5 Skip Lists

Version: 5.1

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5 Skip Lists

Ryan Culpepper <ryanc@racket-lang.org>

(require data/skip-list)

Skip lists are a simple, efficient data structure for mutable dictionaries with totally ordered keys. They were described in the paper “Skip Lists: A Probabilistic Alternative to Balanced Trees” by William Pugh in Communications of the ACM, June 1990, 33(6) pp668-676.

A skip-list is an ordered dictionary (dict? and ordered-dict?). It also supports extensions of the dictionary interface for iterator-based search and mutation.

(make-skip-list	[	ord
		#:key-contract key-contract
		#:value-contract value-contract])		→		skip-list?

ord : order? = datum-order

key-contract : contract? = any/c

value-contract : contract? = any/c

Makes a new empty skip-list. The skip-list uses ord to order keys; in addition, the domain contract of ord is combined with key-contract to check keys.

Examples:
  > (define skip-list (make-skip-list real-order))
  > (skip-list-set! skip-list 3 'apple)
  > (skip-list-set! skip-list 6 'cherry)
  > (dict-map skip-list list)
  '((3 apple) (6 cherry))
  > (skip-list-ref skip-list 3)
  'apple
  > (skip-list-remove! skip-list 6)
  > (skip-list-count skip-list)
  1

(make-adjustable-skip-list	[	#:key-contract key-contract
		#:value-contract value-contract])

→ adjustable-skip-list?

key-contract : contract? = any/c

value-contract : contract? = any/c

Makes a new empty skip-list that permits only exact integers as keys (in addition to any constraints imposed by key-contract). The resulting skip-list answers true to adjustable-skip-list? and supports key adjustment.

(skip-list? v) → boolean?

v : any/c

Returns #t if v is a skip-list, #f otherwise.

(adjustable-skip-list? v) → boolean?

v : any/c

Returns #t if v is a skip-list that supports key adjustment; see skip-list-contract! and skip-list-expand!.

(skip-list-ref skip-list key [default]) → any/c

skip-list : skip-list?

key : any/c

default : any/c = (lambda () (error ....))

(skip-list-set! skip-list key value) → void?

skip-list : skip-list?

key : any/c

value : any/c

(skip-list-remove! skip-list key) → void?

skip-list : skip-list?

key : any/c

(skip-list-count skip-list) → exact-nonnegative-integer?

skip-list : skip-list?

(skip-list-iterate-first skip-list) → (or/c skip-list-iter? #f)

skip-list : skip-list?

(skip-list-iterate-next skip-list iter)

→ (or/c skip-list-iter? #f)

skip-list : skip-list?

iter : skip-list-iter?

(skip-list-iterate-key skip-list iter) → any/c

skip-list : skip-list?

iter : skip-list-iter?

(skip-list-iterate-value skip-list iter) → any/c

skip-list : skip-list?

iter : skip-list-iter?

Implementations of dict-ref, dict-set!, dict-remove!, dict-count, dict-iterate-first, dict-iterate-next, dict-iterate-key, and dict-iterate-value, respectively.

(skip-list-remove-range! skip-list from to) → void?

skip-list : skip-list?

from : any/c

to : any/c

Removes all keys in [from, to); that is, all keys greater than or equal to from and less than to.

(skip-list-contract! skip-list from to) → void?

skip-list : adjustable-skip-list?

from : exact-integer?

to : exact-integer?

Like skip-list-remove-range!, but also decreases the value of all keys greater than or equal to to by (- to from).

This operation takes time proportional to the number of elements with keys greater than or equal to to.

(skip-list-expand! skip-list from to) → void?

skip-list : adjustable-skip-list?

from : exact-integer?

to : exact-integer?

Increases the value of all keys greater than or equal to from by (- to from).

This operation takes time proportional to the number of elements with keys greater than or equal to from.

(skip-list-iterate-least/>? skip-list key)

→ (or/c skip-list-iter? #f)

skip-list : skip-list?

key : any/c

(skip-list-iterate-least/>=? skip-list key)

→ (or/c skip-list-iter? #f)

skip-list : skip-list?

key : any/c

(skip-list-iterate-greatest/<?		skip-list
		key)

→ (or/c skip-list-iter? #f)

skip-list : skip-list?

key : any/c

(skip-list-iterate-greatest/<=?		skip-list
		key)

→ (or/c skip-list-iter? #f)

skip-list : skip-list?

key : any/c

Implementations of dict-iterate-least, dict-iterate-greatest, dict-iterate-least/>?, dict-iterate-least/>=?, dict-iterate-greatest/<?, and dict-iterate-greatest/<=?, respectively.

(skip-list-iter? v) → boolean?

v : any/c

Returns #t if v represents a position in a skip-list, #f otherwise.

(skip-list->list skip-list) → (listof pair?)

skip-list : skip-list?

Returns an association list with the keys and values of skip-list, in order.

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