SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group Binary Search Tree A running demonstration of binary search data structure and algorithms
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SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Binary Search Tree
A running demonstration of binary search data structure and algorithms
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
First value is the 'Root' of the tree.
87
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
Since 50 is Less than 87, we move to the left sub-tree
**Since no sub-tree, 50 is now added as the left leaf**
50
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
Since 27 is Less than 87, we move to the left sub-tree
Since 27 is Less than 50, we move to the left sub-tree
**Since no sub-tree, 27 is now added as the left leaf**
27
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
Since 111 is Greater than 87, we move to the right sub-tree
**Since no sub-tree, 111 is now added as the right leaf**
111
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
111
Since 99 is Greater than 87, we move to the right sub-tree
Since 99 is Less than 111, we move to the left sub-tree
**Since no sub-tree, 99 is now added as the left leaf**
99
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
111
99
Since 42 is Less than 87, we move to the left sub-tree
Since 42 is Less than 50, we move to the left sub-tree
Since 42 is Greater than 27, we move to the right sub-tree
**Since no sub-tree, 42 is now added as the right leaf**
42
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
111
99
42
Since 90 is Greater than 87, we move to the right sub-tree
Since 90 is Less than 111, we move to the left sub-tree
Since 90 is Less than 99, we move to the left sub-tree
**Since no sub-tree, 90 is now added as the left leaf**
90
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
111
99
42 90
Since 105 is Greater than 87, we move to the right sub-tree
Since 105 is Less than 111, we move to the left sub-tree
Since 105 is Greater than 99, we move to the right sub-tree
**Since no sub-tree, 105 is now added as the right leaf**
105
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
111
99
42 90 105
Since 58 is Less than 87, we move to the left sub-tree
Since 58 is Greater than 50, we move to the right sub-tree
**Since no sub-tree, 58 is now added as the right leaf**
58
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
111
99
42 90 105
58
Since 32 is Less than 87, we move to the left sub-tree
Since 32 is Less than 50, we move to the left sub-tree
Since 32 is Greater than 27, we move to the right sub-tree
Since 32 is Less than 42, we move to the left sub-tree
**Since no sub-tree, 32 is now added as the left leaf**
32
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
111
99
42 90 105
58
32
Since 68 is Less than 87, we move to the left sub-tree
Since 68 is Greater than 50, we move to the right sub-tree
Since 68 is Greater than 58, we move to the right sub-tree
**Since no sub-tree, 68 is now added as the right leaf**
68
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
111
99
42 90 105
58
32
68
Since 43 is Less than 87, we move to the left sub-tree
Since 43 is Less than 50, we move to the left sub-tree
Since 43 is Greater than 27, we move to the right sub-tree
Since 43 is Greater than 42, we move to the right sub-tree
**Since no sub-tree, 43 is now added as the right leaf**
43
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
111
99
42 90 105
58
32
68
43
Since 60 is Less than 87, we move to the left sub-tree
Since 60 is Greater than 50, we move to the right sub-tree
Since 60 is Greater than 58, we move to the right sub-tree
Since 60 is Less than 68, we move to the left sub-tree
**Since no sub-tree, 60 is now added as the left leaf**
60
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
111
99
42 90 105
58
32
68
43 60
Since 70 is Less than 87, we move to the left sub-tree
Since 70 is Greater than 50, we move to the right sub-tree
Since 70 is Greater than 58, we move to the right sub-tree
Since 70 is Greater than 68, we move to the right sub-tree
**Since no sub-tree, 70 is now added as the right leaf**
70
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
111
99
42 90 105
58
32
68
43 60 70
Since 51 is Less than 87, we move to the left sub-tree
Since 51 is Greater than 50, we move to the right sub-tree
Since 51 is Less than 58, we move to the left sub-tree
**Since no sub-tree, 51 is now added as the left leaf**
51
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
111
99
42 90 105
58
32
68
43 60 70
51
Since 1 is Less than 87, we move to the left sub-tree
Since 1 is Less than 50, we move to the left sub-tree
Since 1 is Less than 27, we move to the left sub-tree
**Since no sub-tree, 1 is now added as the left leaf**
1
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Insert
87
50
27
111
99
42 90 105
58
32
68
43 60 70
511
Since 11 is Less than 87, we move to the left sub-tree
Since 11 is Less than 50, we move to the left sub-tree
Since 11 is Less than 27, we move to the left sub-tree
Since 11 is Greater than 1, we move to the right sub-tree
**Since no sub-tree, 11 is now added as the right leaf**
11
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Predecessor
The node to delete is 50
Predecessor is found by finding the right most node of the 50 nodes left sub-tree
87
50
27
111
99
42 90 105
58
32
68
43 60 70
511
11
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Sucsessor
Successor is found by finding the left most node of the 50 nodes right sub-tree
87
50
27
111
99
42 90 105
58
32
68
43 60 70
511
11
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
How to delete 50?
There is a left child so we find predecessor
To learn more about finding predecessor insert <Fpred>starting value</Fpred> to data file
87
50
27
111
99
42 90 105
58
32
68
43 60 70
511
11
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Delete
There is a left child so we find predecessor
This is how the new tree would appear
87
43
27
1
11
42
32
58
51 68
60 70
111
99
90 105
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
How to delete 105?
This is a Leaf case
We just remove this node from the tree
87
43
27
1
11
42
32
58
51 68
60 70
111
99
90 105
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Delete
This is a Leaf case
This is how the new tree would appear
87
43
27
1
11
42
32
58
51 68
60 70
111
99
90
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
How to delete 87?
There is a left child so we find predecessor
To learn more about finding predicessor insert <Fpred>starting value</Fpred> to data file
87
43
27
1
11
42
32
58
51 68
60 70
111
99
90
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Delete
There is a left child so we find predecessor
This is how the new tree would appear
70
43
27
1
11
42
32
58
51 68
60
111
99
90
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
How to delete 111?
There is only one child, so replace the node with its only child
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111
99
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SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
After 111 is replaced by its only child
There is only one child, so replace the node with its only child
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51 68
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99
90
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
PreOrder Traversal
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
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1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PreOrder Traversal
1.Visit the root
2.Visit the left sub-tree 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
InOrder Traversal
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
InOrder Traversal
1.Visit the left sub-tree
2.Visit the root 3.Visit the right sub-tree
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
PostOrder Traversal
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
PostOrder Traversal
1.Visit the left sub-tree
2.Visit the right sub-tree 3.Visit the root
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Breadth First Traversal
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Breadth First Traversal
1.Visit the root
2.Visit both Children 3.Visit Their Children
Visit
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Size
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Size
Size is the amount of nodes in a tree
1
2
3
4
5
6
7
8
9 10
11
12
13
14
Size = 14
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Height
SUNY Oneonta Data Structures and Algorithms Visualization Teaching Materials Generation Group
Height
Hight is the number of Levels between
the root and lowest leaf
70
43
27
1
11
42
32
58
51 68
60
111
99
90
Height = 5
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