Arthur Barraux
60 lines
1.5 KiB
Scheme
60 lines
1.5 KiB
Scheme
; PROBLEW
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; W - maximum bag weight
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; {m_1, m_2, ... m_n} = item weights
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; {v_1, v_2, ... v_n} = item values
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; want to choose a subset I so that
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; sum m_i <= W
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; and
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; sum v_i is maximized
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; In other words, if we choose another subset J
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; then sum v_j <= sum v_i
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(define (rand-item max-weight max-cost)
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(cons (random max-weight)
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(random max-cost)))
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(define (build-items n)
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(if (= n 0)
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'()
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(cons (rand-item 100 100)
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(build-items (- n 1)))))
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;(random-seed! (GET-UNIVERSAL-TIME))
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;(define items (build-items 10))
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(define items '((23 . 505) (26 . 352) (18 . 220) (32 . 354) (27 . 414) (29 . 498) (26 . 545) (30 . 473) (27 . 543)))
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(define (knapsack remaining items)
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(if (or (null? items) (<= remaining 0))
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0
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(let ((weight (car (car items)))
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(val (cdr (car items))))
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(max
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(if (>= (- remaining weight) 0)
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(+ val (knapsack (- remaining weight) (cdr items)))
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0)
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(knapsack remaining (cdr items))))))
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(display (knapsack 67 items))
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(assert (= (knapsack 67 items) 1270))
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; https://en.wikipedia.org/wiki/Levenshtein_distance
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(define (edit-distance-list a b eq?)
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(cond ((null? a) (length b))
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((null? b) (length a))
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(else (min
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(+ 1 (edit-distance-list (cdr a) b eq?)) ; insert
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(+ 1 (edit-distance-list a (cdr b) eq?)) ; delete
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(+
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(if (eq? (car a) (car b)) 0 1) ; replace if needed
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(edit-distance-list (cdr a) (cdr b) eq?))))))
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(define (edit-distance a b)
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(edit-distance-list (string->list a) (string->list b) char=?))
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(==> (edit-distance "kitten" "sitting") 3)
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