14 how how many nodes do we we inspect examples

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 03/06/2014 for the course ECE 368 at Purdue.

Ask a homework question - tutors are online