Pfds Scala on LARGE DATA BANK

Exercises from PFDS Section 2.2

Tue, 04 Dec 2012 18:48:00 -0400

Section 2.2’s exercises define some optimizations to the section’s unbalanced tree set implementation.

Exercise 2.2

The implementation of member that Okasaki gives for binary search trees in section 2.2 performs 2d comparisons for a tree of depth d in the worst case, when searching for a number that is the farthest to the right on the tree, and when the right path in the tree is of depth d itself. This is because every call of member checks whether x < y and, if not, whether y < x. This strategy allows immediate detection of the case in which the value being searched for is contained in the current node, permitting short-circuit cases like where the searched-for value is in the root node, at the cost of requiring double the comparisons when traversing rightward.

PFDS Section 2.2

Tue, 01 May 2012 16:33:00 -0400

Section 2.2 presents immutable sets implemented with unbalanced binary search trees, a slightly more complex example of immutable data sharing than the list example in Section 2.1. My first challenge was to reimplement Okasaki’s base implementation of unbalanced binary search tree sets using idiomatic Scala. I had to learn a fair amount more about Scala’s type system to be able to write such an implementation, so I figured I’d write up some of the things I learned about Scala in the process as well as the implementation.

Abstract Generic Collections: PFDS Section 2.1 Redux

Tue, 31 Jan 2012 00:34:00 -0400

At the end of my last post, I mentioned that I ended up reusing Scala’s build-in List collection to implement the exercises instead of writing a generic abstract Stack and sample implementations of those. Since then, I’ve spent some time learning about how to implement generic collections in Scala. I came up with a Stack trait, a la Okasaki’s Stack signature, and three implementations: the first two are straightforward translations of the SML structures given in the book, and the third is a more Scala-idiomatic implementation.

PFDS Section 2.1

Fri, 27 Jan 2012 22:09:00 -0400

This is the inaugural post of the PFDS series.

Section 2.1 discusses the ramifications of implementing lists and stacks in a functional and immutable manner. Using the operation of list catenation as a motivator, Okasaki introduces the idea of data sharing. We see that to catenate two lists, we can share the second list, which doesn’t get modified, but must copy all of the nodes in the first list just to modify the last one.

Notes on Purely Functional Data Structures

Tue, 03 Jan 2012 01:24:00 -0400

I heard a lot of good things about Mike Okasaki’s Purely Functional Data Structures at UChicago, but didn’t ever take the time to check it out. Lately I’ve missed the heady joy of reading and writing code in a strongly typed functional programming language like Standard ML, so when one of my coworkers at Knewton mentioned he was going to read the book I decided to get a copy for myself.