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#lang typed/racket/base/no-check
;; Union-find hardcoded to do symbols.
(provide (all-defined-out))
;; A forest contains a collection of its nodes keyed by element.
;; The elements are compared by eq?
(define-struct: forest
([ht : (HashTable Symbol node)]))
;; A node is an element, a parent node, and a numeric rank.
(define-struct: node
([elt : Symbol]
[p : (U False node)]
[rank : Natural])
;; Builds a new, empty forest.
(: new-forest (-> forest))
(define (new-forest)
(make-forest (make-hash)))
;; lookup-node: forest X -> node
;; Returns the node that's associated with this element.
(: lookup-node (forest Symbol -> node))
(define (lookup-node a-forest an-elt)
(unless (hash-has-key? (forest-ht a-forest) an-elt)
(make-set a-forest an-elt))
(hash-ref (forest-ht a-forest)
;; make-set: forest X -> void
;; Adds a new set into the forest.
(: make-set (forest Symbol -> Void))
(define (make-set a-forest an-elt)
(unless (hash-has-key? (forest-ht a-forest) an-elt)
(let ([a-node (make-node an-elt #f 0)])
(set-node-p! a-node a-node)
(hash-set! (forest-ht a-forest) an-elt a-node))))
(: find-set (forest Symbol -> Symbol))
;; Returns the representative element of elt.
(define (find-set a-forest an-elt)
(let ([a-node (lookup-node a-forest an-elt)])
(node-elt (get-representative-node a-node))))
(: get-representative-node (node -> node))
;; Returns the representative node of a-node, doing path
;; compression if we have to follow links.
(define (get-representative-node a-node)
(let ([p (node-p a-node)])
(cond [(eq? a-node p)
[(node? p)
(let ([rep (get-representative-node p)])
;; Path compression is here:
(set-node-p! a-node rep)
;; impossible situation
(error 'get-representative-node)])))
(: union-set (forest Symbol Symbol -> Void))
;; Joins the two elements into the same set.
(define (union-set a-forest elt1 elt2)
(let ([rep1 (get-representative-node
(lookup-node a-forest elt1))]
[rep2 (get-representative-node
(lookup-node a-forest elt2))])
[(< (node-rank rep1) (node-rank rep2))
(set-node-p! rep1 rep2)]
[(> (node-rank rep1) (node-rank rep2))
(set-node-p! rep2 rep1)]
(set-node-p! rep1 rep2)
(set-node-rank! rep1 (add1 (node-rank rep1)))])))
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