Class 44: Introduction to Sorting

Back to Binary Search. On to Insertion Sort.

This outline is also available in PDF.

Held: Friday, April 20, 2007

Summary: Today we visit the problem of sorting. When you sort a list or vector, you put the elements in order (e.g., alphabetical, numerical, ...).

Related Pages:

Due

Notes:

• I have been asked to meet with some visitors to campus today, so I will not be available in class or during office hours. I apologize.

Overview:

• The problem of sorting, revisited.
• Writing sorting algorithms.
• Examples: Insertion, Selection, etc.
• Formalizing the problem.

## The Problem of Sorting

• As we saw recently, one problem that seems to crop up a lot in programmming (and elsewhere) is that of sorting.
• The problem: Given a list, array, vector, sequence, or file of comparable elements, put the elements in order.
• In order typically means that each element is no bigger than the next element. (You can also sort in decreasing order, in which case each element is no smaller than the next element.)
• We'll look at techniques for sorting vectors and lists.

## Designing Sorting Algorithms

• I suggest that you think about the development of sorting algorithms in Scheme similarly to the way you think about writing many algorithms.
• Start by thinking about the way you might do it by hand.
• We may find a few different ways to sort by hand.
• We'll probably leave the Scheme-ification to the end.
• Generalize what you're doing.
• What is the philosophy of your techinque?
• What are the key steps.
• Come up with some initial test cases.
• Consider whether there are any deficiences to your technique.
• Decide on your parameters (e.g., are you sorting a list or a vector).
• Translate your algorithm into Scheme.
• Test test test.

## Sample Sorting Algorithms

### Insertion Sort

• One simple sorting technique is insertion sort.
• Insertion sort operates by segmenting the list into unsorted and sorted portions, and repeatedly removing the first element from the unsorted portion and inserting it into the correct place in the sorted portion.
• This may be likened to the way typical card players sort their hands.
• How might we code this recursively?
• Does our code differ for lists and arrays?

### Selection Sort

• Selection sort is among the simpler and more natural methods for sorting vectors.
• In this sorting algorithm, you segment the vector into two subparts, a sorted part and an unsorted part. You repeatedly find the largest of the unsorted elements, and swap it into the beginning of the sorted part. This swapping continues until there are no unsorted elements.
```+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
|
Unsorted           Sorted
```
• Note that we can also write selection sort iteratively.

## A More Formal Description

• Before moving on to algorithms for solving the sorting problem, let's take a look at the way we might document one (or all) of the procedures
• Purpose?
• Parameters?
• Produces?
• Preconditions?
• Postconditions?
• Here are some postconditions I typically think about:
• You also need to ensure that all elements in the original list are in the sorted list.
• You also need to ensure that no other elements are in the list.

Back to Binary Search. On to Insertion Sort.

Disclaimer: I usually create these pages on the fly, which means that I rarely proofread them and they may contain bad grammar and incorrect details. It also means that I tend to update them regularly (see the history for more details). Feel free to contact me with any suggestions for changes.

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Samuel A. Rebelsky, rebelsky@grinnell.edu

Copyright © 2007 Samuel A. Rebelsky. This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License. To view a copy of this license, visit `http://creativecommons.org/licenses/by-nc/2.5/` or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA.