Diagram:
Binary Search Tree, Insertion
Assume that the numbers 67, 29, 6,
44, 65, 39, 30, 12, 38, 3, 99, 23, 11, 71, 10, 5, 70, 9, 81, 7, 73, 19 are
going to be inserted. Notice that the tree does not offer the same numbers for
insertion. Therefore, in database aspect, the tree’s node seems like a primary
key with unique. Assume that each number is an element of its node.
67ROOT
67ROOT
PATH because 29 < 67; Notice that lesser goes left
greater goes right
29 LEAF
67ROOT
PATH
29 because 6 < 67 and 6
< 29
6 LEAF
67ROOT
29 because 44 < 67 and
44 > 29
PATH 
6 44 LEAF
67ROOT
29
PATH because
65 < 67 and 65 > 29 and 65 > 44
6 44
65 LEAF
67ROOT
29
because
39 < 67 and 39 > 29 and 39 < 44
6 44
PATH
39 LEAF 65
67ROOT
29
because 30 < 67 and
30 > 29 and 30 < 44 and 30 < 39
6 44
PATH
39 65
30 LEAF
67ROOT
29
PATH because 12 < 67 and 12 < 29 and 12 > 6
6 44
LEAF
12 39 65
30
67ROOT
29 38 < 67 and 38 > 29 and 38 < 44 and 38 < 39 and 38 > 30
PATH
6 44
12 39 65
30
38 LEAF
67ROOT
29 3 < 67 and 3 < 29 and 3 < 6
PATH
6 44
LEAF 3 12 39 65
30
38
67 ROOT
PATH
29 99 LEAF 99 > 67
6 44
3 12 39 65
30
38
67 ROOT
29 99
PATH
6 44
3 12 39 65
LEAF 23 30 23 < 67 and 23 < 29 and 23 > 6 and 23 > 12
38
67 ROOT
29 99
6 44
PATH
3 12 39 65
LEAF 11 23 30
11 <
67 and 11 < 29 and 11 > 6 and 11 < 12
38
67ROOT
PATH 
29 99
6 44 71 LEAF
3 12 39 65
11 23 30 71 > 67 and 71 < 99
38
67ROOT
29 99
PATH
6 44 71
3 12 39 65
11 23 30
10 LEAF 38
10 < 67 and 10 < 29 and 10 > 6 and 10 < 12
and 10 < 11
67ROOT
29 99
PATH
6 44 71
3 12 39 65
LEAF 5 11 23 30
10 38
5 < 67 and 5 < 29 and 5 < 6 and 5 > 3
67ROOT
29 99
PATH
6 44 71
3 12 39 65 70 LEAF
5 11 23 30
10 38
70 > 67 and 70 < 99 and 70 < 71
67ROOT
29 99
6 44 71
PATH
3 12 39 65 70
5 11 23 30
10 38
9 LEAF
9 < 67 and 9 < 29 and 9 > 6 and 9 < 12 and
9 < 11 and 9 < 10
67ROOT
29 99
PATH
6 44 71
3 12 39 65 70 81 LEAF
5 11 23 30
81 > 67 and 81 < 99 and 81 > 71
10 38
9
67ROOT
29 99
6 44 71
3 12 39 65 70 81
5 11 23 30
10 38
PATH
9
7 LEAF 7 < 67 and 7 < 29 and 7 > 6 and 7 < 12 and 7 < 11 and 7
< 10 and 7 < 9
67ROOT
29 99
6 44 71
PATH
3 12 39 65 70 81
5 11 23 30 LEAF 73
10 38
9
73 > 67 and 73 < 99 and 73 > 71 and 73 < 81
7
Tree
Depth
67ROOT
0
29 99 1
6 44 71 2
PATH
3 12 39 65 70 81
3
5 11 23 30
4
10 19 LEAF 38
5
9
6
7
7
19 < 67 and 19 < 29 and 19 > 6 and 19 > 12
and 19 < 23
8
Tree Depth: 7
Balance/Un-balance: Un-balance
_ IFF
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