lec17 - Static Dictionaries Collection of items Each item...

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Static Dictionaries Collection of items. Each item is a pair. (key, element) Pairs have different keys. Operations are: initialize/create get (search) Each item/key/element has an estimated access frequency (or probability). Consider binary search tree only.

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Example Key Probability a 0.8 b 0.1 c 0.1 a < b < c Cost = 0.8 * 2 + 0.1 * 1 + 0.1 * 2 = 1.9 Cost = 0.8 * 1 + 0.1 * 2 + 0.1 * 3 = 1.2
Search Types Successful. Search for a key that is in the dictionary. Terminates at an internal node. Unsuccessful. Search for a key that is not in the dictionary. Terminates at an external/failure node. f 0 a b c f 1 f 2 f 3

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Internal And External Nodes A binary tree with n internal nodes has n + 1 external nodes. Let s 1 , s 2 , …, s n be the internal nodes, in inorder. key(s 1 ) < key(s 2 ) < … < key(s n ) . Let key(s 0 ) = –infinity and key(s n+1 ) = infinity . Let f 0 , f 1 , …, f n be the external nodes, in inorder. f i is reached iff key(s i ) < search key < key(s i+1 ) . f 0 a b c f 1 f 2 f 3
Cost Of Binary Search Tree Let p i = probability for key(s i ) .

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• Spring '10
• sartajsahani
• TI, weighted path length, cik-1 + ckj

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