1. Lecture 14
Traversals of Linked Lists Preorder BST Traversal Postorder BST Traversal Miscellaneous BST Traversals Depth First vs Breadth First Array Traversals

2. Traversals of Linked Lists

3. The Scenario We need to visit each element in the linked list.
At each element, we do some work.
We’ll stop when we reach the end of the list.
Examples:
Printing all elements
Updating/changing the data of all elements

4. Traversals A traversal visits every element in a collection.
Two forms:
Recursive
Iterative (linear structures)

5. Visiting Every Element
head 48 17
142 //
Regardless of whether we use iteration or recursion, we continue until we reach the end (NIL).

6. Don’t De-reference NIL
We must make sure we don’t de-reference (follow) the NIL pointer.
To do this, always test to see if the pointer is NIL.
If so, we can’t use the ‘^’ operator
head //
Can’t follow head! (i.e. head^ doesn’t work!)

7. Testing for NIL Always test for NIL at the beginning of your loop.
Your exitif statement must appear at the top
Always test for NIL at the beginning of your recursive module.
Your terminating condition must appear at the top of your module

8. Iterative Traversal Template
procedure Traverse (cur iot in Ptr toa Node)
// Purpose: call Do_Something on each element
// Precondition: none
// Postcondition: Do_Something on each element
loop
exitif( cur = NIL )
Do_Something( cur^.data )
cur <- cur^.next
endloop
endprocedure // Traverse

9. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List
Called via Print_List(list_head)
cur
list_head 4 17 42

10. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List
cur
list_head 4 17 42

11. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List 4
cur
list_head 4 17 42

12. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List 4
cur
list_head 4 17 42

13. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List 4
cur
list_head 4 17 42

14. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List 4
cur
list_head 4 17 42

15. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List
4 17
cur
list_head 4 17 42

16. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List
4 17
cur
list_head 4 17 42

17. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List
4 17
cur
list_head 4 17 42

18. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List
4 17
cur
list_head 4 17 42

19. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List
cur
list_head 4 17 42

20. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List
cur
list_head 4 17 42

21. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List
cur
list_head 4 17 42

22. An Iterative Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
loop
exitif (cur = NIL)
print(cur^.data)
cur <- cur^.next
endloop
endprocedure //Print_List
cur
list_head 4 17 42

23. Recursive Traversal Template
procedure Traverse (cur iot in Ptr toa Node)
// Purpose: call Do_Something on each element
// Precondition: none
// Postcondition: Do_Something on each element
if (cur <> NIL) then
Do_Something( cur^.data )
Traverse( cur^.next )
endif
endprocedure // Traverse

24. A Recursive Traversal Example
procedure Print_List(cur iot in Ptr toa Node)
if (cur <> NIL) then
print(cur^.data)
Print_List(cur^.next)
endif
endprocedure //Print_List
Called via Print_List(list_head)
cur
list_head 4 17 42
You already know how to do this...

25. A Loophole in Parameter Protection
If a pointer is an in parameter, the pointer cannot be changed.
But, anything to which the pointer points may be changed.
Thus, giving access to a list means giving ability to make changes to it; you cannot protect against this.

26. An Example
procedure DestroyList (cur iot in Ptr toa Node)
if (cur <> nil) then
cur^.data <- -1
DestroyList(cur^.next)
endif
endprocedure // DestroyList
head -1 -1 48 17 -1
142 //

27. Another Example // head 48 48 17 142
procedure DestroyList (cur iot in Ptr toa Node)
cur^.next <- NIL
endprocedure // DestroyList
head 48 48 17
142 //

28. Summary Traversals involve visiting every element
Recursion or iteration
Stop when you reach NIL
Make sure to not de-reference NIL
Be aware that passing a pointer to a module via an IN parameter allows the module to modify the entire list.

29. Questions?

30. Traversing a Binary Search Tree (BST) Pre-Order

31. Outline of Pre-Order Traversal
Three principle steps:
Do work (Current)
Traverse Left
Traverse Right
Work can be anything
Separate work from traversal

32. Traverse the tree “Pre-order”:
Visit the current and do work
Visit the tree’s left sub-tree
Visit right sub-tree

33. Pre-Order Traversal Procedure
procedure Pre_Order(cur iot in Ptr toa Tree_Node)
// Purpose: perform pre-order traversal, call
// DoWhatever for each node
// Preconditions: cur points to a binary tree
// Postcondition: DoWhatever will be performed
// on each tree node in “pre-order” order
if( cur <> NIL ) then
Do_Whatever( cur^.data )
Pre_Order( cur^.left_child )
Pre_Order( cur^.right_child )
endif
endprocedure // Pre_Order

34. 22 9 67 3 14 36 94 44 97 1 7 Proc PreOrderPrint(pointer)
pointer NOT NIL?
print(data)
PreOrderPrint(left child)
PreOrderPrint(right child)
root P 22 L R 9 67 3 14 36 94 44 97 1 7

35. Questions?

36. Traversing a Binary Search Tree (BST) Post-Order

37. Outline of Post-Order Traversal
Three principle steps:
Traverse Left
Traverse Right
Do work (Current)
Work can be anything
Separate work from traversal

38. Traverse the tree “Post order”:
Visit the tree’s left sub-tree
Visit right sub-tree
Visit the current and do work

39. Post-Order Traversal Procedure
procedure Post_Order(cur iot in Ptr toa Tree_Node)
// Purpose: perform post-order traversal, call
// DoWhatever for each node
// Preconditions: cur points to a binary tree
// Postcondition: DoWhatever will be performed
// on each tree node in “post-order” order
if( cur <> NIL ) then
Post_Order( cur^.left_child )
Post_Order( cur^.right_child )
Do_Whatever( cur^.data )
endif
endprocedure // Post_Order

40. 22 9 67 3 14 36 94 44 97 1 7 Proc PostOrderPrint(pointer)
pointer NOT NIL?
PostOrderPrint(left child)
PostOrderPrint(right child)
print(data)
root L 22 R P 9 67 3 14 36 94 44 97 1 7

41. Questions?

42. Miscellaneous BST Traversals

43. Miscellaneous Traversals
Defined Traversals
In-order L C R
Pre-order C L R
Post-order L R C
Other Possibilities:
R C L
C R L
R L C

44. 22 9 67 3 14 36 94 44 97 1 7 Proc MiscTraverse(pointer)
pointer NOT NIL?
print(data)
MiscTraverse(right child)
MiscTraverse(left child)
root P 22 R L 9 67 3 14 36 94 44 97 1 7

45. 22 9 67 3 14 36 94 44 97 1 7 Proc MiscTraverse(pointer)
pointer NOT NIL?
print(data)
MiscTraverse(right child)
MiscTraverse(left child)
root P 22 R L 9 67 3 14 36 94 44 97 1 7

46. 22 9 67 3 14 36 94 44 97 1 7 Proc MiscTraverse(pointer)
pointer NOT NIL?
print(data)
MiscTraverse(right child)
MiscTraverse(left child)
root P P 22 R L 9 67
Output: 22 3 14 36 94 44 97 1 7

47. 22 9 67 3 14 36 94 44 97 1 7 Proc MiscTraverse(pointer)
pointer NOT NIL?
print(data)
MiscTraverse(right child)
MiscTraverse(left child)
root P P 22 R R L
Output: 22 9 67 3 14 36 94 44 97 1 7

48. 22 9 67 3 14 36 94 44 97 1 7 Proc MiscTraverse(pointer)
pointer NOT NIL?
print(data)
MiscTraverse(right child)
MiscTraverse(left child)
root P P 22 R R L P
Output: 22 67 9 67 3 14 36 94 44 97 1 7

49. 22 67 9 3 14 36 94 44 97 1 7 Proc MiscTraverse(pointer)
pointer NOT NIL?
print(data)
MiscTraverse(right child)
MiscTraverse(left child)
root P P 22 R R L P 67
Output: 22 67 9 R 3 14 36 94 44 97 1 7

50. 22 9 67 3 14 36 94 44 97 1 7 Proc MiscTraverse(pointer)
pointer NOT NIL?
print(data)
MiscTraverse(right child)
MiscTraverse(left child)
root P P 22 R R L P 9 67
Output: R 3 14 P 36 94 44 97 1 7

51. 22 9 67 3 14 36 94 44 97 1 7 Proc MiscTraverse(pointer)
pointer NOT NIL?
print(data)
MiscTraverse(right child)
MiscTraverse(left child)
root P P 22 R R L P
Output: 9 67 R 3 14 P 36 94 R 44 97 1 7

52. 22 9 67 3 14 36 94 44 97 1 7 Proc MiscTraverse(pointer)
pointer NOT NIL?
print(data)
MiscTraverse(right child)
MiscTraverse(left child)
root P P 22 R R L P
Output: 9 67 R 3 14 P 36 94 R P 44 97 1 7

53. 22 9 67 3 14 36 94 44 97 1 7 Proc MiscTraverse(pointer)
pointer NOT NIL?
print(data)
MiscTraverse(right child)
MiscTraverse(left child)
root P P 22 R R L P
Output: 9 67 R 3 14 P 36 94 R P 44 97 1 7 R

54. 22 9 67 3 14 36 94 44 97 1 7 Proc MiscTraverse(pointer)
pointer NOT NIL?
print(data)
MiscTraverse(right child)
MiscTraverse(left child)
root P P 22 R R L L P P
Output: 9 67 R R L L P 3 P 14 P P 36 94 R R R R L L L L P P P P 44 97 1 7 R R R R L L L L

55. Questions?

56. Depth First vs. Breadth First Traversal

57. Depth vs. Breadth First Traversals
Depth First Traversals
Go down (deep)
In-, Pre-, Post-order
Breadth First Traversals
Go across (shallow)
Require a queue to help

58. Depth-First Traversal
root 22 9 67 3 14 36 94 44 97 1 7

59. Breadth-First Traversal
root 22 9 67 3 14 36 94 44 97 1 7

60. Depth First Traversal (In-Order)
Procedure DFT
(current isoftype in Ptr toa Node)
// In order DFT
if(current <> NIL) then
DFT(current^.left)
print(current^.data)
DFT(Current^.right)
endif
endprocedure

61. Depth First Traversal (Pre-Order)
Procedure DFT
(current isoftype in Ptr toa Node)
// In order DFT
if(current <> NIL) then
DFT(current^.left)
print(current^.data)
DFT(Current^.right)
endif
endprocedure
Move this here
to make a
Preorder DFT

62. Depth First Traversal (Post-Order)
Procedure DFT
(current isoftype in Ptr toa Node)
// In order DFT
if(current <> NIL) then
DFT(current^.left)
print(current^.data)
DFT(Current^.right)
endif
endprocedure
Move this here
to make a
Postorder DFT

63. We have already seen these!
Proc DFT(pointer)
pointer NOT NIL?
DFT(left child)
print(data)
DFT(right child)
root 22 9 67
We have already
seen these! 3 14 36 94 44 97 1 7

64. Breadth-First Traversal
Requires a queue to maintain which nodes to visit next.
Enqueue the root pointer
Loop until no elements in the queue
Dequeue(current)
Enqueue current’s left and right children
Do work at current

65. Breadth-First TraversalLB
Breadth-First Traversal
Procedure BFT(root isoftype in Ptr toa Node)
Q isoftype Queue
Initialize(Q)
temp isoftype Ptr toa Node
OK isoftype Boolean
enqueue(Q, root)
// continued

66. Breadth-First TraversalLB
Breadth-First Traversal
loop
dequeue(temp, OK, Q)
exitif(NOT OK)
if(temp^.left <> NIL) then
enqueue(temp^.left, Q))
endif
if(temp^.right <> NIL) then
enqueue(temp^.right, Q)
print(temp^.data) // processing node
endloop
endprocedure

67. 22 9 67 Q: 3 14 36 94 aNode: 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode: 44 97 1 7

68. 22 9 67 Q:22 3 14 36 94 aNode: 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(data)
endloop
root 22 9 67
Q:22 3 14 36 94
aNode: 44 97 1 7

69. 22 9 67 Q:22 3 14 36 94 aNode: 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(data)
endloop
root 22 9 67
Q:22 3 14 36 94
aNode: 44 97 1 7

70. 22 9 67 Q: 3 14 36 94 aNode:22 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:22 44 97 1 7

71. 22 9 67 Q:9 67 3 14 36 94 aNode:22 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:9 67 3 14 36 94
aNode:22 44 97 1 7

72. 22 9 67 Q:9 67 3 14 36 94 aNode:22 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:9 67 3 14 36 94
aNode:22 44 97 1 7

73. 22 9 67 Q:9 67 3 14 36 94 aNode:22 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:9 67 3 14 36 94
aNode:22 44 97 1 7

74. 22 9 67 Q:67 3 14 36 94 aNode:9 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:67 3 14 36 94
aNode:9 44 97 1 7

75. 22 9 67 Q:67 3 14 3 14 36 94 aNode:9 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:9 44 97 1 7

76. 22 9 67 Q:67 3 14 3 14 36 94 aNode:9 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:9 44 97 1 7

77. 22 9 67 Q:67 3 14 3 14 36 94 aNode:9 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:9 44 97 1 7

78. 22 9 67 Q:3 14 3 14 36 94 aNode:67 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:3 14 3 14 36 94
aNode:67 44 97 1 7

79. 22 9 67 Q:3 14 36 94 3 14 36 94 aNode:67 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:67 44 97 1 7

80. 22 9 67 Q:3 14 36 94 3 14 36 94 aNode:67 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:67 44 97 1 7

81. 22 9 67 Q:3 14 36 94 3 14 36 94 aNode:67 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:67 44 97 1 7

82. 22 9 67 Q:14 36 94 3 14 36 94 aNode:3 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:3 44 97 1 7

83. 22 9 67 Q:14 36 94 1 7 3 14 36 94 aNode:3 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:3 44 97 1 7

84. 22 9 67 Q:14 36 94 1 7 3 14 36 94 aNode:3 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:3 44 97 1 7

85. 22 9 67 Q:14 36 94 1 7 3 14 36 94 aNode:3 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:3 44 97 1 7

86. 22 9 67 Q:36 94 1 7 3 14 36 94 aNode:14 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:14 44 97 1 7

87. 22 9 67 Q:36 94 1 7 3 14 36 94 aNode:14 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:14 44 97 1 7

88. 22 9 67 Q:36 94 1 7 3 14 36 94 aNode:14 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:14 44 97 1 7

89. 22 9 67 Q:36 94 1 7 3 14 36 94 aNode:14 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:14 44 97 1 7

90. 22 9 67 Q:94 1 7 3 14 36 94 aNode:36 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:94 1 7 3 14 36 94
aNode:36 44 97 1 7

91. 22 9 67 Q:94 1 7 44 3 14 36 94 aNode:36 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:36 44 97 1 7

92. 22 9 67 Q:94 1 7 44 3 14 36 94 aNode:36 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:36 44 97 1 7

93. 22 9 67 Q:94 1 7 44 3 14 36 94 aNode:36 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:36 44 97 1 7

94. 22 9 67 Q:1 7 44 3 14 36 94 aNode:94 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:1 7 44 3 14 36 94
aNode:94 44 97 1 7

95. 22 9 67 Q:1 7 44 97 3 14 36 94 aNode:94 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:94 44 97 1 7

96. 22 9 67 Q:1 7 44 97 3 14 36 94 aNode:94 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:94 44 97 1 7

97. 22 9 67 Q:1 7 44 97 3 14 36 94 aNode:94 44 97 1 7 Enqueue(root) loop
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:94 44 97 1 7

98. 22 9 67 Q:7 44 97 3 14 36 94 aNode:1 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:1 44 97 1 7

99. 22 9 67 Q:7 44 97 3 14 36 94 aNode:1 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:1 44 97 1 7

100. 22 9 67 Q:7 44 97 3 14 36 94 aNode:1 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:1 44 97 1 7

101. 22 9 67 Q:7 44 97 3 14 36 94 aNode:1 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:1 44 97 1 7

102. 22 9 67 Q:44 97 3 14 36 94 aNode:7 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:44 97 3 14 36 94
aNode:7 44 97 1 7

103. 22 9 67 Q:44 97 3 14 36 94 aNode:7 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:44 97 3 14 36 94
aNode:7 44 97 1 7

104. 22 9 67 Q:44 97 3 14 36 94 aNode:7 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:44 97 3 14 36 94
aNode:7 44 97 1 7

105. 22 9 67 Q:44 97 3 14 36 94 aNode:7 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:44 97 3 14 36 94
aNode:7 44 97 1 7

106. 22 9 67 Q:97 3 14 36 94 aNode:44 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:97 3 14 36 94
aNode:44 44 97 1 7

107. 22 9 67 Q:97 3 14 36 94 aNode:44 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:97 3 14 36 94
aNode:44 44 97 1 7

108. 22 9 67 Q:97 3 14 36 94 aNode:44 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:97 3 14 36 94
aNode:44 44 97 1 7

109. 22 9 67 Q:97 3 14 36 94 aNode:44 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67
Q:97 3 14 36 94
aNode:44 44 97 1 7

110. 22 9 67 Q: 3 14 36 94 aNode:97 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:97 44 97 1 7

111. 22 9 67 Q: 3 14 36 94 aNode:97 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:97 44 97 1 7

112. 22 9 67 Q: 3 14 36 94 aNode:97 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:97 44 97 1 7

113. 22 9 67 Q: 3 14 36 94 aNode:97 44 97 1 7 Enqueue(root) loop root
exitif Q empty
dequeue(aNode)
enqueue(children)
print(aNode.data)
endloop
root 22 9 67 Q: 3 14 36 94
aNode:97 44 97 1 7

114. Queuestions?

115. Traversals of Arrays

116. The Scenario We need to visit each element in the array.
At each element, we do some work.
We’ll stop when we reach the end of the array (when we reach MAX).
Examples:
Printing all elements
Updating/changing the data of all elements

117. Traversals A traversal visits every element in a collection.
Two forms:
Recursive
Iterative (linear structures)

118. Recursive Array Traversal Template
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Purpose: call Do_Something on each element
// Precondition: i = 1 on first call
// Postcondition: Do_Something on each element
if (i <= MAX) then
Do_Something(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure

119. Recursive Array Traversal Example
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure

120. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 1
NumArray 12 43 11 9 98

121. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 1 12
NumArray 12 43 11 9 98

122. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 1 12
NumArray 12 43 11 9 98

123. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 1
i = 2 12
NumArray 12 43 11 9 98

124. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 1
i = 2
NumArray 12 43 11 9 98

125. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 1
i = 2
NumArray 12 43 11 9 98

126. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 3
i = 1
NumArray 12 43 11 9 98

127. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 3
i = 1
NumArray 12 43 11 9 98

128. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 3
i = 1
NumArray 12 43 11 9 98

129. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 3
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 4
i = 1
NumArray 12 43 11 9 98

130. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 3
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 4
i = 1
NumArray 12 43 11 9 98

131. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 3
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 4
i = 1
NumArray 12 43 11 9 98

132. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 3
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 4
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 5
i = 1
NumArray 12 43 11 9 98

133. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 3
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 4
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 5
i = 1
NumArray 12 43 11 9 98

134. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 3
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 4
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 5
i = 1
NumArray 12 43 11 9 98

135. i = 2 i = 3 i = 4 i = 5 i = 6 i = 1 12 43 11 9 98 NumArray 12 43 11 9
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 3
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 4
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 5
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 6
i = 1
NumArray 12 43 11 9 98

136. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 3
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 4
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 5
i = 1
NumArray 12 43 11 9 98

137. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 3
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 4
i = 1
NumArray 12 43 11 9 98

138. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 3
i = 1
NumArray 12 43 11 9 98

139. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 2
i = 1
NumArray 12 43 11 9 98

140. procedure RecursiveTraverse (i iot in num, NumArray iot in NumArrayType)
// Pre: i = 1 on first call
if (i <= MAX) then
print(NumArray[i])
RecursiveTraverse (i+1, NumArray)
endif
endprocedure
i = 1
NumArray 12 43 11 9 98

141. Iterative Traversal Template
procedure Traverse (my_array iot in/out ArrayType)
// Purpose: call Do_Something on each element
// Precondition: none
// Postcondition: Do_Something on each element
i isoftype Num
i <- 1
loop
exitif( i > MAX )
Do_Something( my_array[i] )
i <- i + 1
endloop
endprocedure // Traverse

142. An Iterative Traversal Example
Traverse the array and fill in every element so that the ith element contains the value i. 1 2 3 4 5 6 7 8 9 10

143. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop

144. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop

145. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data

146. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data i

147. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data i 1

148. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data i 1

149. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 i

150. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 i 1

151. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 i 2

152. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 i 2

153. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 i 2

154. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 i 2

155. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 i 2

156. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 i 3

157. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 i 3

158. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 i 3

159. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 i 3

160. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 i 3

161. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 i 4

162. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 i 4

163. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 i 4

164. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 i 5

165. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 i 6

166. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 i 7

167. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 8 i 8

168. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 8 i 9

169. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 8 9 i 9

170. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 8 9 i 10

171. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 8 9 i 10

172. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 8 9 i 10

173. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 8 9 i 10

174. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 8 9 10 i 10

175. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 8 9 10 i 11

176. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 8 9 10 i 11

177. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 8 9 10 i 11

178. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 8 9 10 i 11

179. MAX is 10
Vec_max definesa Array[1..MAX] of Num
data isoftype Vec_max
i isoftype Num
i <- 1
loop
exitif(i > MAX)
data[i] <- i
i <- i + 1
endloop
data 1 2 3 4 5 6 7 8 9 10 i 11

180. A More Complex Problem
Write a module which returns an array with the following characteristics:
Every odd element has the first half of the alphabet in ascending order & every even element has the second half of the alphabet in descending order.
A[1] = ‘A’
A[2] = ‘Z’
A[3] = ‘B’
A[4] = ‘Y’
A[5] = ‘C’
A[6] = ‘X’ .
A[23] = ‘L’
A[24] = ‘O’
A[25] = ‘M’
A[26] = ‘N’

181. A A 1 2 3 4 5
. . . 23 24 25 26 Z B Y C L O M N
Every odd element has the first half of the alphabet in ascending order & every even element has the second half of the alphabet in descending order.

182. A First Try ALPHAS is 26 A isoftype CharArrayType i isoftype Num
up isoftype char
i <- 1
up <- ‘A’
loop
exitif( i > ALPHAS )
A[i] <- up
up <- next_character(up)
i <- i + 2
endloop

183. A 1 2 3 4 5
. . . 23 24 25 26 A B C L M
Every odd element has the first half of the alphabet in ascending order & every even element has the second half of the alphabet in descending order.

184. ALPHAS is 26
A isoftype Array_Type
i isoftype Num
up, down isoftype char
i <- 1
up <- ‘A’
down <- ‘Z’
loop
exitif( i > ALPHAS )
A[i] <- up
A[i + 1] <- down
up <- next_character(up)
down <- previous_character(down)
i <- i + 2
endloop

185. A A 1 2 3 4 5
. . . 23 24 25 26 Z B Y C L O M N
Every odd element has the first half of the alphabet in ascending order & every even element has the second half of the alphabet in descending order.

186. A 2-D Iterative Traversal Example
We have a 2-D array
We want to traverse the array and set each element to the product of it’s row position and column position
(i.e. the element at position [i,j] should contain the value i*j) 1 2 3 1 2 3 4 i 2 4 6 8 3 6 9 12 j

187. MAX_COLS is 4
Row_Type definesa Array[1..MAX_COLS] of Num
Sample isoftype Row_type
Sample:

188. 1 Data: 2 3 1 2 3 4 MAX_ROWS is 3 MAX_COLS is 4
Row_Type definesa Array[1..MAX_COLS] of Num
Matrix definesa Array[1..MAX_ROWS] of Row_Type
Data isoftype Matrix
Data: 1 2 3

189. MAX_ROWS is 3
MAX_COLS is 4
Row_Type definesa Array[1..MAX_COLS] of Num
Matrix definesa Array[1..MAX_ROWS] of Row_Type
Data isoftype Matrix
Row, Col isoftype Num
Row <- 1
loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1

190. 1 Data: 2 3 Row: Col: 1 2 3 4 MAX_ROWS is 3 MAX_COLS is 4
Row_Type definesa Array[1..MAX_COLS] of Num
Matrix definesa Array[1..MAX_ROWS] of Row_Type
Data isoftype Matrix
Row, Col isoftype Num
Data: 1 2 3
Row:
Col:

191. Data: 1 2 3 Row: 1 Col: 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4
Data: 1 2 3
Row: 1
Col:

192. Data: 1 2 3 Row: 1 Col: 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4
Data: 1 2 3
Row: 1
Col:

193. Data: 1 2 3 Row: 1 Col: 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4
Data: 1 2 3
Row: 1
Col:

194. Data: 1 2 3 Row: 1 Col: 1 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4
Data: 1 2 3
Row: 1
Col: 1

195. Data: 1 2 3 Row: 1 Col: 1 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4
Data: 1 2 3
Row: 1
Col: 1

196. Data: 1 2 3 Row: 1 Col: 1 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4
Data: 1 2 3
Row: 1
Col: 1

197. 1 Data: 1 2 3 Row: 1 Col: 1 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 1
Data: 1 2 3
Row: 1
Col: 1

198. 1 Data: 1 2 3 Row: 1 Col: 2 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 1
Data: 1 2 3
Row: 1
Col: 2

199. 1 Data: 1 2 3 Row: 1 Col: 2 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 1
Data: 1 2 3
Row: 1
Col: 2

200. 1 Data: 1 2 3 Row: 1 Col: 2 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 1
Data: 1 2 3
Row: 1
Col: 2

201. 2 1 Data: 1 2 3 Row: 1 Col: 2 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 2 1
Data: 1 2 3
Row: 1
Col: 2

202. 2 1 Data: 1 2 3 Row: 1 Col: 3 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 2 1
Data: 1 2 3
Row: 1
Col: 3

203. 2 1 Data: 1 2 3 Row: 1 Col: 3 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 2 1
Data: 1 2 3
Row: 1
Col: 3

204. 2 1 Data: 1 2 3 Row: 1 Col: 3 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 2 1
Data: 1 2 3
Row: 1
Col: 3

205. 3 2 1 Data: 1 2 3 Row: 1 Col: 3 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 3 2 1
Data: 1 2 3
Row: 1
Col: 3

206. 3 2 1 Data: 1 2 3 Row: 1 Col: 4 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 3 2 1
Data: 1 2 3
Row: 1
Col: 4

207. 3 2 1 Data: 1 2 3 Row: 1 Col: 4 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 3 2 1
Data: 1 2 3
Row: 1
Col: 4

208. 3 2 1 Data: 1 2 3 Row: 1 Col: 4 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 3 2 1
Data: 1 2 3
Row: 1
Col: 4

209. 4 3 2 1 Data: 1 2 3 Row: 1 Col: 4 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1
Data: 1 2 3
Row: 1
Col: 4

210. 4 3 2 1 Data: 1 2 3 Row: 1 Col: 5 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1
Data: 1 2 3
Row: 1
Col: 5

211. 4 3 2 1 Data: 1 2 3 Row: 1 Col: 5 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1
Data: 1 2 3
Row: 1
Col: 5

212. 4 3 2 1 Data: 1 2 3 Row: 1 Col: 5 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1
Data: 1 2 3
Row: 1
Col: 5

213. 4 3 2 1 Data: 1 2 3 Row: 2 Col: 5 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1
Data: 1 2 3
Row: 2
Col: 5

214. 4 3 2 1 Data: 1 2 3 Row: 2 Col: 5 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1
Data: 1 2 3
Row: 2
Col: 5

215. 4 3 2 1 Data: 1 2 3 Row: 2 Col: 5 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1
Data: 1 2 3
Row: 2
Col: 5

216. 4 3 2 1 Data: 1 2 3 Row: 2 Col: 1 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4
What would happen
if we did this outside
first loop? 4 3 2 1
Data: 1 2 3
Row: 2
Col: 1

217. 4 3 2 1 Data: 1 2 3 Row: 2 Col: 1 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1
Data: 1 2 3
Row: 2
Col: 1

218. 4 3 2 1 Data: 1 2 3 Row: 2 Col: 1 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1
Data: 1 2 3
Row: 2
Col: 1

219. 4 3 2 1 Data: 1 2 3 Row: 2 Col: 1 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1
Data: 1 2 3
Row: 2
Col: 1

220. 4 3 2 1 Data: 1 2 3 Row: 2 Col: 2 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1
Data: 1 2 3
Row: 2
Col: 2

221. 4 3 2 1 6 Data: 1 2 3 Row: 2 Col: 3 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1 6
Data: 1 2 3
Row: 2
Col: 3

222. 4 3 2 1 8 6 Data: 1 2 3 Row: 2 Col: 4 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1 8 6
Data: 1 2 3
Row: 2
Col: 4

223. 4 3 2 1 8 6 Data: 1 2 3 Row: 3 Col: 1 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1 8 6
Data: 1 2 3
Row: 3
Col: 1

224. 4 3 2 1 8 6 Data: 1 2 3 Row: 3 Col: 2 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1 8 6
Data: 1 2 3
Row: 3
Col: 2

225. 4 3 2 1 8 6 9 Data: 1 2 3 Row: 3 Col: 3 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1 8 6 9
Data: 1 2 3
Row: 3
Col: 3

226. 4 3 2 1 8 6 12 9 Data: 1 2 3 Row: 3 Col: 4 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1 8 6 12 9
Data: 1 2 3
Row: 3
Col: 4

227. 4 3 2 1 8 6 12 9 Data: 1 2 3 Row: 3 Col: 5 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1 8 6 12 9
Data: 1 2 3
Row: 3
Col: 5

228. 4 3 2 1 8 6 12 9 Data: 1 2 3 Row: 3 Col: 5 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1 8 6 12 9
Data: 1 2 3
Row: 3
Col: 5

229. 4 3 2 1 8 6 12 9 Data: 1 2 3 Row: 4 Col: 5 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1 8 6 12 9
Data: 1 2 3
Row: 4
Col: 5

230. 4 3 2 1 8 6 12 9 Data: 1 2 3 Row: 4 Col: 5 1 2 3 4 Row <- 1 loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4 4 3 2 1 8 6 12 9
Data: 1 2 3
Row: 4
Col: 5

231. and continue… 4 3 2 1 8 6 12 9 Data: 1 2 3 Row: 4 Col: 5 1 2 3 4
loop
exitif(Row > MAX_ROWS)
Col <- 1
exitif(Col > MAX_COLS)
Data[Row][Col] <- Row * Col
Col <- Col + 1
endloop
Row <- Row + 1
MAX_ROWS is 3
MAX_COLS is 4
and continue… 4 3 2 1 8 6 12 9
Data: 1 2 3
Row: 4
Col: 5

232. Summary Traversals involve visiting every element.
Recursion or iteration
Do some work at each element
When doing iterative traversals on arrays
Use a loop for each dimension of the array
Embed loops
Typically perform work in innermost loop

233. Questions?