Count primitive that extracts value of count count

Unformatted text preview: ind Kth element Add Count field to each node ! Count(): primitive that extracts value of Count(): count count from specified node ! Find_Kth(Node, k) if if ( (Empty(Left_Child(Node)) && && (Empty(Right_Child(Node))) return Info(Node) if (k <= Count(Node)) return Find_Kth(Left_Child(Node), k) return Find_Kth(Right_Child(Node), k – Count(Node)) 12 Add_Kth(Node, Info, k) if (Empty(Node)) return Create(Info, null, null) if ( (Empty(Left_Child(Node)) && (Empty(Right_Child(Node))) B1 ← Create(Info, null, null) if (k == 1) B2 ← Create(Info, B1, Node) else B2 ← Create(Info, Node, B1) Count(B2) ← 1 return B2 if (k <= Count(Node)) Left_Child(Node) ← Add_Kth(Left_Child(Node), Info, k) Count(Node) ← Count(Node) + 1 return Node else Right_Child(Node) ← Add_Kth(Right_Child(Node), Info, k – Count(Node)) 13 return Node Example of Add_Kth() ! Add_Kth(Root, Z, 4): 3 (Z, 4) " Right (Z, 1) " Left Create (Z, , ) Create (Z, B1, D) Count = 1 1 Z 1 A 1 B Z 1 D E C 14 Example of Add_Kth() ! Add_Kth(Root, Z, 4): 3 (Z, 4) " Right (Z, 1) " Left update Left update Count 1 1 A 1 B Z 2 1 D E C 15 Example of Add_Kth() ! Add_Kth(Root, Z, 4): 3 (Z, 4) " Right 1 A Done! 2 1 B 1 C Z E D 16 Notes Notes on Lists as BTs ! Time Complexity – Due to the same properties of BST, all three Due functions functions on average function in O(log2n) O(log ! Memory efficiency – Need to store n-1 additional nodes (non-leaf leaf node) node) – About half of memory is “wasted” 17...
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