#lang typed-scheme
;;; priority-queue.scm  --  Jens Axel Søgaard
;;; PURPOSE

; This file implements priority queues on top of
; a heap library.
(define-type-alias number Number)
(define-type-alias boolean Boolean)
(define-type-alias symbol Symbol)
(define-type-alias top Any)
(define-type-alias list-of Listof)
(require (prefix-in heap: "leftist-heap.ss")
	 (except-in (lib "67.ss" "srfi") number-compare current-compare =? <?)
	 (only-in "leftist-heap.ss" comparator))
(require/typed number-compare (number number -> number) (lib "67.ss" "srfi"))
(require/typed current-compare (-> (top top -> number)) (lib "67.ss" "srfi"))
(require/typed =? ((top top -> number) top top -> boolean) (lib "67.ss" "srfi"))
(require/typed <? ((top top -> number) top top -> boolean) (lib "67.ss" "srfi"))

; a priority-queue is a heap of  (cons <priority> <element>)

(define-type-alias (elem a) (cons number a))

(define-typed-struct (a) priority-queue ([heap : (heap:Heap (elem a))]))

(define-type-alias (pqh a) (heap:Heap (elem a)))

; conveniences
(pdefine: (a) (heap [pq : (priority-queue a)]) : (pqh a) (priority-queue-heap pq))
(pdefine: (a) (pri [p : (elem a)]) : number (car p))
(pdefine: (a) (elm [p : (elem a)]) : a  (cdr p))
(pdefine: (a) (make [h : (pqh a)]) : (priority-queue a)  (make-priority-queue h))

; sort after priority
; TODO: and then element?
(pdefine: (a) (compare [p1 : (elem a)] [p2 : (elem a)]) : number
	  (number-compare (pri p1) (pri p2)))

;;; OPERATIONS

(define: (num-elems [h : (heap:Heap (cons number number))]) : (list-of (cons number number))
  (heap:elements h))

(pdefine: (a) (elements [pq : (priority-queue a)]) : (list-of a)
          (map #{elm :: ((elem a) -> a)} (heap:elements (heap pq))))

(pdefine: (a) (elements+priorities [pq : (priority-queue a)]) : (values (list-of a) (list-of number))
	  (let: ([eps : (list-of (elem a)) (heap:elements (heap pq))])
		(values (map #{elm :: ((elem a) -> a)} eps)
			(map #{pri :: ((elem a) -> number)} eps))))

(pdefine: (a) (empty? [pq : (priority-queue a)]) : boolean
	  (heap:empty? (heap pq)))

(define: empty : (All (a) (case-lambda (-> (priority-queue a)) (comparator -> (priority-queue a))))
  (pcase-lambda: (a)
		 [()    (#{empty @ a} (current-compare))]
		 [([cmp : comparator]) (make (#{heap:empty :: (case-lambda (-> (pqh a))
									   (comparator -> (pqh a)))} cmp))]))

(pdefine: (e r) (fold [f : ((cons number e) r -> r)] [b : r] [a : (priority-queue e)]) : r
	  (heap:fold f b (#{heap :: ((priority-queue e) -> (pqh e))} a)))


;; "bug" found - handling of empty heaps
(pdefine: (a) (find-min [pq : (priority-queue a)]) : a 
	  (let ([h (heap pq)])
	    (if (heap:heap-node? h)
		(elm (heap:find-min h))
		(error "priority queue empty"))))

(pdefine: (a) (find-min-priority [pq : (priority-queue a)]) : number
	  (let ([h (heap pq)])
	    (if (heap:heap-node? h)
		(pri (heap:find-min h))
		(error "priority queue empty"))))

(pdefine: (a) (insert [x : a] [p : number] [pq : (priority-queue a)]) : (priority-queue a)
	  (make (heap:insert (cons p x) (heap pq))))

;; FIXME -- too many annotations needed on cons
(pdefine: (a) (insert* [xs : (list-of a)] [ps : (list-of number)] [pq : (priority-queue a)]) : (priority-queue a)
          (make (heap:insert* (map #{cons @ number a} ps xs) (heap pq))))

(pdefine: (a) (delete-min [pq : (priority-queue a)]) : (priority-queue a)
	  (let ([h (heap pq)])
	    (if (heap:heap-node? h)
		(make (heap:delete-min h))
		(error "priority queue empty"))))


(pdefine: (a) (size [pq : (priority-queue a)]) : number
	  (heap:size (heap pq)))

(pdefine: (a) (union [pq1 : (priority-queue a)] [pq2 : (priority-queue a)]) : (priority-queue a)
	  (make (heap:union (heap pq1) (heap pq2))))


#;(require "signatures/priority-queue-signature.scm")
#;(provide-priority-queue)

