The document discusses traversing a binary tree without recursion. It describes using an activation stack to simulate recursion by tracking the nodes to visit at each level of the tree. It provides pseudocode for in-order, pre-order and post-order traversal algorithms using an activation stack instead of recursion. It also covers inserting nodes into a binary search tree by recursively finding the correct location to add new nodes while maintaining the tree's search properties.

1. Traversing a Binary Tree without recursion
In-order Traversal
Pre-order Traversal
Post-order Traversal

2. The Scenario
• Imagine we have a binary tree
• We want to traverse the tree
– It’s not linear
– We need a way to visit all nodes
• Three things must happen:
– Deal with the entire left sub-tree
– Deal with the current node
– Deal with the entire right sub-tree
In-order Traversal

3. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42

4. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do left

5. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do left
At 9 – do left

6. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do left
At 9 – do left
At 2 – do left

7. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do left
At 9 – do left
At 2 – do left
At NIL

8. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do left
At 9 – do left
At 2 – do current

9. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do left
At 9 – do left
At 2 – do right

10. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do left
At 9 – do left
At 2 – do right
At NIL

11. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do left
At 9 – do left
At 2 - done

12. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do left
At 9 – do current

13. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do left
At 9 – do right

14. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do left
At 9 – do right
At NIL

15. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do left
At 9 – done

16. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do current

17. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do right

18. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do right
At 42 – do left

19. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do right
At 42 – do left
At NIL

20. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do right
At 42 – do current

21. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do right
At 42 – do right

22. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do right
At 42 – do right
At NIL

23. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – do right
At 42 – done

24. Use the Activation Stack
• With a recursive module, we
can make use of the
activation stack to visit the
sub-trees and “remember”
where we left off.
13
9
2
42
At 13 – done

25. Outline of In-Order Traversal
• Three principle steps:
– Traverse Left
– Do work (Current)
– Traverse Right

26. In-Order Traversal Procedure
typedef struct node
{
char data;
struct node *left;
struct node *right;
}node;
void inorder_non_recursive(node *t)
{
stack s;
while(t!=NULL)
{
s.push(t);
t=t->left;
}
while(s.isempty()!=1)
{
t=s.pop();
cout<<t->data;
t=t->right;
while(t!=NULL)
{
s.push(t);
t=t->left;
}
}
}

28. Pre-Order Traversal Procedure
void preorder_non_recursive(node *t)
{
stack s;
while(t!=NULL)
{
cout<<t->data;
s.push(t);
t=t->left;
}
while(s.isempty()!=1)
{
t=s.pop();
t=t->right;
while(t!=NULL)
{
cout<<t->data;
s.push(t);
t=t->left;
}
}
}

30. Post-Order Traversal Procedure

31. Binary Search Tree

32. Finding the Correct Location
12
3
7
41
98
Start with
this tree

33. Finding the Correct Location
12
3
7
41
98
Where would
4 be added?

34. Finding the Correct Location
12
3
7
41
98
To the top
doesn’t work
4

35. Finding the Correct Location
12
3
7
41
98
In the middle
doesn’t work
4

36. Finding the Correct Location
12
3
7
41
98
At the bottom
DOES work!
4

37. Finding the Correct Location
• Must maintain “search” structure
– Everything to left is less than current
– Everything to right is greater than current
• Adding at the “bottom” guarantees
we keep search structure.
• We’ll recurse to get to the “bottom”
(i.e. when current = nil)

38. Finding the Correct Location
if (current = nil)
DO “ADD NODE” WORK HERE
elseif (current^.data > value_to_add) then
// recurse left
Insert(current^.left, value_to_add)
else
// recurse right
Insert(current^.right, value_to_add)
endif

39. Adding the Node
• Current is an in/out pointer
– We need information IN to evaluate current
– We need to send information OUT because
we’re changing the tree (adding a node)
• Once we’ve found the correct location:
– Create a new node
– Fill in the data field
(with the new value to add)
– Make the left and right pointers point to nil
(to cleanly terminate the tree)

40. Adding the Node
current <- new(Node)
current^.data <- value_to_add
current^.left <- nil
current^.right <- nil

41. The Entire Module
procedure Insert(cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert

42. Tracing Example
The following example shows a trace of
the BST insert.
• Begin with an empty BST (a pointer)
• Add elements 42, 23, 35, 47 in the
correct positions.

43. Head iot Ptr toa Node
head <- NIL
Insert(head, 42)

44. Head iot Ptr toa Node
head <- NIL
Insert(head, 42)
head

45. Head iot Ptr toa Node
head <- NIL
Insert(head, 42)
head

46. Head iot Ptr toa Node
head <- NIL
Insert(head, 42)
head

47. Head iot Ptr toa Node
head <- NIL
Insert(head, 42)
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
head

48. Head iot Ptr toa Node
head <- NIL
Insert(head, 42)
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
head

49. Head iot Ptr toa Node
head <- NIL
Insert(head, 42)
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
head
42

50. Head iot Ptr toa Node
head <- NIL
Insert(head, 42)
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
head
42

51. Head iot Ptr toa Node
head <- NIL
Insert(head, 42)
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
head
42

52. Head iot Ptr toa Node
head <- NIL
Insert(head, 42)
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
head
42

53. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.

54. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 23

55. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 23

56. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 23

57. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert

58. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert

59. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
23

60. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
23

61. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
23

62. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
23

63. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 23
23

64. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23

65. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35

66. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35

67. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35

68. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35

69. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35

70. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35

71. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert

72. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert

73. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
35

74. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
35

75. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
35

76. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
35

77. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
35

78. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
data_in = 35
35

79. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
35

80. Continue?
yes... I’ve had enough!

81. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
data_in = 47
35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert

82. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
data_in = 47
35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert

83. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
data_in = 47
35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert

84. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
data_in = 47
35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert

85. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
data_in = 47
35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert

86. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
data_in = 47
35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
47

87. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
data_in = 47
35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
47

88. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
data_in = 47
35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
47

89. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
data_in = 47
35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
47

90. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
data_in = 47
35
procedure Insert(
cur iot in/out Ptr toa Node,
data_in iot in num)
if(cur = NIL) then
cur <- new(Node)
cur^.data <- data_in
cur^.left <- NIL
cur^.right <- NIL
elseif(cur^.data > data_in)
Insert(cur^.left, data_in)
else
Insert(cur^.right, data_in)
endif
endprocedure // Insert
47

91. head
42
.
.
Insert(head, 23)
Insert(head, 35)
Insert(head, 47)
.
.
23
35
47

92. Summary
• Preserve “search” structure!
• Inserting involves 2 steps:
– Find the correct location
• For a BST insert, always insert at the
“bottom” of the tree
– Do commands to add node
• Create node
• Add data
• Make left and right pointers point to nil

93. Deleting from a Binary Search Tree
(BST)

94. The Scenario
• We have a Binary Search Tree and
want to remove some element based
upon a match.
• Must preserve “search” property
• Must not lose any elements (i.e. only
remove the one element)

95. BST Deletion
• Search for desired item.
• If not found, then return NIL or print error.
• If found, perform steps necessary to
accomplish removal from the tree.

96. Four Cases for Deletion
• Delete a leaf node
• Delete a node with only one child (left)
• Delete a node with only one child (right)
• Delete a node with two children
Cases 2 and 3 are comparable and only
need slight changes in the conditional
statement used

97. Delete a Leaf Node
Simply use an “in/out”
pointer and assign it
to “nil”. This will
remove the node from
the tree.
cur <- nil
14
50
94
9 71 116
108
66
13
42

98. Delete a Leaf Node
Simply use an “in/out”
pointer and assign it
to “nil”. This will
remove the node from
the tree.
cur <- nil
Let’s delete 42.
14
50
94
9 71 116
108
66
13
42

99. Delete a Leaf Node
Simply use an “in/out”
pointer and assign it
to “nil”. This will
remove the node from
the tree.
cur <- nil
Move the pointer;
now nothing points
to the node.
14
50
94
9 71 116
108
66
13
42

100. Delete a Leaf Node
Simply use an “in/out”
pointer and assign it
to “nil”. This will
remove the node from
the tree.
cur <- nil
The resulting tree.
14
50
94
9 71 116
108
66
13

101. Delete a Node with One Child
Use an “in/out” pointer.
Determine if it has a left
or a right child.
Point the current
pointer to the
appropriate child:
cur <- cur^.left_child
or
cur <- cur^.right_child
14
50
94
71 116
108
66
42

102. Delete a Node with One Child
Use an “in/out” pointer.
Determine if it has a left
or a right child.
Point the current
pointer to the
appropriate child:
cur <- cur^.left_child
or
cur <- cur^.right_child
Let’s delete 14.
14
50
94
71 116
108
66
42

103. Delete a Node with One Child
Use an “in/out” pointer.
Determine if it has a left
or a right child.
Point the current
pointer to the
appropriate child:
cur <- cur^.right_child
Move the pointer; now
nothing points to the
node.
14
50
94
71 116
108
66
42

104. Delete a Node with One Child
Use an “in/out” pointer.
Determine if it has a left
or a right child.
Point the current
pointer to the
appropriate child:
cur <- cur^.right_child
The resulting tree.
50
94
71 116
108
66
42

105. Delete a Node with One Child
Use an “in/out” pointer.
Determine if it has a left
or a right child.
Point the current
pointer to the
appropriate child:
cur <- cur^.left_child
or
cur <- cur^.right_child
Let’s delete 71.
14
50
94
71 116
108
66
42

106. Delete a Node with One Child
Use an “in/out” pointer.
Determine if it has a left
or a right child.
Point the current
pointer to the
appropriate child:
cur <- cur^.left_child
Move the pointer; now
nothing points to the
node.
14
50
94
71 116
108
66
42

107. Delete a Node with One Child
Use an “in/out” pointer.
Determine if it has a left
or a right child.
Point the current
pointer to the
appropriate child:
cur <- cur^.left_child
The resulting tree.
14
50
94
116
108
66
42

108. Delete a Node with Two Children
14
50
94
71 116
108
66
42
Let’s delete 94.

109. Delete a Node with Two Children
14
50
94
71 116
108
66
42
Look to the right
sub-tree.

110. Delete a Node with Two Children
14
50
94
71 116
108
66
42
Find and copy the
smallest value
(this will erase the
old value but creates
a duplicate).
108

111. 108
Delete a Node with Two Children
14
50
71 116
108
66
42
The resulting tree
so far.

112. 108
Delete a Node with Two Children
14
50
71 116
108
66
42
Now delete the
duplicate from
the left sub-tree.

113. Delete a Node with Two Children
14
50
71 116
66
42
The final resulting
tree – still has search
structure.
108

114. tnode *del(tnode *t,int key)
{
tnode *temp;
if(t==NULL)
{
return NULL;
}
if(key<t->data)
{
t->left=del(t->left,key);
return t;
}
if(key>t->data)
{
t->right=del(t->right,key);
return t;
}
//element found
//no child
if(t->left==NULL&t->right==NULL)
{
temp=t;
delete temp;
return NULL;
}
typedef struct tnode
{
int data;
struct tnode*left;
struct tnode*right;
}tnode;

115. //one child
if(t->left!=NULL&&t->right==NULL)
{
temp=t;
t=t->left;
delete temp;
return t;
}
if(t->left==NULL&&t->right!=NULL)
{
temp=t;
t=t->right;
delete temp;
return t;
}
//both child present
temp=find_min(t->right);
t->data=temp->data;
t->right=del(t->right,temp->data);
return t;
tnode *find_min(tnode *r)
{
while(r->left!=NULL)
{
r=r->left;
}
return r;
}