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Problem of the Day  Can you move exactly one glass to arrange the glasses containing orange juice to be next to one another?

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Presentation on theme: "Problem of the Day  Can you move exactly one glass to arrange the glasses containing orange juice to be next to one another?"— Presentation transcript:

1 Problem of the Day  Can you move exactly one glass to arrange the glasses containing orange juice to be next to one another?

2 Problem of the Day  Can you move exactly one glass to arrange the glasses containing orange juice to be next to one another?  Take the 2 nd glass & pour it into the 5 th glass!

3 CSC 212 – Data Structures

4 Trees  Represent hierarchical relationships  Parent-child basis of this abstract data type  Real-world example: organization chart IdiotKiss-upUseless Unknown Lead ?Blob Carbon Rod Lackey Boot-LickThief DroneMoron Worker Hard Worker Knowledgeable Person You

5 Traversing Linear Collections  Trees are another Collection of data  Position s required in the Tree ADT methods  ADT uses generic type to specify type of element  Want to iterate through tree’s elements  Not required, but order obvious for linear structures  Follow IndexList ’s indices from lowest to highest  Iterator for NodeList follows Position s

6 Traversing Linear Collections  Trees are another Collection of data  Position s required in the Tree ADT methods  ADT uses generic type to specify type of element  Want to iterate through tree’s elements  Not required, but order obvious for linear structures  Follow IndexList ’s indices from lowest to highest  Iterator for NodeList follows Position s Tree s? But how do we do this for Tree s?

7 Tree Traversals  Several different, predictable orderings  Preorder honors thy elders and treats them well

8 Tree Traversals  Several different, predictable orderings  Preorder honors thy elders and treats them well  This traversal will start with parent THEN do kids

9 Tree Traversals  Several different, predictable orderings  Preorder honors thy elders and treats them well start with parent THEN do kids  This traversal will start with parent THEN do kids

10 Tree Traversals  Several different, predictable orderings  Preorder honors thy elders and treats them well start with parent THEN do kids  This traversal will start with parent THEN do kids

11 Preorder Traversal Algorithm preOrder(tree, v) /* Process v */ foreach (w : v.children()) preOrder(tree, w); Table of Contents Chapter 1Appendix A Chapter 2 Section 2.1Section 2.2 Section 1.1 Section 1.2 Section 1.2.1Section 1.2.2Section 1.2.3

12 Preorder Traversal Algorithm preOrder(tree, v) /* Process v */ foreach (w : v.children()) preOrder(tree, w); Table of Contents Chapter 1Appendix A Chapter 2 Section 2.1Section 2.2 Section 1.1 Section 1.2 Section 1.2.1Section 1.2.2Section 1.2.3

13 Preorder Traversal Table of Contents Chapter 1Appendix A Chapter 2 Section 2.1Section 2.2 Section 1.1 Section 1.2 Section 1.2.1Section 1.2.2Section 1.2.3 Algorithm preOrder(tree, v) /* Process v */ foreach (w : v.children()) preOrder(tree, w);

14 Preorder Traversal Table of Contents Chapter 1Appendix A Chapter 2 Section 2.1Section 2.2 Section 1.1 Section 1.2 Section 1.2.1Section 1.2.2Section 1.2.3 Algorithm preOrder(tree, v) /* Process v */ foreach (w : v.children()) preOrder(tree, w);

15 Preorder Traversal Table of Contents Chapter 1Appendix A Chapter 2 Section 2.1Section 2.2 Section 1.1 Section 1.2 Section 1.2.1Section 1.2.2Section 1.2.3 Algorithm preOrder(tree, v) /* Process v */ foreach (w : v.children()) preOrder(tree, w);

16 Preorder Traversal Table of Contents Chapter 1Appendix A Chapter 2 Section 2.1Section 2.2 Section 1.1 Section 1.2 Section 1.2.1Section 1.2.2Section 1.2.3 Algorithm preOrder(tree, v) /* Process v */ foreach (w : v.children()) preOrder(tree, w);

17 Preorder Traversal Table of Contents Chapter 1Appendix A Chapter 2 Section 2.1Section 2.2 Section 1.1 Section 1.2 Section 1.2.1Section 1.2.2Section 1.2.3 Algorithm preOrder(tree, v) /* Process v */ foreach (w : v.children()) preOrder(tree, w);

18 Preorder Traversal Table of Contents Chapter 1Appendix A Chapter 2 Section 2.1Section 2.2 Section 1.1 Section 1.2 Section 1.2.1Section 1.2.2Section 1.2.3 Algorithm preOrder(tree, v) /* Process v */ foreach (w : v.children()) preOrder(tree, w);

19 Preorder Traversal Table of Contents Chapter 1Appendix A Chapter 2 Section 2.1Section 2.2 Section 1.1 Section 1.2 Section 1.2.1Section 1.2.2Section 1.2.3 Algorithm preOrder(tree, v) /* Process v */ foreach (w : v.children()) preOrder(tree, w);

20 Preorder Traversal Table of Contents Chapter 1Appendix A Chapter 2 Section 2.1Section 2.2 Section 1.1 Section 1.2 Section 1.2.1Section 1.2.2Section 1.2.3 Algorithm preOrder(tree, v) /* Process v */ foreach (w : v.children()) preOrder(tree, w);

21 Preorder Traversal Table of Contents Chapter 1Appendix A Chapter 2 Section 2.1Section 2.2 Section 1.1 Section 1.2 Section 1.2.1Section 1.2.2Section 1.2.3 Algorithm preOrder(tree, v) /* Process v */ foreach (w : v.children()) preOrder(tree, w);

22 Preorder Traversal Table of Contents Chapter 1Appendix A Chapter 2 Section 2.1Section 2.2 Section 1.1 Section 1.2 Section 1.2.1Section 1.2.2Section 1.2.3 Algorithm preOrder(tree, v) /* Process v */ foreach (w : v.children()) preOrder(tree, w);

23 Preorder Traversal Table of Contents Chapter 1Appendix A Chapter 2 Section 2.1Section 2.2 Section 1.1 Section 1.2 Section 1.2.1Section 1.2.2Section 1.2.3 Algorithm preOrder(tree, v) /* Process v */ foreach (w : v.children()) preOrder(tree, w);

24 Preorder Traversal  Visit node first, then visit its children  Normal ordering found in every chapter book  Start each section before going into contents: Table of Contents §1, §1.1, §1.2, §1.2.1, §1.2.2, §1.2.3 §2, §2.1, §2.2 Appendix A

25 Tree Traversals  Several different, predictable orderings  Preorder honors thy elders and treats them well  Morals also important: postorder places children first

26 Postorder Traversal  Several different, predictable orderings  Postorder places children first: morals also important  For postorder traversal do children THEN do parent

27 Postorder Traversal  Several different, predictable orderings  Postorder places children first: morals also important do children THEN do parent  For postorder traversal do children THEN do parent

28 Postorder Traversal  Several different, predictable orderings  Postorder places children first: morals also important do children THEN do parent  For postorder traversal do children THEN do parent

29 Postorder Traversal Csc212/ Activities/Midterm1.tex Projects/ Project01.texProject02.tex Activity01.tex Activity02/ Problems.texSolution.texSolution02.png Algorithm postOrder(tree, v) foreach (w : v.children()) postOrder(tree, w); /* Process v */

30 Postorder Traversal Csc212/ Activities/Midterm1.tex Projects/ Project01.texProject02.tex Activity01.tex Activity02/ Problems.texSolution.texSolution02.png Algorithm postOrder(tree, v) foreach (w : v.children()) postOrder(tree, w); /* Process v */

31 Postorder Traversal Csc212/ Activities/Midterm1.tex Projects/ Project01.texProject02.tex Activity01.tex Activity02/ Problems.texSolution.texSolution02.png Algorithm postOrder(tree, v) foreach (w : v.children()) postOrder(tree, w); /* Process v */

32 Postorder Traversal Csc212/ Activities/Midterm1.tex Projects/ Project01.texProject02.tex Activity01.tex Activity02/ Problems.texSolution.texSolution02.png Algorithm postOrder(tree, v) foreach (w : v.children()) postOrder(tree, w); /* Process v */

33 Postorder Traversal Csc212/ Activities/Midterm1.tex Projects/ Project01.texProject02.tex Activity01.tex Activity02/ Problems.texSolution.texSolution02.png Algorithm postOrder(tree, v) foreach (w : v.children()) postOrder(tree, w); /* Process v */

34 Postorder Traversal Csc212/ Activities/Midterm1.tex Projects/ Project01.texProject02.tex Activity01.tex Activity02/ Problems.texSolution.texSolution02.png Algorithm postOrder(tree, v) foreach (w : v.children()) postOrder(tree, w); /* Process v */

35 Postorder Traversal Csc212/ Activities/Midterm1.tex Projects/ Project01.texProject02.tex Activity01.tex Activity02/ Problems.texSolution.texSolution02.png Algorithm postOrder(tree, v) foreach (w : v.children()) postOrder(tree, w); /* Process v */

36 Postorder Traversal Csc212/ Activities/Midterm1.tex Projects/ Project01.texProject02.tex Activity01.tex Activity02/ Problems.texSolution.texSolution02.png Algorithm postOrder(tree, v) foreach (w : v.children()) postOrder(tree, w); /* Process v */

37 Postorder Traversal Csc212/ Activities/Midterm1.tex Projects/ Project01.texProject02.tex Activity01.tex Activity02/ Problems.texSolution.texSolution02.png Algorithm postOrder(tree, v) foreach (w : v.children()) postOrder(tree, w); /* Process v */

38 Postorder Traversal Csc212/ Activities/Midterm1.tex Projects/ Project01.texProject02.tex Activity01.tex Activity02/ Problems.texSolution.texSolution02.png Algorithm postOrder(tree, v) foreach (w : v.children()) postOrder(tree, w); /* Process v */

39 Postorder Traversal Csc212/ Activities/Midterm1.tex Projects/ Project01.texProject02.tex Activity01.tex Activity02/ Problems.texSolution.texSolution02.png Algorithm postOrder(tree, v) foreach (w : v.children()) postOrder(tree, w); /* Process v */

40 Postorder Traversal Csc212/ Activities/Midterm1.tex Projects/ Project01.texProject02.tex Activity01.tex Activity02/ Problems.texSolution.texSolution02.png Algorithm postOrder(tree, v) foreach (w : v.children()) postOrder(tree, w); /* Process v */

41 Postorder Traversal  Node visits children before it is processed  Needed to compute directory’s disk space  First look at size of contents then the main directory  Important whenever leaves contain actual data  Visits external nodes, then works way up the tree  In this traversal, after its descendants node processed

42 Binary Trees  Pre- & post-order identical for binary trees  Also offer additional type of traversal  Traversals used again, so do not let this slip  Equation trees are canonical examples  Using them, the different approaches can be seen  Lets (old) Professors reminisce over HP calculators  Kind of stupid, but is actually used in programs

43 Inorder Traversal    1 63 42 Algorithm inOrder(tree, v) if (tree.hasLeft(v)) inOrder(tree, tree.left(v)) /* Process v */ if (tree.hasRight(v)) inOrder(tree, tree.right(v));

44 Inorder Traversal    1 63 42 Algorithm inOrder(tree, v) if (tree.hasLeft(v)) inOrder(tree, tree.left(v)) /* Process v */ if (tree.hasRight(v)) inOrder(tree, tree.right(v));

45 Inorder Traversal    1 63 42 Algorithm inOrder(tree, v) if (tree.hasLeft(v)) inOrder(tree, tree.left(v)) /* Process v */ if (tree.hasRight(v)) inOrder(tree, tree.right(v));

46 Inorder Traversal    1 63 42 Algorithm inOrder(tree, v) if (tree.hasLeft(v)) inOrder(tree, tree.left(v)) /* Process v */ if (tree.hasRight(v)) inOrder(tree, tree.right(v));

47 Inorder Traversal    1 63 42 Algorithm inOrder(tree, v) if (tree.hasLeft(v)) inOrder(tree, tree.left(v)) /* Process v */ if (tree.hasRight(v)) inOrder(tree, tree.right(v));

48 Inorder Traversal    1 63 42 Algorithm inOrder(tree, v) if (tree.hasLeft(v)) inOrder(tree, tree.left(v)) /* Process v */ if (tree.hasRight(v)) inOrder(tree, tree.right(v));

49 Inorder Traversal    1 63 42 Algorithm inOrder(tree, v) if (tree.hasLeft(v)) inOrder(tree, tree.left(v)) /* Process v */ if (tree.hasRight(v)) inOrder(tree, tree.right(v));

50 Inorder Traversal  Traversal visits equation in proper order: (1 + (6 * 3)) - (4 / 2)  Binary search trees use this again & again    1 63 42 Algorithm inOrder(tree, v) if (tree.hasLeft(v)) inOrder(tree, tree.left(v)) /* Process v */ if (tree.hasRight(v)) inOrder(tree, tree.right(v));

51 Postorder Traversal Algorithm postOrder(tree, v) if (tree.hasLeft(v)) postOrder(tree, tree.left(v)) if (tree.hasRight(v)) postOrder(tree, tree.right(v)); /* Process v */    1 63 42

52 Postorder Traversal  Traversal follows order equation is computed: 1 6 3 * + 4 2 / -  Java compiles equations using this format    1 63 42 Algorithm postOrder(tree, v) if (tree.hasLeft(v)) postOrder(tree, tree.left(v)) if (tree.hasRight(v)) postOrder(tree, tree.right(v)); /* Process v */

53 Your Turn  Get into your groups and complete activity

54 For Next Lecture  Week #12 assignment due tomorrow  Programming Assignment #3  Programming Assignment #3 available  Have a great thanksgiving!

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