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improvements to union find suggested by Sam and Danny

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This commit is contained in:
Robby Findler 2013-01-29 17:37:34 -06:00
parent f0450d716b
commit 8013ccf60e
2 changed files with 59 additions and 12 deletions
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28
collects/data/scribblings/union-find.scrbl
View File

@ -22,6 +22,8 @@ These operations are not thread-safe.
Makes a new set with the canonical element @racket[c].
This is a constant time operation.
@examples[#:eval the-eval
(uf-new 'whale)
(uf-new 'dwarf-lantern)]
@ -32,6 +34,8 @@ Makes a new set with the canonical element @racket[c].
Returns @racket[#t] if @racket[x] was created with @racket[uf-new],
and @racket[#f] otherwise.
This is a constant time operation.
@examples[#:eval the-eval
(uf-set? (uf-new 'spiny-dogfish))
@ -40,6 +44,8 @@ Returns @racket[#t] if @racket[x] was created with @racket[uf-new],
@defproc[(uf-find [a uf-set?]) any/c]{
Returns the canonical element of @racket[a].
This is an amortized (essentially) constant time operation.
@examples[#:eval the-eval
(uf-find (uf-new 'tasselled-wobbegong))]
@ -52,6 +58,8 @@ them both have the same canonical element. Either
of @racket[a] or @racket[b]'s canonical elements may
become the canonical element for the union.
This is an amortized (essentially) constant time operation.
@examples[#:eval the-eval
(define a (uf-new 'sand-devil))
(define b (uf-new 'pigeye))
@ -61,9 +69,27 @@ become the canonical element for the union.
]
}
@defproc[(uf-same-set? [a uf-set?] [b uf-set?]) boolean?]{
Returns @racket[#t] if the sets @racket[a] and @racket[b]
have been unioned.
This is an amortized (essentially) constant time operation.
@examples[#:eval the-eval
(define a (uf-new 'finetooth))
(define b (uf-new 'speartooth))
(uf-same-set? a b)
(uf-union! a b)
(uf-same-set? a b)
]
}
@defproc[(uf-set-canonical! [a uf-set?] [c any/c]) void?]{
Changes @racket[a] to have a new canonical element
Changes @racket[a] to have a new canonical element.
This is an amortized (essentially) constant time operation.
@examples[#:eval the-eval
(define a (uf-new 'sand-devil))

43
collects/data/union-find.rkt
View File

@ -1,10 +1,12 @@
#lang racket/base
(provide uf-set?
uf-new
uf-union!
uf-find
uf-set-canonical!)
(require racket/contract)
(provide uf-set? uf-new)
(provide
(contract-out
[uf-union! (-> uf-set? uf-set? void?)]
[uf-find (-> uf-set? any/c)]
[uf-set-canonical! (-> uf-set? any/c void?)]
[uf-same-set? (-> uf-set? uf-set? boolean?)]))
(struct uf-set (x rank) #:mutable
#:methods gen:custom-write
@ -28,22 +30,22 @@
[else
(set-uf-set-x! b a)
(when (= a-rank b-rank)
(set-uf-set-rank! a 1))]))
(set-uf-set-rank! a (+ a-rank 1)))]))
(define (uf-find a)
(define bx (uf-get-box a))
(unbox bx))
(define (uf-set-canonical! a b)
(set-box! (uf-get-box a) b))
(define (uf-get-box a)
(let loop ([a a])
(let loop ([a (uf-set-x a)])
(cond
[(box? (uf-set-x a))
(uf-set-x a)]
[(box? a) a]
[else
(define fnd (loop (uf-set-x a)))
(set-uf-set-x! a fnd)
fnd])))
(define (uf-same-set? a b)
(eq? (uf-get-box a) (uf-get-box b)))
(module+ test
(require rackunit
@ -72,6 +74,13 @@
(uf-find b)
(uf-find b))
1)
(check-equal? (uf-same-set? (uf-new 1) (uf-new 2)) #f)
(check-equal? (uf-same-set? (uf-new 1) (uf-new 1)) #f)
(check-equal? (let ([a (uf-new 1)]
[b (uf-new 1)])
(uf-union! a b)
(uf-same-set? a b))
#t)
(check-equal? (let ([sp (open-output-string)])
(display (uf-new "x") sp)
(get-output-string sp))
@ -98,6 +107,18 @@
(get-output-string sp))
"#0=#<uf-set: #0#>")
(check-equal? (let ([a (uf-new 1)]
[b (uf-new 2)]
[c (uf-new 3)]
[d (uf-new 4)])
(uf-union! a b)
(uf-union! c d)
(uf-union! a c)
(max (uf-set-rank a)
(uf-set-rank b)
(uf-set-rank c)
(uf-set-rank d)))
2)
(define (check-ranks uf)
(let loop ([uf/box uf]