#lang scribble/manual @(require "helper.rkt") @(defmodule "lazypairingheap.ss") @(require (for-label "lazypairingheap.ss")) @(require scribble/eval) @(define evaluate (make-base-eval)) @(evaluate '(require typed/scheme)) @(evaluate '(require "lazypairingheap.ss")) @title{Lazy Pairing Heap} Lazy Pairing Heap is very similar to Pairing Heap. The only difference between the two is, as the name suggests, Lazy Pairing Heap is lazy in nature. @;section{Lazy Pairing Heap Construction and Operations} @defproc[(heap [comp (A A -> Boolean)] [a A] ...) (Heap A)]{ Function @scheme[heap] creates a Lazy Pairing Heap with the given inputs. @examples[#:eval evaluate (heap < 1 2 3 4 5 6) ] In the above example, the lazy pairing heap obtained will have elements 1 thru' 6 with < as the comparison function.} @;subsection{empty} @;An empty lazy pairing heap. @defproc[(empty? [heap (Heap A)]) Boolean]{ Function @scheme[empty?] checks if the given lazy pairing heap is empty or not. @examples[#:eval evaluate (empty? (heap < 1 2 3 4 5 6)) (empty? (heap <)) ]} @defproc[(insert [a A] [heap (Heap A)] ...) (Heap A)]{ Function @scheme[insert] takes an element and a lazy pairing heap and inserts the given element into the lazy pairing heap. @examples[#:eval evaluate (insert 10 (heap < 1 2 3 4 5 6)) ] In the above example, @scheme[(insert 10 (heap < 1 2 3 4 5 6))] adds the element 10 to the heap @scheme[(heap < 1 2 3 4 5 6)].} @defproc[(find-min/max [heap (Heap A)]) A]{ Function @scheme[find-min/max] takes a lazy pairing heap and gives the largest or the smallest element in the heap if lazy pairing heap is not empty else throws an error. The element returned is max or min depends on the comparison function of the heap. @examples[#:eval evaluate (find-min/max (heap < 1 2 3 4 5 6)) (find-min/max (heap > 1 2 3 4 5 6)) (find-min/max (heap <)) ]} @defproc[(delete-min/max [heap (Heap A)]) (Heap A)]{ Function @scheme[delete-min/max] takes a lazy pairing heap and returns the same heap with out the min or max element in the given heap. The element removed from the heap is max or min depends on the comparison function of the heap. @examples[#:eval evaluate (delete-min/max (heap < 1 2 3 4 5 6)) (delete-min/max (heap > 1 2 3 4 5 6)) (delete-min/max (heap >)) ]} @defproc[(merge [pheap1 (Heap A)] [pheap2 (Heap A)]) (Heap A)]{ Function @scheme[merge] takes two lazy pairing heaps and returns a merged lazy pairing heap. Uses the comparison function in the first heap for merging and the same function becomes the comparison function for the merged heap. @margin-note{If the comparison functions do not have the same properties, merged heap might lose its heap-order.} @examples[#:eval evaluate (define pheap1 (heap < 1 2 3 4 5 6)) (define pheap2 (heap (λ: ([a : Integer] [b : Integer]) (< a b)) 10 20 30 40 50 60)) (merge pheap1 pheap2) ] In the above example, @scheme[(merge pheap1 pheap2)], merges the heaps and < will become the comparison function for the merged heap.} @defproc[(sorted-list [heap (Heap A)]) (Listof A)]{ Function @scheme[sorted-list] takes a lazy pairing heap and returns a list which is sorted according to the comparison function of the heap. @examples[#:eval evaluate (sorted-list (heap > 1 2 3 4 5 6)) (sorted-list (heap < 1 2 3 4 5 6)) ]} @defproc[(map [comparer (C C -> Boolean)] [func (A B ... B -> C)] [hep1 (Heap A)] [hep2 (Heap B)] ...) (Heap A)]{ Function @scheme[map] is similar to @|racket-map| for lists. @examples[#:eval evaluate (sorted-list (map < add1 (heap < 1 2 3 4 5 6))) (sorted-list (map < * (heap < 1 2 3 4 5 6) (heap < 1 2 3 4 5 6))) ]} @defproc[(fold [func (C A B ... B -> C)] [init C] [hep1 (Heap A)] [hep2 (Heap B)] ...) C]{ Function @scheme[fold] is similar to @|racket-foldl| or @|racket-foldr| @margin-note{@scheme[fold] currently does not produce correct results when the given function is non-commutative.} @examples[#:eval evaluate (fold + 0 (heap < 1 2 3 4 5 6)) (fold * 1 (heap < 1 2 3 4 5 6) (heap < 1 2 3 4 5 6)) ]} @defproc[(filter [func (A -> Boolean)] [hep (Heap A)]) (Heap A)]{ Function @scheme[filter] is similar to @|racket-filter|. @examples[#:eval evaluate (define hep (heap < 1 2 3 4 5 6)) (sorted-list (filter (λ: ([x : Integer]) (> x 5)) hep)) (sorted-list (filter (λ: ([x : Integer]) (< x 5)) hep)) (sorted-list (filter (λ: ([x : Integer]) (<= x 5)) hep)) ]} @defproc[(remove [func (A -> Boolean)] [hep (Heap A)]) (Heap A)]{ Function @scheme[remove] is similar to @|racket-filter| but @scheme[remove] removes the elements which match the predicate. @examples[#:eval evaluate (sorted-list (remove (λ: ([x : Integer]) (> x 5)) (heap < 1 2 3 4 5 6))) (sorted-list (remove (λ: ([x : Integer]) (< x 5)) (heap < 1 2 3 4 5 6))) (sorted-list (remove (λ: ([x : Integer]) (<= x 5)) (heap < 1 2 3 4 5 6))) ]} @(close-eval evaluate)