Binary Search Tree (BST) 15 < > 7 17 3 9 19 What is - - PowerPoint PPT Presentation

Binary Search Tree (BST)

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What is the inorder traversal

• f a BST?

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BST Definition

BST is a binary tree Each node stores a value from an ordered domain, e.g., numbers or strings The value of any node is ≥ all values in the left subtree, and ≤ all values in the right subtree

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BST ADT

Initialize() – Initializes an empty BST Find(x) – Searches for x in the tree and returns true or false Insert(x) – Inserts the value x into the BST Delete(x) – Deletes the value x from the tree if it is in the tree FindMin() – Returns the minimum value in the tree without deleting it FindMax() – Returns the maximum value in the tree without deleting it

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BST.Find

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Find 8 Find 14

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BST.Find

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bool find(Node* node, T x) { if (node == null) return false; if (x == node.value) return true; if (x < node.value) find(node.____, x); if (x > node.value) find(node.____, x); }

BST.Find

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bool find(Node* node, T x) { if (node == null) return false; if (x == node.value) return true; if (x < node.value) find(node.left, x); if (x > node.value) find(node.right, x); } FindMin() FindMax()

BST.Insert

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Insert 18

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BST.Insert

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Insert 14

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BST.Remove

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Remove 11

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BST.Remove

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Remove 9

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BST.Remove

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Remove 7

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BST.Remove

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Remove 7

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BST.Remove

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Remove 7

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BST.Remove

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Remove 7

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BST.Remove

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Remove 7

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Analysis of BST Algorithms

Operations:

Find Insert FindMin FindMax Delete

All O(h) where h is the height of the tree h = O(n) (worst case) h = Ω(log n) (best case) How to guarantee O(log n) performance?

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