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.

1. Trees
www.tudorgirba.com

2. n5
n2
n6
n10
n1
n7
n4
n9
n3
n8

3. n5
n2
n6
n10
n1
n7
n4
n9
n3
n8

4. n5
n2
n6
n10
n1
n7
n4
n9
n3
n8

5. n5
n2
n6
n10
n1
n7
n4
n9
n3
n8
edge
node

6. n5
n2
n6
n10
n1
n7
n4
n9
n3
n8
leaf
root

7. n5
n2
n6
n10
n1
n7
n4
n9
n3
n8
parent
child

8. n5
n2
n6
n10
n1
n7
n4
n9
n3
n8
subtree

9. n5
n2
n6
n10
n1
n7
n4
n9
n3
n8
path

10. n5
n2
n6
n10
n1
n7
n4
n9
n3
n8
height = 1
depth = level = 2
degree = 1

11. n5
n2
n6
n10
n1
n7
n4
n9
n3
n8
height = 1
depth = level = 1
degree = 3

12. n5
n2
n6
n10
n1
n7
n4
n9
n3
n8
0
1
2
3

13. n5
n2
n6
n10
n1
n7
n4
n9
n3
n8
ordered tree
leftmost rightmost

14. n5
n2
n6
n10
n1
n7
n4
n9
n3
n8 n7
n4
n9n8
n1
n5
n4
n6
n3
n10
isomorphic trees

15. n4
n2
n5
n1
n6
n3
n7
left right
left leftright right

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. breadth-first traversal
n4
n2
n5
n1
n6
n3

18. breadth-first traversal
n4
n2
n5
n1
n6
n3
1

19. breadth-first traversal
n4
n2
n5
n1
n6
n3
2
1

20. breadth-first traversal
n4
n2
n5
n1
n6
n3
2 3
1

21. breadth-first traversal
n4
n2
n5
n1
n6
n3
2 3
4
1

22. breadth-first traversal
n4
n2
n5
n1
n6
n3
2 3
4 5
1

23. breadth-first traversal
n4
n2
n5
n1
n6
n3
2 3
4 65
1

24. n4
n2
n5
n1
n6
n3
preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

25. n4
n2
n5
n1
n6
n3
1
preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

26. n4
n2
n5
n1
n6
n3
2
1
preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

27. n4
n2
n5
n1
n6
n3
2
3
1
preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

28. n4
n2
n5
n1
n6
n3
2
3 4
1
preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

29. n4
n2
n5
n1
n6
n3
2 5
3 4
1
preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

30. n4
n2
n5
n1
n6
n3
2 5
3 64
1
preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

31. n4
n2
n5
n1
n6
n3
inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

32. n4
n2
n5
n1
n6
n3
1
inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

33. n4
n2
n5
n1
n6
n3
2
1
inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

34. n4
n2
n5
n1
n6
n3
2
1 3
inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

35. n4
n2
n5
n1
n6
n3
2
1 3
4
inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

36. n4
n2
n5
n1
n6
n3
2
1 53
4
inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

37. n4
n2
n5
n1
n6
n3
2 6
1 53
4
inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

38. n4
n2
n5
n1
n6
n3
postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

39. n4
n2
n5
n1
n6
n3
1
postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

40. n4
n2
n5
n1
n6
n3
1 2
postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

41. n4
n2
n5
n1
n6
n3
3
1 2
postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

42. n4
n2
n5
n1
n6
n3
3
1 42
postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

43. n4
n2
n5
n1
n6
n3
3 5
1 42
postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

44. n4
n2
n5
n1
n6
n3
3 5
1 42
6
postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

45. !"#$%&'(")$*
!
"#$#%&'!&$()*+,%&)$!&-!.,--#/!)$!(*)+!0#$#*,%&)$!%)!
Example (group 15)

46. !"#$%&'(")$*
!
"#$#%&'!&$()*+,%&)$!&-!.,--#/!)$!(*)+!0#$#*,%&)$!%)!
Example (group 15)

47. Hierarchical structure

48. Binary search tree
n4
n2
n5
n1
n6
n3
2 6
1 53
4

49. n4 n2 n5 n1 n6 n3
2 61 53 4

50. n4 n2 n5 n1 n6 n3
2 61 53 4

51. n4
n2
n5
n1
n6
n3
2 6
1 53
4

52. n4
n2
n5
n1
n6
n3
2
6
1
5
3
4

53. Binary search tree
n4
n2
n5
n1
n6
n3
2 6
1 53
4

54. a + b - c * d

55. a + b - c * d

56. a
+
b
-
c
*
d

57. a
+
b
-
c
*
d
operator
operand

58. Infix notation
a
+
b
-
c
*
d
Postfix notation
Prefix notation

59. Infix notation
a
+
b
-
c
*
d
Postfix notation
Prefix notation -+ab*cd

60. Infix notation
a
+
b
-
c
*
d
a+b-c*d
Postfix notation
Prefix notation -+ab*cd

61. Infix notation
a
+
b
-
c
*
d
a+b-c*d
Postfix notation ab+cd*-
Prefix notation -+ab*cd

62. Tudor Gîrba
www.tudorgirba.com
creativecommons.org/licenses/by/3.0/