2021-08-01 22:15:58 -04:00
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(with_import "./match.kp"
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(let (
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2021-08-01 23:48:41 -04:00
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; This is based on https://www.cs.cornell.edu/courses/cs3110/2020sp/a4/deletion.pdf
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; and the figure references refer to it
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; Insert is taken from the same paper, but is origional to Okasaki, I belive
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; I think this is actually pretty cool - instead of having a bunch of seperate ['B]
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; be our leaf node, we use ['B] with all nils. This allows us to not use -B, as
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; both leaf and non-leaf 'BB has the same structure with children! Also, we make
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; sure to use empty itself so we don't make a ton of empties...
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empty ['B nil nil nil]
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E empty
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EE ['BB nil nil nil]
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2021-08-01 22:15:58 -04:00
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contains? (rec-lambda recurse (t v) (match t
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2021-08-01 23:48:41 -04:00
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~E false
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2021-08-01 22:15:58 -04:00
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[c a x b] (cond (< v x) (recurse a v)
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(= v x) true
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true (recurse b v))))
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blacken (lambda (t) (match t
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['R a x b] ['B a x b]
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t t))
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balance (lambda (t) (match t
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; figures 1 and 2
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2021-08-01 22:15:58 -04:00
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['B ['R ['R a x b] y c] z d] ['R ['B a x b] y ['B c z d]]
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['B ['R a x ['R b y c]] z d] ['R ['B a x b] y ['B c z d]]
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['B a x ['R ['R b y c] z d]] ['R ['B a x b] y ['B c z d]]
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['B a x ['R b y ['R c z d]]] ['R ['B a x b] y ['B c z d]]
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; figure 8, double black cases
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['BB ['R a x ['R b y c]] z d] ['B ['B a x b] y ['B c z d]]
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['BB a x ['R ['R b y c] z d]] ['B ['B a x b] y ['B c z d]]
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; already balenced
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2021-08-01 22:15:58 -04:00
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t t))
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insert (lambda (t v) (let (
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ins (rec-lambda ins (t) (match t
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2021-08-01 23:48:41 -04:00
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~E ['R t v t]
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2021-08-01 22:15:58 -04:00
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[c a x b] (cond (< v x) (balance [c (ins a) x b])
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(= v x) [c a x b]
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true (balance [c a x (ins b)]))))
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) (blacken (ins t))))
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2021-08-01 23:48:41 -04:00
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rotate (lambda (t) (match t
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; case 1, fig 6
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['R ['BB a x b] y ['B c z d]] (balance ['B ['R ['B a x b] y c] z d])
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['R ['B a x b] y ['BB c z d]] (balance ['B a x ['R b y ['B c z d]]])
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; case 2, figure 7
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['B ['BB a x b] y ['B c z d]] (balance ['BB ['R ['B a x b] y c] z d])
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['B ['B a x b] y ['BB c z d]] (balance ['BB a x ['R b y ['B c z d]]])
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; case 3, figure 9
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['B ['BB a w b] x ['R ['B c y d] z e]] ['B (balance ['B ['R ['B a w b] x c] y d]) z e]
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['B ['R a w ['B b x c]] y ['BB d z e]] ['B a w (balance ['B b x ['R c y ['B d z e]]])]
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; fall through
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t t))
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redden (lambda (t) (match t
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['B a x b] (if (and (= 'B (idx a 0)) (= 'B (idx b 0))) ['R a x b]
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t)
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t t))
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min_delete (rec-lambda recurse (t) (match t
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~E (error "min_delete empty tree")
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['R ~E x ~E] [x E]
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['B ~E x ~E] [x EE]
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['B ~E x ['R a y b]] [x ['B a y b]]
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[c a x b] (let ((v ap) (recurse a)) [v (rotate [c ap x b])])))
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delete (lambda (t v) (let (
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del (rec-lambda del (t v) (match t
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; figure 3
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~E t
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; figure 4
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['R ~E ~v ~E] E
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['B ['R a x b] ~v ~E] ['B a x b]
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; figure 5
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['B ~E ~v ~E] EE
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[c a x b] (cond (< v x) (rotate [c (del a v) x b])
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(= v x) (let ((vp bp) (min_delete b))
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(rotate [c a vp bp]))
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true (rotate [c a x (del b v)]))))
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) (del (redden t) v)))
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)
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2021-08-01 23:48:41 -04:00
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(provide empty contains? insert delete)
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2021-08-01 22:15:58 -04:00
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))
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