heap

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Mutable heap with priority-queue operations and O(1) membership-testing

heap

heaprecord

The heap data-structure

>?: Greater-than relation for keys
<?: Less-than relation for keys
inf: Infinity w.r.t. the inequality `>?'
data: Vector data-store underlying heap
size: Size of the heap as distinct from size of data
membership: Mapping from data to indices

(define-record-and-printer heap >? <? inf data size membership)

heap-empty?

heap-empty? heapprocedure

Is the heap empty?

heap: The heap to check

(define (heap-empty? heap) (zero? (heap-size heap)))

heap-member?

heap-member? heap datumprocedure

Is this datum a member in the heap?

heap: The heap in which to check
datum: The datum to check for

(define (heap-member? heap datum) (and (heap-index heap datum) #t))

heap-key

heap-key heap datumprocedure

Find the key, given the datum.

heap: The heap in which to search
datum: The datum whose key to find

(define (heap-key heap datum)
  (let ((index (heap-index heap datum)))
    (and index (element-key (heap-ref heap index)))))

initial-heap-size

initial-heap-sizeparameter

Initial size of the heap data-store; exponentially resized on overflow.

(define initial-heap-size (make-parameter 100))

make-max-heap

make-max-heapprocedure

make-max-heap initial-heap-sizeprocedure

Make a max-heap.

size: Initial heap-size

(define make-max-heap
  (case-lambda
    (() (make-max-heap (initial-heap-size)))
    ((initial-heap-size)
     (make-heap
       >
       <
       -inf.0
       (make-vector initial-heap-size)
       0
       (make-hash-table)))))

make-min-heap

make-min-heapprocedure

make-min-heap initial-heap-sizeprocedure

Make a min-heap.

size: Initial heap-size

(define make-min-heap
  (case-lambda
    (() (make-min-heap (initial-heap-size)))
    ((initial-heap-size)
     (make-heap
       <
       >
       +inf.0
       (make-vector initial-heap-size)
       0
       (make-hash-table)))))

heap-extremum

heap-extremum heapprocedure

Peak at the heap's extremum (min or max).

heap: The heap at which to peek

(define (heap-extremum heap)
  (if (heap-empty? heap)
    (error "Heap underflow -- HEAP-EXTREMUM")
    (element-datum (heap-ref heap 0))))

heap-extract-extremum!

heap-extract-extremum! heapprocedure

Return and delete the heap's extremum (min or max).

heap: The heap from which to extract

(define (heap-extract-extremum! heap)
  (let ((extremum (heap-extremum heap)))
    (heap-set! heap 0 (heap-ref heap (- (heap-size heap) 1)))
    (heap-size-set! heap (- (heap-size heap) 1))
    (heapify!/index heap 0)
    extremum))

heap-change-key!

heap-change-key! heap datum new-keyprocedure

Change the key of the element with datum to new-key along the heap-gradient.

heap: The heap in which to change
datum: The datum whose key to change
new-key: The new key to assign to element with datum

(define (heap-change-key! heap datum new-key)
  (let ((i (heap-index heap datum)))
    (if i
      (heap-change-key!/index heap i new-key)
      (error "Datum not found -- HEAP-CHANGE-KEY!"))))

heap-insert!

heap-insert! heap key datumprocedure

Insert a new element into the heap if the datum does not exist; otherwise, adjust its key.

heap: The heap in which to insert
element: The element to be inserted

(define (heap-insert! heap key datum)
  (if (heap-member? heap datum)
    (heap-change-key! heap datum key)
    (let ((heap-size (heap-size heap)))
      (if (= heap-size (heap-length heap))
        (heap-data-set! heap (vector-resize (heap-data heap) (* 2 heap-size))))
      (heap-size-set! heap (+ heap-size 1))
      (let ((element (make-element (heap-inf heap) datum)))
        (heap-set! heap heap-size element)
        (heap-change-key!/index heap heap-size key)))))

heap-delete!

heap-delete! heap datumprocedure

Delete the element with datum

heap: The heap from which to delete
datum: The datum whose element to delete

(define (heap-delete! heap datum)
  (let ((i (heap-index heap datum)))
    (if i
      (heap-delete!/index heap i)
      (error "Datum not found -- HEAP-DELETE!"))))

heap->list

heap->list heapprocedure

Convert the heap into a key-sorted list of values by iteratively extracting the extremum; see also heap->alist.

heap: The heap to convert

(define (heap->list heap)
  (let ((heap (heap-copy heap)))
    (do ((list '() (cons (heap-extract-extremum! heap) list)))
        ((heap-empty? heap) list))))

heap->alist

heap->alist heapprocedure

Convert the heap into a key-sorted list of key-value pairs by iteratively extracting the extremum; see also heap->list.

heap: The heap to convert

(define (heap->alist heap)
  (let ((heap (heap-copy heap)))
    (do ((list '()
               (let ((datum (heap-extremum heap)))
                 (alist-cons
                   (heap-key heap datum)
                   (heap-extract-extremum! heap)
                   list))))
        ((heap-empty? heap) list))))