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Held: Monday, 23 November 2009
We explore the problem of sorting. When you sort a list, vector,
or other collection, you put the elements in order. The order of the
elements usually corresponds to the type of the elements. We might
sort strings alphabetically, grades numerically, colors by brightness,
and so on and so forth.
- The problem of sorting.
- Writing sorting algorithms.
- Examples: Insertion, selection, etc.
- Formalizing the problem.
- 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.
- 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.
- 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 is among the simpler and more natural methods for
- 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
- Here's a potentially-helpful picture:
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- Note that we can also write selection sort iteratively.
- 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
- 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.