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Finger Trees

Finger trees are a versatile family of fully persistent collections. This library includes everything you need to make your own, as well a few ready-to-use collection types:

  • double-list is a sequential collection that provides constant-time access to both the left and right ends.

  • counted-double-list provides all the features of double-list plus constant-time count and log-n nth.

  • counted-sorted-set is sorted set that also provides log-n nth

There are examples of all these later in the README.

Finger Tree Quickstart

CLI/deps.edn dependency information:

org.clojure/data.finger-tree {:mvn/version "0.1.0"}

project.clj

If you use leiningen or cake, add this to the :dependencies in your project.clj:

[org.clojure/data.finger-tree "0.1.0"]

pom.xml

If you use maven, add this to the <dependencies> in your pom.xml:

<dependency>
  <groupId>org.clojure</groupId>
  <artifactId>data.finger-tree</artifactId>
  <version>0.1.0</version>
</dependency>

You'll need git and maven, then execute the following at a shell prompt to fetch finger trees and all its dependencies (including a recent snapshot of Clojure itself) and start a REPL:

use/require

Regardless of how you fetch the dependency, to use a finger-tree function in your project you'll need to add something like this to your ns declaration:

(:use [clojure.data.finger-tree :only [double-list]])

Talk

Thanks to heroku for hosting the slides for my Clojure Conj talk about this library. The rather raw sources and enormous PDF of the slides are at github.

Examples

The finger-tree lib actually includes several collections built on top of Ralf Hinze and Ross Paterson's finger trees. Here are some examples of each of them:

double-list

The double-list is a sequential collection that provides constant-time access to both the left and right ends:

(def dl (double-list 4 5 6 7))

dl
;=> (4 5 6 7)

[(first dl) (rest dl)]
;=> [4 (5 6 7)]

(conjl dl 'x)
;=> (x 4 5 6 7)

[(pop dl) (peek dl)]
;=> [(4 5 6) 7]

(conj dl 'x)
;=> (4 5 6 7 x)

counted-double-list

This provides all the features of double-list plus constant-time count and log-n nth:

(def cdl
  (apply counted-double-list '[a b c d e f g h i j k l m]))

(nth cdl 5)
;=> f

(assoc cdl 5 'XX)
;=> (a b c d e XX g h i j k l m)

(def parts
  (let [[left _ right] (ft-split-at cdl 5)]
    {:left left, :right right}))

parts
;=> {:left (a b c d e), :right (g h i j k l m)}

(ft-concat (conj (:left parts) 'XX) (:right parts))
;=> (a b c d e XX g h i j k l m)

(ft-concat (:left parts) (:right parts))
;=> (a b c d e g h i j k l m)
;             ^-- missing f

(ft-concat (into (:left parts) '[X Y Z]) (:right parts))
;=> (a b c d e X Y Z g h i j k l m)

counted-sorted-set

This is like counted-double-list, but does not support conjl. Instead, conj is used to insert items in sorted order.

(def css (apply counted-sorted-set
                '[m j i e d a f k b c f g h l]))
css
;=> (a b c d e f g h i j k l m)

(get css 'e)      ; O(log(n))
;=> e

(get css 'ee)     ; O(log(n))
;=> nil

(count css)       ; O(1)
;=> 13

(nth css 5)       ; O(log(n))
;=> f

Build-your-own finger tree

(def empty-cost-tree (finger-tree (meter :cost 0 +)))

(def ct (conj empty-cost-tree
              {:id :h, :cost 5} {:id :i, :cost 1}
              {:id :j, :cost 2} {:id :k, :cost 3}
              {:id :l, :cost 4}))

(measured ct)
;=> 15

(next (split-tree ct #(> % 7)))
;=> ({:cost 2, :id :j}
     ({:cost 3, :id :k} {:cost 4, :id :l}))

(next (split-tree (rest ct) #(> % 7)))
;=> ({:cost 4, :id :l} ())