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make-splay-tree
make-adjustable-splay-tree
splay-tree?
adjustable-splay-tree?
splay-tree-ref
splay-tree-set!
splay-tree-remove!
splay-tree-count
splay-tree-iterate-first
splay-tree-iterate-next
splay-tree-iterate-key
splay-tree-iterate-value
splay-tree-remove-range!
splay-tree-contract!
splay-tree-expand!
splay-tree-iterate-least
splay-tree-iterate-greatest
splay-tree-iterate-least/  >?
splay-tree-iterate-least/  >=?
splay-tree-iterate-greatest/  <?
splay-tree-iterate-greatest/  <=?
splay-tree-iter?
splay-tree->list
6.2
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4 Splay Trees

Ryan Culpepper <ryanc@racket-lang.org>

 (require data/splay-tree) package: data-lib

Splay trees are an efficient data structure for mutable dictionaries with totally ordered keys. They were described in the paper “Self-Adjusting Binary Search Trees” by Daniel Sleator and Robert Tarjan in Journal of the ACM 32(3) pp652-686.

A splay-tree is a ordered dictionary (dict? and ordered-dict?).

Operations on splay-trees are not thread-safe. If a key in a splay-tree is mutated, the splay-tree’s internal invariants may be violated, causing its behavior to become unpredictable.

procedure

(make-splay-tree [ord    
  #:key-contract key-contract    
  #:value-contract value-contract]) → splay-tree?
  ord : order? = datum-order
  key-contract : contract? = any/c
  value-contract : contract? = any/c
Makes a new empty splay-tree. The splay tree uses ord to order keys; in addition, the domain contract of ord is combined with key-contract to check keys.

Examples:

> (define splay-tree
    (make-splay-tree (order 'string-order string? string=? string<?)))
> (splay-tree-set! splay-tree "dot" 10)
> (splay-tree-set! splay-tree "cherry" 500)
> (dict-map splay-tree list)

'(("cherry" 500) ("dot" 10))

> (splay-tree-ref splay-tree "dot")

10

> (splay-tree-remove! splay-tree "cherry")
> (splay-tree-count splay-tree)

1

> (splay-tree-set! splay-tree 'pear 3)

splay-tree-set!: contract violation

  expected: string?

  given: 'pear

  in: the key argument of

      (->i

       ((s splay-tree?)

        (key (s) (key-c s))

        (v (s) (val-c s)))

       (_r void?))

  contract from:

      <pkgs>/data-lib/data/splay-tree.rkt

  blaming: top-level

   (assuming the contract is correct)

  at: <pkgs>/data-lib/data/splay-tree.rkt:1115.2

procedure

(make-adjustable-splay-tree [#:key-contract key-contract 
  #:value-contract value-contract]) 
 → splay-tree?
  key-contract : contract? = any/c
  value-contract : contract? = any/c
Makes a new empty splay-tree that permits only exact integers as keys (in addition to any constraints imposed by key-contract). The resulting splay tree answers true to adjustable-splay-tree? and supports efficient key adjustment.

Examples:

> (define splay-tree (make-adjustable-splay-tree))
> (splay-tree-set! splay-tree 3 'apple)
> (splay-tree-set! splay-tree 6 'cherry)
> (dict-map splay-tree list)

'((3 apple) (6 cherry))

> (splay-tree-ref splay-tree 3)

'apple

> (splay-tree-remove! splay-tree 6)
> (splay-tree-count splay-tree)

1

procedure

(splay-tree? x) → boolean?

  x : any/c
Returns #t if x is a splay-tree, #f otherwise.

procedure

(adjustable-splay-tree? x) → boolean?

  x : any/c
Returns #t if x is a splay-tree that supports key adjustment; see splay-tree-contract! and splay-tree-expand!.

procedure

(splay-tree-ref s key [default]) → any

  s : splay-tree?
  key : any/c
  default : any/c = (lambda () (error ....))

procedure

(splay-tree-set! s key value) → void?

  s : splay-tree?
  key : any/c
  value : any/c

procedure

(splay-tree-remove! s key) → void?

  s : splay-tree?
  key : any/c

procedure

(splay-tree-count s) → exact-nonnegative-integer?

  s : splay-tree?

procedure

(splay-tree-iterate-first s) → (or/c #f splay-tree-iter?)

  s : splay-tree?

procedure

(splay-tree-iterate-next s iter) → (or/c #f splay-tree-iter?)

  s : splay-tree?
  iter : splay-tree-iter?

procedure

(splay-tree-iterate-key s iter) → any/c

  s : splay-tree?
  iter : splay-tree-iter?

procedure

(splay-tree-iterate-value s iter) → any/c

  s : splay-tree?
  iter : splay-tree-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.

procedure

(splay-tree-remove-range! s from to) → void?

  s : splay-tree?
  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.

This operation takes O(N) time, or O(log N) time if (adjustable-splay-tree? s).

procedure

(splay-tree-contract! s from to) → void?

  s : adjustable-splay-tree?
  from : exact-integer?
  to : exact-integer?
Like splay-tree-remove-range!, but also decreases the value of all keys greater than or equal to to by (- to from).

This operation is only allowed on adjustable splay trees, and it takes O(log N) time.

procedure

(splay-tree-expand! s from to) → void?

  s : adjustable-splay-tree?
  from : exact-integer?
  to : exact-integer?
Increases the value of all keys greater than or equal to from by (- to from).

This operation is only allowed on adjustable splay trees, and it takes O(log N) time.

procedure

(splay-tree-iterate-least s) → (or/c #f splay-tree-iter?)

  s : splay-tree

procedure

(splay-tree-iterate-greatest s) → (or/c #f splay-tree-iter?)

  s : splay-tree

procedure

(splay-tree-iterate-least/>? s key) → (or/c #f splay-tree-iter?)

  s : splay-tree?
  key : any/c

procedure

(splay-tree-iterate-least/>=? s key)

 → (or/c #f splay-tree-iter?)
  s : splay-tree?
  key : any/c

procedure

(splay-tree-iterate-greatest/<? s key)

 → (or/c #f splay-tree-iter?)
  s : splay-tree?
  key : any/c

procedure

(splay-tree-iterate-greatest/<=? s key)

 → (or/c #f splay-tree-iter?)
  s : splay-tree?
  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.

procedure

(splay-tree-iter? x) → boolean?

  x : any/c
Returns #t if x represents a position in a splay-tree, #f otherwise.

procedure

(splay-tree->list s) → (listof pair?)

  s : splay-tree?
Returns an association list with the keys and values of s, in order.

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