Possible Binary Search Trees

Computer Science Level 1

Suppose each number in the list [ 1 , 2 , 3 , 4 , 5 , 6 , 7 ] [ 1,2,3,4,5,6,7 ] is assigned to each node in the tree above. How many of the possible 5040 trees are binary search trees?


The answer is 1.

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Thaddeus Abiy by Thaddeus Abiy , 25, Ethiopia

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1 solution

Eli Ross Staff
Jan 26, 2016

In a BST, all elements in any left sub-tree must be smaller than the root, and all elements in any right sub-tree must be larger.

Since there are 3 elements in the left and right trees, this means that 4 has to be the root of the tree. In the left sub-tree, using a similar argument, 2 has to be the root with 1 and 3 as the leaves. On the right sub-tree, 6 has to be the root, with 5 and 7 as the leaves. This gives only 1 valid BST.

5 Helpful 1 Interesting 0 Brilliant 2 Confused

Strictly speaking the assignments in this case are only uniquly determined with respect to fhe ordering function. So there is e.g. another perfectly valid tree if you order descending instead of ascending.

J T - 1 year, 9 months ago

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