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Tree Traversal

Tree Traversal. Traversal Algorithms. preorder inorder postorder. PreOrder Traversal. Inorder Traversal. Postorder Traversal. 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

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Tree Traversal

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  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? procedurepreorder(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? procedurepreorder(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? procedurepreorder(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 for each of {b, c, d} output: a

  9. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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 for each of {b, c, d} output: a

  10. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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? procedurepreorder(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 for each of {e, f} output: a b

  12. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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 for each of {e, f} output: a b

  13. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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? procedurepreorder(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 for each of {j, k} output: a b e

  15. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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 for each of {j, k} output: a b e

  16. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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? procedurepreorder(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 for each of {} output: a b e j

  18. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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 for each of {j, k} output: a b e j

  19. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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? procedurepreorder(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 for each of {n, o, p} output: a b e j k

  21. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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 for each of {n, o, p} output: a b e j k

  22. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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? procedurepreorder(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 for each of {} output: a b e j k n

  24. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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 for each of {n, o, p} output: a b e j k n

  25. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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? procedurepreorder(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 for each of {} output: a b e j k n o

  27. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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 for each of {n, o, p} output: a b e j k n o

  28. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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? procedurepreorder(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 for each of {} output: a b e j k n o p

  30. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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 for each of {n, o, p} output: a b e j k n o p

  31. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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 for each of {j, k} output: a b e j k n o p

  32. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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 for each of {e, f} output: a b e j k n o p

  33. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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? procedurepreorder(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 for each of {} output: a b e j k n o p f

  35. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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 for each of {e, f} output: a b e j k n o p f

  36. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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 for each of {b, c, d} output: a b e j k n o p f

  37. In which order does a preorder traversal visit the vertices in this ordered rooted tree? procedurepreorder(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? procedureinorder(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. call stack In which order does a inorder traversal visit the vertices in this ordered rooted tree? r = a, l = ? s = {} procedureinorder(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:

  40. call stack In which order does a inorder traversal visit the vertices in this ordered rooted tree? r = a, l = b s = {} procedureinorder(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:

  41. call stack In which order does a inorder traversal visit the vertices in this ordered rooted tree? r = a, l = b s = {} procedureinorder(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 r = b, l = ? s = {} output:

  42. call stack In which order does a inorder traversal visit the vertices in this ordered rooted tree? r = a, l = b s = {} procedureinorder(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 r = b, l = e s = {} output:

  43. call stack In which order does a inorder traversal visit the vertices in this ordered rooted tree? r = a, l = b s = {} procedureinorder(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 r = b, l = e s = {} r = e, l = ? s = {} output:

  44. call stack In which order does a inorder traversal visit the vertices in this ordered rooted tree? r = a, l = b s = {} procedureinorder(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 r = b, l = e s = {} r = e, l = j s = {} output: j

  45. call stack In which order does a inorder traversal visit the vertices in this ordered rooted tree? r = a, l = b s = {} procedureinorder(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 r = b, l = e s = {} r = e, l = j s = {} r = j, l = ? s = {} output: j

  46. call stack In which order does a inorder traversal visit the vertices in this ordered rooted tree? r = a, l = b s = {} procedureinorder(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 r = b, l = e s = {} r =e, l = j s = {} output: j e

  47. call stack In which order does a inorder traversal visit the vertices in this ordered rooted tree? r = a, l = b s = {} procedureinorder(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 r = b, l = e s = {} r = e, l = j s = {k} output: j e

  48. call stack In which order does a inorder traversal visit the vertices in this ordered rooted tree? r = a, l = b s = {} procedureinorder(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 r = b, l = e s = {} r = e, l = j s = {k} r = k, l = ? s = {} output: j e

  49. call stack In which order does a inorder traversal visit the vertices in this ordered rooted tree? r = a, l = b s = {} procedureinorder(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 r = b, l = e s = {} r = e, l = j s = {k} r = k, l = n s = {} output: j e

  50. call stack In which order does a inorder traversal visit the vertices in this ordered rooted tree? r = a, l = b s = {} procedureinorder(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 r = b, l = e s = {} r = e, l = j s = {k} r = k, l = n s = {} r = n, l = ? s = {} output: j e n

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