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Data Structure (Tree)
Tree is a non-linear data structure that can represent hierarchical relationships. It consists of nodes connected by edges. The root node has child nodes, and nodes may be leaf nodes or have child nodes themselves. Binary trees restrict nodes to having at most two children. General trees can be converted to binary trees by making the first child the left child and next siblings the right child. Binary trees can be built from input data by comparing values to determine left or right placement, or from traversal operations.
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Introduction to tree data structure, its non-linear properties, and hierarchical representation.
Components of tree such as root, leaf, level, subtree, node, and edge.
Terminology related to trees: predecessor, successor, ancestor, descendant, parent, sibling.
Introduction to binary trees, their characteristics, and definitions of full and complete binary trees.
Methods to create binary trees from input data, including examples and explanation of binary search trees.
Process of converting general trees to binary trees, including representation and linked list forms.
Exercises on making binary trees from a general tree and from a data statement.
Contact details for Adam M.B. including email and blog for further inquiries.
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Data Structure (Tree)
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- 3. Tree Tree is datastructure that is non linear and can be used to represents data in hierarchy between those elements. For example: organization structure, family tree, and the tournament.
- 4. Components of Tree A BC D E F G Root (akar) Leaf (daun) Level/Tingkat 1 2 3 Subtree Node/Vertex/Simpul Edge/Link
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- 6. Terminology of Tree •Predecessor node that is above certain node. • Successor node that is below certain node • Ancestor all nodes that is before certain node and in the same path. • Descendant all nodes that is after certain node and in the same path.
- 7. Terminology of Tree •Parent predecessor that is one level above certain node. • Sibling nodes that have same parent • Degree number of child in one node.
- 8. Ilustration Predecessor(B) : A Successor(A): B,C,D Ancestor(E) : B,A Descendant(B) : E,F A B C D E F G Parent(E) : B Sibling(E) : F Degree(A) : 3
- 9. Binary Tree Binary Tree The maximum degree ofone node is 2. Maximum node until level N is 2N - 1 The maximum number of node each level is 2 (N-1)
- 10. Binary Tree A B G C D EF Left Child Right Child Root Maximum node on 3rd level = 2(N-1) Maximum node until 3rd level = 2N - 1 Parent = 2(3-1) = 22 = 4 = 23- 1 = 8 - 1 = 7
- 11. Types of BinaryTree Full Binary Tree Complete Binary Tree A B G C D E F A B C D E • All nodes (except leaf) have two children. • Each subtree has same length of path. • All nodes (except leaf) have two children. • Each subtree can has different length of path.
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- 13. Making of BinaryTree • From input data • From general tree • From result of traversal process
- 14. From Input Data •If value of inserted node is bigger than parent then it will be right subtree. • If value of inserted node is smaller than parent then it will be left subtree. • This tree is known as binary search tree.
- 15. From Input Data Example: Hwill be root A < H : A will be left child of H K > H : K will be right child of H C < H C > A : C will be right child of A B < H B > A B < C : B will be left child of C L > H L > K : L will be right child of K J < H J < K : J will be left child of K H A L K B C J AH KCBLJ
- 16. Make binary treefrom these input data: • GHCKJALBEFD • KGMDLSBRJP Exercise
- 17. From General Tree •First son in general tree will be left son in binary tree • Next brother of first son in general tree will be right son in binary tree.
- 18. From General Tree GeneralTree Binary Tree A B H C D E F G I A B H CD E F GI
- 19. From General Tree(Program) One node in general tree One node in binary tree First Son (FS) Next Brother (NB) Data Field (Info) Left Son (LS) Right Son (RS) Data Field (Info)
- 20. From General Tree(Program) General Tree A B H C D E F G I General Tree (Linked List) A B Head CD F G H I E
- 21. From General Tree(Program) Binary Tree (Linked List) A B D E F C I G H Head Binary Tree A B H CD E F GI
- 22. From General Tree(Program) General Tree (Linked List) A B Head CD F G H I E Binary Tree (Linked List) Head A B D E F C I G H
- 23. Make binary treefrom this general tree: Exercise K L Y W M O X ZR N P Q
- 24. Make binary treefrom this statement: • K, C, P, E, M, B, R, G, Q, F, W • E = A + BDH – F G - K Exercise
- 25. Contact Person: Adam MukharilBachtiar Informatics Engineering UNIKOM Jalan Dipati Ukur Nomor. 112-114 Bandung 40132 Email: adfbipotter@gmail.com Blog: http://adfbipotter.wordpress.com Copyright © Adam Mukharil Bachtiar 2012