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General Trees

General Trees. Root. Make Money Fast!. Bank Robbery. Stock Fraud. Ponzi Scheme. Root. 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

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General Trees

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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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