How many different binary trees can be made from three nodes that contain the key values...

Question

Question

How many different binary trees can be made from three nodes that contain the key values 1, 2, and 3?

Answer 1

Answer #1

Binary tree :- 30 as follows

1 1 2 2 3 3
/ \ / \ / \ / \ / \ / \
2 3 3 2 1 3 3 1 1 2 2 1

1 1 1 1 1 1 1 1
/ / / / \ \ \ \
2 3 2 3 2 3 2 3
/ / \ \ / / \ \
3 2 3 2 3 2 3 2

2 2 2 2 2 2 2 2
/ / / / \ \ \ \
1 3 1 3 1 3 1 3
/ / \ \ / / \ \
3 1 3 1 3 1 3 1

3 3 3 3 3 3 3 3
/ / / / \ \ \ \
2 1 2 1 2 1 2 1
/ / \ \ / / \ \
1 2 1 2 1 2 1 2

Binary search tree :-5 as follows

1 1 2 3 3
\ \ / \ / /
2 3 1 3 1 2
\ / \ /
3 2 2 1

Answer 2

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