Question

How many binary trees exist with n nodes and level k = 3? Do not count isomorphic tree (ones with the same physical structure). Justify your answer.

EXPERT ANSWER

The total number of binary trees with n nodes at level 3 can be calculated with the help of Catalan number({eq}C_n)

{/eq}

The total number of possible Binary Trees with n different keys can be calculated by the formula as:

{eq}(countBT(n)) = countBST(n) * n!

{/eq}

where countBT