14 how how many nodes do we we inspect examples

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Unformatted text preview: e), k); }; 5 BST BST search, cont. 14 How How many nodes do we we inspect? ! Examples: Examples: – BT_Search(4): 3 – BT_Search(17): 2 – BT_Search(16): 4 ! ! 9 4 17 14 8 18 15 Better Better question: What is the maximum number of nodes we need to explore to answer answer our search for any number? tree Depth + 1 6 BST BST search complexity ! ! ! ! ! ! ! Given a complete BST n (number of nodes) = 2Depth+1 – 1 (number But But with BST search, only explore at most Depth+1 Depth+1 nodes Let E = Depth+1 So n = 2E – 1, solving for E results with E = log2(n+1) ≅ log2n (n+1) Therefore, # of explored nodes <= E ≅ log2n <= Thus, Thus, BST search is O(log2n) ! 7 Follow Follow-up 4 Assumption: complete Assumption: complete BST ! What about other trees? ! – worst case: narrow tree – Example: BT_Search(19): 8 Example: BT_Search(19): (the (the number of nodes) – Complexity: O(n) Complexity: ! 8 9 14 14 In In general (if proper care is taken in balancing the tree, or selecting good pivot pivot nodes), BST are searchable in O(log2n) 15...
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This document was uploaded on 03/06/2014 for the course ECE 368 at Purdue.

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