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CS 225
Data Structures
- Feb. 23 – BST Rem
emove
Wad ade Fag agen-Ulm lmschneid ider
CS 225 Data Structures Feb. 23 BST Rem emove Wad ade Fag - - PowerPoint PPT Presentation
CS 225 Data Structures Feb. 23 BST Rem emove Wad ade Fag - - PowerPoint PPT Presentation
CS 225 Data Structures Feb. 23 BST Rem emove Wad ade Fag agen-Ulm lmschneid ider template<typename K, typename V> 1 2 3 void BST::_insert(TreeNode *& root, K & key, V & value) { 4 TreeNode *t = _find(root, key);
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template<typename K, typename V> void BST::_insert(TreeNode *& root, K & key, V & value) { TreeNode *t = _find(root, key); t = new TreeNode(key, value); } 13 10 25 12 37 38 51 40 84 89 66 95 1 2 3 4 5 6
root_
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template<typename K, typename V> void BST::_insert(TreeNode *& root, K & key, V & value) { TreeNode *t = _find(root, key); t = new TreeNode(key, value); } 13 10 25 12 37 38 51 40 84 89 66 95 1 2 3 4 5 6
root_
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template<typename K, typename V> ________________________ _remove(TreeNode *& root, const K & key) { }
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root
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remove(40);
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remove(25);
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remove(10);
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remove(13);
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BST Analysis – Running Time
Operation
BST Worst Case find insert delete traverse
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BST Analysis
Every operation that we have studied on a BST depends on the height of the tree: O(h). …what is this in terms of n, the amount of data? We need a relationship between h and n: f(n) ≤ h ≤ g(n)
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BST Analysis
Q: What is the maximum number of nodes in a tree of height h?
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BST Analysis
Q: What is the minimum number of nodes in a tree of height h? What is the maximum height for a tree
- f n nodes?
A X S 2
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BST Analysis
Therefore, for all BST: Lower bound: Upper bound:
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BST Analysis
The height of a BST depends on the order in which the data is inserted into it. ex: 1 3 2 4 5 7 6 vs. 4 2 3 6 7 1 5 Q: How many different ways are there to insert keys into a BST? Q: What is the average height of all the arrangements?
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BST Analysis
Q: How many different ways are there to insert keys into a BST? Q: What is the average height of all the arrangements?
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BST Analysis – Running Time
Operation
BST Average case BST Worst case Sorted array Sorted List find insert delete traverse
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Height-Balanced Tree
What tree makes you happier? Height balance: b = height(TL) - height(TR) A tree is height balanced if:
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