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Tree Data Structures: A Comprehensive Guide

Learn about tree data structures, terminologies, ADT, traversal methods, and iterative implementations. Explore examples of trees in file systems, organization charts, and programming applications. Master the concepts of roots, internal and external nodes, ancestors, height, and subtrees. Dive deep into preorder and postorder traversals with hands-on demos. This comprehensive guide is ideal for beginners and advanced learners in computer science.

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Tree Data Structures: A Comprehensive Guide

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  1. General Trees Root Make Money Fast! BankRobbery StockFraud PonziScheme Root Trees

  2. Computers”R”Us Sales Manufacturing R&D US International Laptops Desktops Europe Asia Canada What is a Tree Root • In CS, a tree is an abstract model of a hierarchical structure • A tree consists of nodes with a parent-child relation • Applications: • Organization charts • File systems • Function invocation in programming Trees

  3. A C D B E G H F K I J Tree Terminologies • Root: node without parent (A) • Internal node: node with at least one child (A, B, C, F) • External node (a.k.a. leaf): node without children (E, I, J, K, G, H, D) • Ancestors of a node: parent, grandparent, grand-grandparent, etc. • Depth (or level) of a node: number of ancestors • Height of a tree: maximum depth of any node • Descendant of a node: child, grandchild, grand-grandchild, etc. • Subtree: tree consisting of a node and its descendants Subtree Trees

  4. Examples of Trees • File system • Internal nodes: directories (folders) • External nodes: files Trees

  5. Tree ADT • Query methods: • boolean p.isRoot() • boolean p.isExternal() • Additional methods may be defined for specific applications • We use positions to access nodes • Generic methods: • integer size() • boolean empty() • Accessor methods: • position root() • list<position> positions() • Position-based methods: • position p.parent() • list<position> p.children() position = pointer list = linked list or vector Trees

  6. Trees

  7. Preorder Traversal • A traversal visits the nodes of a tree in a systematic manner • Preorder traversal: a node is visited before its descendants • Application: print a structured document AlgorithmpreOrder(v) visit(v) foreachchild w of v preOrder (w) 1 Quiz! Make Money Fast! 2 5 9 1. Motivations 2. Methods References 6 7 8 3 4 2.3 BankRobbery 2.1 StockFraud 2.2 PonziScheme 1.1 Greed 1.2 Avidity Trees

  8. Preorder Traversal: Example • How to print this document? Trees

  9. Postorder Traversal • Postorder traversal: a node is visited after its descendants • Application: compute space used by files in a directory and its subdirectories AlgorithmpostOrder(v) foreachchild w of v postOrder (w) visit(v) Quiz! 9 cs16/ 8 3 7 todo.txt1K homeworks/ programs/ 4 5 6 1 2 h1c.doc3K h1nc.doc2K Robot.cpp20K DDR.cpp10K Stocks.cpp25K Trees

  10. Postorder Traversal: Example Trees

  11. Comparison • Preorder • Euler Tour Traversal • Preorder: Visit a node at the first sight • Postorder: Visit a node at the last sight • Postorder B E F K I J Trees

  12. Iterative Implementation of Preorder Traversal • Steps • Push the root to the stack • Pop the stack and visit it • Push the children in a reverse order (via the use of another stack) • Repeat 2) and 3) until the stack is empty See the animation in the subsequent slides! Trees

  13. A C D B E G H F K I J Iterative Implementation of Preorder Traversal: Demo A Stack Preorder: Trees

  14. A C D B E G H F K I J Iterative Implementation of Preorder Traversal: Demo B C D By using another stack Preorder: A Trees

  15. A C D B E G H F K I J Iterative Implementation of Preorder Traversal: Demo E F C D Preorder: A B Trees

  16. A C D B E G H F K I J Iterative Implementation of Preorder Traversal: Demo F C D Preorder: A B E Trees

  17. A C D B E G H F K I J Iterative Implementation of Preorder Traversal: Demo I J K C D Preorder: A B E F Trees

  18. A C D B E G H F K I J Iterative Implementation of Preorder Traversal: Demo J K C D Preorder: A B E F I Trees

  19. A C D B E G H F K I J Iterative Implementation of Preorder Traversal: Demo K C D Preorder: A B E F I J Trees

  20. A C D B E G H F K I J Iterative Implementation of Preorder Traversal: Demo C D Preorder: A B E F I J k Trees

  21. A C D B E G H F K I J Iterative Implementation of Preorder Traversal: Demo G H D Preorder: A B E F I J k C Trees

  22. A C D B E G H F K I J Iterative Implementation of Preorder Traversal: Demo H D Preorder: A B E F I J k C G Trees

  23. A C D B E G H F K I J Iterative Implementation of Preorder Traversal: Demo D Preorder: A B E F I J k C G H Trees

  24. A C D B E G H F K I J Iterative Implementation of Preorder Traversal: Demo Preorder: A B E F I J k C G H D Trees

  25. A C D B E G H F K I J Iterative Implementation of Preorder Traversal: Demo Done! Preorder: A B E F I J k C G H D Trees

  26. Iterative Implementation of Postorder Traversal • Steps • Push the root node to stack1 . • Pop a node from stack 1, and push it to stack 2. • Then push its children sequentially to stack 1. • Repeat step 2) and 3) until stack 1 is empty. • Pop all nodes from stack 2 to obtain the traversal in postorder. See the animation in the subsequent slides! Trees

  27. A C D B E G H F K I J Iterative Implementation of Postorder Traversal: Demo A Stack 1 Stack 2 Trees

  28. A C D B E G H F K I J Iterative Implementation of Postorder Traversal: Demo D C B A Stack 1 Stack 2 Trees

  29. A C D B E G H F K I J Iterative Implementation of Postorder Traversal: Demo C B D A Stack 1 Stack 2 Trees

  30. A C D B E G H F K I J Iterative Implementation of Postorder Traversal: Demo H G B C D A Stack 1 Stack 2 Trees

  31. A C D B E G H F K I J Iterative Implementation of Postorder Traversal: Demo G B H C D A Stack 1 Stack 2 Trees

  32. A C D B E G H F K I J Iterative Implementation of Postorder Traversal: Demo B G H C D A Stack 1 Stack 2 Trees

  33. A C D B E G H F K I J Iterative Implementation of Postorder Traversal: Demo F E B G H C D A Stack 1 Stack 2 Trees

  34. A C D B E G H F K I J Iterative Implementation of Postorder Traversal: Demo K J I E F B G H C D A Stack 1 Stack 2 Trees

  35. A C D B E G H F K I J Iterative Implementation of Postorder Traversal: Demo J I E K F B G H C D A Stack 1 Stack 2 Trees

  36. A C D B E G H F K I J Iterative Implementation of Postorder Traversal: Demo I E J K F B G H C D A Stack 1 Stack 2 Trees

  37. A C D B E G H F K I J Iterative Implementation of Postorder Traversal: Demo E I J K F B G H C D A Stack 1 Stack 2 Trees

  38. A C D B E G H F K I J Iterative Implementation of Postorder Traversal: Demo E I J K F B G H C D A Stack 1 Stack 2 Trees

  39. A C D B E G H F K I J Iterative Implementation of Postorder Traversal: Demo E I J K F B G H C D A By popping all elements in stack 2 Stack 1 Stack 2 Postorder: E I J K F B G H C D A Trees

  40. A B C D E G H F I J K Other Traversal • Breadth-first traversal (aka level-order traversal) • Idea: Visit all the nodes at depth d before visiting the nodes at depth d+1 • Implementation: Using a queue level-order traversal: A B C D E F G H I J K Trees

  41. A C D B E G H F K I J Breadth-first Traversal: Demo Front End Queue A Output: Trees

  42. A C D B E G H F K I J Breadth-first Traversal: Demo Queue BCD Output: A Trees

  43. A C D B E G H F K I J Breadth-first Traversal: Demo Queue CDEF Output: AB Trees

  44. A C D B E G H F K I J Breadth-first Traversal: Demo Queue DEFGH Output: ABC Trees

  45. A C D B E G H F K I J Breadth-first Traversal: Demo Queue EFGH Output: ABCD Trees

  46. A C D B E G H F K I J Breadth-first Traversal: Demo Queue FGH Output: ABCDE Trees

  47. A C D B E G H F K I J Breadth-first Traversal: Demo Queue GHIJK Output: ABCDEF Trees

  48. A C D B E G H F K I J Breadth-first Traversal: Demo Queue HIJK Output: ABCDEFG Trees

  49. A C D B E G H F K I J Breadth-first Traversal: Demo Queue IJK Output: ABCDEFGH Trees

  50. A C D B E G H F K I J Breadth-first Traversal: Demo Queue JK Output: ABCDEFGHI Trees

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