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Heap

Mutable heap with priority-queue functions and O(1) membership-testing, which is useful for implementing e.g. A*

Heap

`heap`

[record] heap

The heap data-structure

>?: Greater-than relation for keys
=?: Equal-to relation for keys
inf: Infinity w.r.t. the inequality `>?'
key: Key-accessor for heap-elements
key-set!: Key-mutator for heap-elements
data: Vector data-store underlying heap
size: Size of the heap as distinct from size of data

(define-record-and-printer heap >? =? inf key key-set! data size)

`heap-empty?`

[procedure] (heap-empty? heap) → boolean

Is the heap empty?

heap: The heap to check

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

`heapify!`

[procedure] (heapify! heap i) → unspecified

Given a heap-index, reëstablish the heap-property.

heap: The heap in which to heapify
i: The element-index to heapify

(define (heapify! heap i)
  (let ((heap->? (heap->? heap)) (heap-key (heap-key heap)))
    (let ((left (left i)) (right (right i)))
      (let* ((extremum
               (if (and (< left (heap-size heap))
                        (heap->?
                          (heap-key (heap-ref heap left))
                          (heap-key (heap-ref heap i))))
                 left
                 i))
             (extremum
               (if (and (< right (heap-size heap))
                        (heap->?
                          (heap-key (heap-ref heap right))
                          (heap-key (heap-ref heap extremum))))
                 right
                 extremum)))
        (if (not (= extremum i))
          (begin (heap-swap! heap i extremum) (heapify! heap extremum)))))))

`initial-heap-size`

[parameter] initial-heap-size → 100

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

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

[procedure] (make-max-heap) → max-heap
[procedure] (make-max-heap key key-set!) → max-heap
[procedure] (make-max-heap key key-set! data) → max-heap
[procedure] (make-max-heap key key-set! data size) → max-heap

Make a max-heap.

key: Key-accessor for heap-elements
key-set!: Key-mutator for heap-elements
data: Vector data-store underlying heap
size: Size of the heap as distinct from size of data

(define make-max-heap
  (case-lambda
    (() (make-max-heap car set-car!))
    ((key key-set!)
     (make-max-heap key key-set! (make-vector (initial-heap-size)) 0))
    ((key key-set! data)
     (make-max-heap key key-set! data (vector-length data)))
    ((key key-set! data size) (make-heap > = -inf key key-set! data size))))

`make-min-heap`

[procedure] (make-min-heap) → min-heap
[procedure] (make-min-heap key key-set!) → min-heap
[procedure] (make-min-heap key key-set! data) → min-heap
[procedure] (make-min-heap key key-set! data size) → min-heap

Make a min-heap.

key: Key-accessor for heap-elements
key-set!: Key-mutator for heap-elements
data: Vector data-store underlying heap
size: Size of the heap as distinct from size of data

(define make-min-heap
  (case-lambda
    (() (make-max-heap car set-car!))
    ((key key-set!)
     (make-max-heap key key-set! (make-vector (initial-heap-size)) 0))
    ((key key-set! data)
     (make-max-heap key key-set! data (vector-length data)))
    ((key key-set! data size) (make-heap < = +inf key key-set! data size))))

`build-heap!`

[procedure] (build-heap! heap) → unspecified

Heapify the entire data-store.

heap: The heap to heapify

(define (build-heap! heap)
  (heap-size-set! heap (vector-length (heap-data heap)))
  (let ((median (inexact->exact (floor (/ (heap-size heap) 2)))))
    (do ((i (sub1 median) (sub1 i))) ((negative? i)) (heapify! heap i))))

`heap-extremum`

[procedure] (heap-extremum heap) → extreme element

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

heap: The heap at which to peek

(define (heap-extremum heap) (heap-ref heap 0))

`heap-extract-extremum!`

[procedure] (heap-extract-extremum! heap) → extreme element

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

heap: The heap from which to extract

(define (heap-extract-extremum! heap)
  (if (zero? (heap-size heap))
    (error "Heap underflow -- HEAP-EXTRACT-EXTREMUM!")
    (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! heap 0)
      extremum)))

`heap-change-key!`

[procedure] (heap-change-key! heap i new-key) → unspecified

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

heap: The heap in which to change
i: The index of the element whose key to change
new-key: The new key to assign to element i

(define (heap-change-key! heap i new-key)
  (let ((heap->? (heap->? heap))
        (heap-=? (heap-=? heap))
        (heap-key (heap-key heap)))
    (let ((old-key (heap-key (heap-ref heap i))))
      (if (or (heap->? new-key old-key) (heap-=? new-key old-key))
        (begin
          ((heap-key-set! heap) (heap-ref heap i) new-key)
          (do ((i i (parent i)))
              ((or (zero? i)
                   (heap->?
                     (heap-key (heap-ref heap (parent i)))
                     (heap-key (heap-ref heap i)))))
            (heap-swap! heap i (parent i))))
        (error "Key violates heap-gradient -- HEAP-CHANGE-KEY!")))))

`heap-insert!`

[procedure] (heap-insert! heap element) → unspecified

Insert a new element into the heap.

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

(define (heap-insert! heap element)
  (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 ((key ((heap-key heap) element)))
      ((heap-key-set! heap) element (heap-inf heap))
      (heap-set! heap heap-size element)
      (heap-change-key! heap heap-size key))))

`heap-delete!`

[procedure] (heap-delete! heap i) → unspecified

Delete the ith element from the heap

heap: The heap from which to delete
i: The index of the element to delete

(define (heap-delete! heap i)
  (let ((heap-size (- (heap-size heap) 1)))
    (if (negative? heap-size)
      (error "Heap underflow -- HEAP-DELETE!")
      (begin
        (heap-size-set! heap heap-size)
        (heap-set! heap i (heap-ref heap heap-size))
        (heapify! heap i)))))