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# 06 - Trees

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I used this set of slides for the lecture on Trees I gave at the University of Zurich for the 1st year students following the course of Formale Grundlagen der Informatik.

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### 06 - Trees

1. 1. Trees www.tudorgirba.com
2. 2. n5 n2 n6 n10 n1 n7 n4 n9 n3 n8
3. 3. n5 n2 n6 n10 n1 n7 n4 n9 n3 n8
4. 4. n5 n2 n6 n10 n1 n7 n4 n9 n3 n8
5. 5. n5 n2 n6 n10 n1 n7 n4 n9 n3 n8 edge node
6. 6. n5 n2 n6 n10 n1 n7 n4 n9 n3 n8 leaf root
7. 7. n5 n2 n6 n10 n1 n7 n4 n9 n3 n8 parent child
8. 8. n5 n2 n6 n10 n1 n7 n4 n9 n3 n8 subtree
9. 9. n5 n2 n6 n10 n1 n7 n4 n9 n3 n8 path
10. 10. n5 n2 n6 n10 n1 n7 n4 n9 n3 n8 height = 1 depth = level = 2 degree = 1
11. 11. n5 n2 n6 n10 n1 n7 n4 n9 n3 n8 height = 1 depth = level = 1 degree = 3
12. 12. n5 n2 n6 n10 n1 n7 n4 n9 n3 n8 0 1 2 3
13. 13. n5 n2 n6 n10 n1 n7 n4 n9 n3 n8 ordered tree leftmost rightmost
14. 14. n5 n2 n6 n10 n1 n7 n4 n9 n3 n8 n7 n4 n9n8 n1 n5 n4 n6 n3 n10 isomorphic trees
15. 15. n4 n2 n5 n1 n6 n3 n7 left right left leftright right
16. 16. n4 n2 n5 n1 n3 n6 n4 n2 n5 n1 n6 n3 not a binary tree binary tree n4 n2 n5 n1 n6 n3 n7 complete binary tree
17. 17. breadth-ﬁrst traversal n4 n2 n5 n1 n6 n3
18. 18. breadth-ﬁrst traversal n4 n2 n5 n1 n6 n3 1
19. 19. breadth-ﬁrst traversal n4 n2 n5 n1 n6 n3 2 1
20. 20. breadth-ﬁrst traversal n4 n2 n5 n1 n6 n3 2 3 1
21. 21. breadth-ﬁrst traversal n4 n2 n5 n1 n6 n3 2 3 4 1
22. 22. breadth-ﬁrst traversal n4 n2 n5 n1 n6 n3 2 3 4 5 1
23. 23. breadth-ﬁrst traversal n4 n2 n5 n1 n6 n3 2 3 4 65 1
24. 24. n4 n2 n5 n1 n6 n3 preorder(node) visit(node). preorder(node.left). preorder(node.right).
25. 25. n4 n2 n5 n1 n6 n3 1 preorder(node) visit(node). preorder(node.left). preorder(node.right).
26. 26. n4 n2 n5 n1 n6 n3 2 1 preorder(node) visit(node). preorder(node.left). preorder(node.right).
27. 27. n4 n2 n5 n1 n6 n3 2 3 1 preorder(node) visit(node). preorder(node.left). preorder(node.right).
28. 28. n4 n2 n5 n1 n6 n3 2 3 4 1 preorder(node) visit(node). preorder(node.left). preorder(node.right).
29. 29. n4 n2 n5 n1 n6 n3 2 5 3 4 1 preorder(node) visit(node). preorder(node.left). preorder(node.right).
30. 30. n4 n2 n5 n1 n6 n3 2 5 3 64 1 preorder(node) visit(node). preorder(node.left). preorder(node.right).
31. 31. n4 n2 n5 n1 n6 n3 inorder(node) inorder(node.left). visit(node). inorder(node.right).
32. 32. n4 n2 n5 n1 n6 n3 1 inorder(node) inorder(node.left). visit(node). inorder(node.right).
33. 33. n4 n2 n5 n1 n6 n3 2 1 inorder(node) inorder(node.left). visit(node). inorder(node.right).
34. 34. n4 n2 n5 n1 n6 n3 2 1 3 inorder(node) inorder(node.left). visit(node). inorder(node.right).
35. 35. n4 n2 n5 n1 n6 n3 2 1 3 4 inorder(node) inorder(node.left). visit(node). inorder(node.right).
36. 36. n4 n2 n5 n1 n6 n3 2 1 53 4 inorder(node) inorder(node.left). visit(node). inorder(node.right).
37. 37. n4 n2 n5 n1 n6 n3 2 6 1 53 4 inorder(node) inorder(node.left). visit(node). inorder(node.right).
38. 38. n4 n2 n5 n1 n6 n3 postorder (node) postorder(node.left). postorder(node.right). visit(node).
39. 39. n4 n2 n5 n1 n6 n3 1 postorder (node) postorder(node.left). postorder(node.right). visit(node).
40. 40. n4 n2 n5 n1 n6 n3 1 2 postorder (node) postorder(node.left). postorder(node.right). visit(node).
41. 41. n4 n2 n5 n1 n6 n3 3 1 2 postorder (node) postorder(node.left). postorder(node.right). visit(node).
42. 42. n4 n2 n5 n1 n6 n3 3 1 42 postorder (node) postorder(node.left). postorder(node.right). visit(node).
43. 43. n4 n2 n5 n1 n6 n3 3 5 1 42 postorder (node) postorder(node.left). postorder(node.right). visit(node).
44. 44. n4 n2 n5 n1 n6 n3 3 5 1 42 6 postorder (node) postorder(node.left). postorder(node.right). visit(node).
45. 45. !"#\$%&'(")\$* ! "#\$#%&'!&\$()*+,%&)\$!&-!.,--#/!)\$!(*)+!0#\$#*,%&)\$!%)! Example (group 15)
46. 46. !"#\$%&'(")\$* ! "#\$#%&'!&\$()*+,%&)\$!&-!.,--#/!)\$!(*)+!0#\$#*,%&)\$!%)! Example (group 15)
47. 47. Hierarchical structure
48. 48. Binary search tree n4 n2 n5 n1 n6 n3 2 6 1 53 4
49. 49. n4 n2 n5 n1 n6 n3 2 61 53 4
50. 50. n4 n2 n5 n1 n6 n3 2 61 53 4
51. 51. n4 n2 n5 n1 n6 n3 2 6 1 53 4
52. 52. n4 n2 n5 n1 n6 n3 2 6 1 5 3 4
53. 53. Binary search tree n4 n2 n5 n1 n6 n3 2 6 1 53 4
54. 54. a + b - c * d
55. 55. a + b - c * d
56. 56. a + b - c * d
57. 57. a + b - c * d operator operand
58. 58. Inﬁx notation a + b - c * d Postﬁx notation Preﬁx notation
59. 59. Inﬁx notation a + b - c * d Postﬁx notation Preﬁx notation -+ab*cd
60. 60. Inﬁx notation a + b - c * d a+b-c*d Postﬁx notation Preﬁx notation -+ab*cd
61. 61. Inﬁx notation a + b - c * d a+b-c*d Postﬁx notation ab+cd*- Preﬁx notation -+ab*cd
62. 62. Tudor Gîrba www.tudorgirba.com creativecommons.org/licenses/by/3.0/