48 lines
1.6 KiB
Text
48 lines
1.6 KiB
Text
inductive Color where
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| Red
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| Black
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open Color
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inductive rbnode : Nat → Color → Type where
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| Leaf : rbnode 1 Black
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| R {h}
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(left : rbnode h Black)
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(value : Int)
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(right : rbnode h Black) : rbnode h Red
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| B {h cl cr}
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(left : rbnode h cl)
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(value : Int)
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(right : rbnode h cr) : rbnode (h+1) Black
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open rbnode
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inductive hiddenTree : Nat → Type
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| HR {h} (node : rbnode h Red) : hiddenTree h
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| HB {h} (node : rbnode (h+1) Black) : hiddenTree (h+1)
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open hiddenTree
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inductive almostNode : Nat → Type
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| LR {h cR} (left:rbnode h Red) (value:Int) (right:rbnode h cR) : almostNode h
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| RR {h cL} (left:rbnode h cL) (value:Int) (right:rbnode h Red) : almostNode h
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| V {h c} (node:rbnode h c) : almostNode h
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open almostNode
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def balanceRR (left : rbnode h c) (y : Int) (right : hiddenTree h) : almostNode h :=
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match h, c, left, right with
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| _, _, left, HR c => RR left y c
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| _, _, R a x b, HB c => LR (R a x b) y c
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| _, _, B a x b, HB c => V (R (B a x b) y c)
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| _, _, Leaf, HB c => V (R Leaf y c)
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def balanceRR' (left : rbnode h c) (y : Int) (right : hiddenTree h) : almostNode h :=
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match h, c, right, left with
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| _, _, HR c, left => RR left y c
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| _, _, HB c, R a x b => LR (R a x b) y c
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| _, _, HB c, B a x b => V (R (B a x b) y c)
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| _, _, HB c, Leaf => V (R Leaf y c)
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def balanceRR'' (left : rbnode h c) (y : Int) (right : hiddenTree h) : almostNode h :=
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match left, right with
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| left, HR c => RR left y c
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| R a x b, HB c => LR (R a x b) y c
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| B a x b, HB c => V (R (B a x b) y c)
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| Leaf, HB c => V (R Leaf y c)
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