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ufrac-branch.scm
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ufrac-branch.scm
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(define-record-type br
(fields
(immutable sum-denoms)
(immutable rs-denoms)
(immutable r)
(immutable original-r)
(immutable diff)
(immutable gpp) ; greatest prime power that divides the denominator of diff ; TODO rename it
(immutable rs-rsvd) ; reciprocal sum of reserved denominators
(immutable rsvd) ; reserved denominators
(immutable denoms)
(immutable denoms-sol))
(protocol
(lambda (new)
(case-lambda [(sum-NM rs-NM rs-M subset-M NM parent)
(let* ([rs-subset-M (rec-sum subset-M)]
[new-r (- (br-r parent) rs-subset-M)]
[new-diff (- rs-NM new-r)]
[new-rsvd (append subset-M (br-rsvd parent))])
(new sum-NM ; sum-denoms
rs-NM ; rs-denoms
new-r ; r
(br-original-r parent) ; original-r
new-diff ; diff
(cond [(integer? new-diff) #f]
[else
(greatest-prime-power
(factor (denominator new-diff)))]) ; gpp
(+ rs-subset-M (br-rs-rsvd parent)) ;rs-rsvd
new-rsvd ; rsvd
NM ; denoms
(cond [(zero? new-diff) (sort < (append new-rsvd NM))]
[(zero? new-r) (sort < new-rsvd)]
[else #f]) ; denoms-sol
))]
[(denoms r)
(let* ([rs-denoms (rec-sum denoms)]
[diff (- rs-denoms r)])
(new (sum denoms) ; sum-denoms
rs-denoms ; rs-denoms
r ; r
r ; original-r
diff ; diff
(cond [(integer? diff) #f]
[else
(greatest-prime-power
(factor (denominator diff)))]) ; gpp
0 ; rs-rsvd
'() ; rsvd
(sort < denoms) ; denoms
(cond [(zero? diff) (sort < denoms)]
[(zero? r) '()]
[else #f]) ; denoms-sol
))]
[(sum-denoms rs-denoms r original-r diff gpp
rs-rsvd rsvd denoms denoms-sol)
(new sum-denoms rs-denoms r original-r diff gpp
rs-rsvd rsvd denoms denoms-sol)]
))))
(define (br-equal? br-a br-b)
(and (equal? (br-sum-denoms br-a)
(br-sum-denoms br-b))
(equal? (br-rs-denoms br-a)
(br-rs-denoms br-b))
(equal? (br-r br-a)
(br-r br-b))
(equal? (br-original-r br-a)
(br-original-r br-b))
(equal? (br-rs-rsvd br-a)
(br-rs-rsvd br-b))
(equal? (sort < (br-rsvd br-a)) ; rsvd must be sorted
(sort < (br-rsvd br-b)))
(equal? (sort < (br-denoms br-a)) ; denoms must be sorted
(sort < (br-denoms br-b)))
(equal? ((br-denoms-sol br-a)) ; br-denoms-sol is already sorted
(br-denoms-sol br-b))))
(define (br-equal-as-sol? br-a br-b)
(if (not (br-denoms-sol br-a))
(error
'<procedure-BR-EQUAL-AS-SOL?>
"\nThe first branch is not a solution."
br-a))
(if (not (br-denoms-sol br-b))
(error
'<procedure-BR-EQUAL-AS-SOL?>
"\nThe second branch is not a solution."
br-b))
(and (equal? (br-original-r br-a)
(br-original-r br-b))
(equal? (br-denoms-sol br-a)
(br-denoms-sol br-b))))
(define (br-reserve-first-d br)
;; Only to be called when diff is a positive integer and r is nonnegative.
(let ([diff (br-diff br)])
;; diff should be the same as original diff, which is expected
;; to be a positive integer.
(if (not (and (integer? diff) (positive? diff)))
(error
'<procedure-BR-RESERVE-FIRST-D>
(format "\ndiff ~s is not a positive integer." diff)))
(let* ([d (car (br-denoms br))
;; denoms must be nonempty in this case (diff must be
;; strictly positive), otherwise it is a solution.
]
[rec-d (/ 1 d)]
[r (- (br-r br) rec-d)])
(if (negative? r)
(error
'<procedure-BR-RESERVE-FIRST-D>
(format "\nInvalid new branch. New r = ~s is negative."
(- r rec-d))))
(make-br (- (br-sum-denoms br) d) ; sum-denoms
(- (br-rs-denoms br) rec-d) ; rs-denoms
r ; r
(br-original-r br) ; original-r
diff ; diff
#f ; gpp
(+ (br-rs-rsvd br) (/ 1 d)) ; rs-rsvd
(append (list d) (br-rsvd br)) ; rsvd
(cdr (br-denoms br)) ; denoms
(if (zero? r)
(sort < (append (list d) (br-rsvd br)))
#f) ; denoms-sol
))))
(define (br-discard-first-d br)
;; Only to be called when diff is a positive integer.
(let ([old-diff (br-diff br)])
(if (not (and (integer? old-diff)
(positive? old-diff)))
(error
'<procedure-BR-DISCARD-FIRST-D>
(format "\ndiff ~s is not a positive integer." old-diff)))
(let* ([d (car (br-denoms br))
;; denoms must be nonempty in this case,
;; because diff is strictly positive.
]
[rec-d (/ 1 d)]
[diff (- old-diff rec-d)])
(make-br (- (br-sum-denoms br) d) ; sum-denoms
(- (br-rs-denoms br) rec-d) ; rs-denoms
(br-r br) ; r
(br-original-r br) ; original-r
diff ; diff
(cond [(integer? diff) #f]
[else (greatest-prime-power (factor d))]) ; gpp
(br-rs-rsvd br)
(br-rsvd br)
(cdr (br-denoms br))
(if (zero? diff)
(sort < (append (br-rsvd br) (cdr (br-denoms br))))
#f)))))
(define (br-reduce br)
;; This function recursively
;; discards denominators whose reciprocals are greater than r
;; and reserves denominators whose reciprocals are greater than diff.
;; In a reduced branch, no denominator will have a reciprocal that is
;; greater than r or diff.
(define (recur r diff denoms rsvd)
(cond [(or (<= r 0) (<= diff 0))
(list r diff denoms rsvd)]
[else
(let ([denoms<1/r (filter (lambda (x) (< x (/ 1 r))) denoms)]
[denoms<1/diff (filter (lambda (x) (< x (/ 1 diff))) denoms)])
(cond [(and (null? denoms<1/r) (null? denoms<1/diff))
(list r diff denoms rsvd)]
[(null? denoms<1/diff) ; denoms<1/r is not null and we need to discard them
(recur r
(- diff (rec-sum denoms<1/r))
(remp (lambda (x) (< x (/ 1 r))) denoms)
rsvd)]
[else ; denoms<1/diff is not null and we need to reserve them
(recur (- r (rec-sum denoms<1/diff))
diff
(remp (lambda (x) (< x (/ 1 diff))) denoms)
(append rsvd denoms<1/diff))]))]))
(let* ([result (recur (br-r br)
(br-diff br)
(br-denoms br)
(br-rsvd br))]
[new-r (car result)]
[new-diff (cadr result)]
[new-denoms (caddr result)]
[new-rsvd (cadddr result)])
(make-br (sum new-denoms)
(rec-sum new-denoms)
new-r
(br-original-r br)
new-diff
(cond [(integer? new-diff) #f]
[else
(greatest-prime-power
(factor (denominator new-diff)))]) ;gpp
(rec-sum new-rsvd)
new-rsvd
new-denoms
(cond [(zero? new-diff)
(sort < (append new-rsvd new-denoms))]
[(zero? new-r) (sort < new-rsvd)]
[else #f])
)))
(define (br-display br)
(printf " original r: ~s\n"
(br-original-r br))
(printf " r: ~s\n"
(br-r br))
(printf " sum of denominators: ~s\n"
(br-sum-denoms br))
(printf " reciprocal sum of denominators: ~s\n"
(br-rs-denoms br))
(printf " difference (reciprocal sum of denominators - r): ~10f\n"
(br-diff br))
(printf " factorization of denominator of difference: ~s\n"
(factor (denominator (br-diff br))))
(printf "greatest prime power in denominator of difference: ~s\n"
(br-gpp br))
(printf " reserved denominators: ~s\n"
(br-rsvd br))
(printf " remaining denominators: ~s\n"
(br-denoms br))
(printf " solution to r: ~s\n"
(br-denoms-sol br)))