Sunday, April 28, 2013

Number of ordered binary trees

The no of possible ordered binary trees with 5 nodes A, B, C, D, E is

a. 15               b. 9               c. 41           d. 42


The answer is  d. 42

The number of possible ordered binary trees is given by the formula :
1/n+1 (2n C n)
Here n is 5, 1/n+1 (2n C n) = 1/6 (10 C 5) = 42.

The formula 1/n+1 (2n C n) is bit more complex. The derivation of the formula we shall discuss in one of the future posts.

Note: nCr = n! / (r! * (n-r)!)

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