1. Tree Traversal

2. Traversal Algorithms preorder inorder postorder

3. PreOrder Traversal

4. Inorder Traversal

5. Postorder Traversal

6. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output:

7. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a

8. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a for each of {b, c, d}

9. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a for each of {b, c, d}

10. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b

11. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b for each of {e, f}

12. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b for each of {e, f}

13. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e

14. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e for each of {j, k}

15. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e for each of {j, k}

16. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j

17. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j for each of {}

18. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j for each of {j, k}

19. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k

20. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k for each of {n, o, p}

21. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k for each of {n, o, p}

22. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n

23. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n for each of {}

24. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n for each of {n, o, p}

25. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n o

26. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n o for each of {}

27. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n o for each of {n, o, p}

28. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n o p

29. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n o p for each of {}

30. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n o p for each of {n, o, p}

31. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n o p for each of {j, k}

32. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n o p for each of {e, f}

33. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n o p f

34. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n o p f for each of {}

35. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n o p f for each of {e, f}

36. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n o p f for each of {b, c, d}

37. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedure preorder(T: ordered rooted tree) r := root of T list r for each child c of r from left to right begin T(c) := subtree with c as its root preorder(T(c)) end output: a b e j k n o p f c d g l m h i

38. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output:

39. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: call stack r = a, l = ? s = {}

40. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: r = a, l = b s = {} call stack

41. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: r = a, l = b s = {} r = b, l = ? s = {} call stack

42. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: r = a, l = b s = {} r = b, l = e s = {} call stack

43. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: r = a, l = b s = {} r = b, l = e s = {} r = e, l = ? s = {} call stack

44. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j r = a, l = b s = {} r = b, l = e s = {} r = e, l = j s = {} call stack

45. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j r = a, l = b s = {} r = b, l = e s = {} r = e, l = j s = {} r = j, l = ? s = {} call stack

46. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e r = a, l = b s = {} r = b, l = e s = {} r =e, l = j s = {} call stack

47. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e r = a, l = b s = {} r = b, l = e s = {} r = e, l = j s = {k} call stack

48. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e r = a, l = b s = {} r = b, l = e s = {} r = e, l = j s = {k} r = k, l = ? s = {} call stack

49. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e r = a, l = b s = {} r = b, l = e s = {} r = e, l = j s = {k} r = k, l = n s = {} call stack

50. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n r = a, l = b s = {} r = b, l = e s = {} r = e, l = j s = {k} r = k, l = n s = {} call stack r = n, l = ? s = {}

51. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k r = a, l = b s = {} r = b, l = e s = {} r = e, l = j s = {k} r = k, l = n s = {} call stack

52. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k r = a, l = b s = {} r = b, l = e s = {} r = e, l = j s = {k} r = k, l = n s = {o,p} call stack

53. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k o r = a, l = b s = {} r = b, l = e s = {} r = e, l = j s = {k} r = k, l = n s = {o,p} call stack r = o, l = ? s = {}

54. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k o r = a, l = b s = {} r = b, l = e s = {} r = e, l = j s = {k} r = k, l = n s = {o,p} call stack

55. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k o p r = a, l = b s = {} r = b, l = e s = {} r = e, l = j s = {k} r = k, l = n s = {o,p} call stack r = k, l = ? s = {}

56. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k o p r = a, l = b s = {} r = b, l = e s = {} r = e, l = j s = {k} r = k, l = n s = {o,p} call stack

57. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k o p r = a, l = b s = {} r = b, l = e s = {} r = e, l = j s = {k} call stack

58. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k o p b r = a, l = b s = {} r = b, l = e s = {} call stack

59. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k o p b r = a, l = b s = {} r = b, l = e s = {f} call stack

60. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k o p b f r = a, l = b s = {} r = b, l = e s = {f} r = f, l = e s = {} call stack

61. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k o p b f r = a, l = b s = {} r = b, l = e s = {f} call stack

62. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k o p b f r = a, l = b s = {} call stack

63. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k o p b f r = a, l = b s = {c,d} call stack

64. In which order does a inorder traversal visit the vertices in this ordered rooted tree? procedure inorder(T: ordered rooted tree) r := root of T if r is a leaf then list r else begin l:= first child of r from left to right T(l) := subtree with l as its root inorder(T(l)) list r for each child c of r except for l left to right T(c) := subtree with c as its root preorder(T(c)) end output: j e n k o p b f a c l g m d h i

65. In which order does a postorder traversal visit the vertices in this ordered rooted tree?

66. Infix, Prefix, and Postfix Notation represent complicated expressions using an ordered rooted tree (typically binary) Algebraic expressions preorder – Polish notation inorder – infix notation postorder – reverse Polish notation

67. Express in: a.Polish b.infix c.reverse Polish

68. Evaluating a prefix expression

69. Evaluate postfix expression 7 2 3 * - 4 ^ 9 e / +

71. How do you do trees in Java?