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CS 225
Data Structures
Fe February 24 – Tr Traversal
G G Carl Evans
Tr Trees aren’t new:
A X S 2 C 2 5 Y
C S X A 2 2 5 Y
Ø Ø Ø Ø Ø Ø Ø Ø Ø
CS 225 Data Structures Fe February 24 Tr Traversal G G Carl - - PowerPoint PPT Presentation
CS 225 Data Structures Fe February 24 Tr Traversal G G Carl - - PowerPoint PPT Presentation
CS 225 Data Structures Fe February 24 Tr Traversal G G Carl Evans Tr Trees arent new: C C S X S X A 2 2 5 A 2 2 5 Y Y Ho How many nul nullptrs? Theorem: If there are n data items
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Ho How many nul nullptrs?
Theorem: If there are n data items in our representation of a binary tree, then there are ___________ nullptrs.
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Ho How many nul nullptrs?
Base Cases: NULLS(0): NULLS(1): NULLS(2):
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Ho How many nul nullptrs?
Base Cases: NULLS(3):
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Ho How many nul nullptrs?
Induction Hypothesis:
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Ho How many nul nullptrs?
Consider an arbitrary tree T containing k nodes:
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Tr Traversals
*
- b
+ / c d e a
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Tr Traversals
*
- b
+ / c d e
template<class T> void BinaryTree<T>::__Order(TreeNode * cur) { } 49 50 51 52 53 54 55 56 57 58
a
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Tr Traversals
*
- b
+ / c d e
template<class T> void BinaryTree<T>::___Order(TreeNode * cur) { if (cur != NULL) { ______________________; ___Order(cur->left); ______________________; ___Order(cur->right); ______________________; } } 49 50 51 52 53 54 55 56 57 58
a
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Tr Traversals
*
- b
+ / c d e
template<class T> void BinaryTree<T>::___Order(TreeNode * cur) { if (cur != NULL) { ______________________; ___Order(cur->left); ______________________; ___Order(cur->right); ______________________; } } 49 50 51 52 53 54 55 56 57 58
a
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A D A Different T Type o
- f T
Traversal
*
- b
+ / c d e a
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template<class T> void BinaryTree<T>::levelOrder(TreeNode * root) { } 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
A D A Different T Type o
- f T
Traversal
*
- b
+ / c d e a
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Tr Traversal vs. Search
Traversal Search
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Se Search ch: Br : Breadth F First v
- vs. D
Depth F First
Strategy: Breadth First Search (BFS) Strategy: Depth First Search (DFS)
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Dic Dictio tionar ary ADT
Data is often organized into key/value pairs: UIN è Advising Record Course Number è Lecture/Lab Schedule Node è Incident Edges Flight Number è Arrival Information URL è HTML Page …
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#pragma once class Dictionary { public: private: // ... };
Dictionary.h
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Bi Binary T Tree a as a a Se Search St Stru ructure
U O M C W A T E S I N
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Bi Binary _ ___________ T Tree ( (BS BST)
A BST is a binary tree T such that:
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#pragma once template <class K, class V> class BST { public: BST(); void insert(const K key, V value); V remove(const K & key); V find(const K & key) const; TreeIterator traverse() const; private: };
BST.h
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template<class K, class V> ________________________ _find(TreeNode *& root, const K & key) const { }
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root
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template<class K, class V> ________________________ _insert(TreeNode *& root, const K & key) { }
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root
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template<class K, class 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);