Catalan Number Using Dynamic Programming in Data Structure And Algorithm : Practice MCQ Questions & Answers with Explanations

The space complexities are as follows:

Dynamic programming: O(n)

Recursion: O(1)

Binomial coefficients: O(1).

The time complexities are as follows:

Dynamic programming: O(n^{2})

Recursion: Exponential

Binomial coefficients: O(n).

The line arr[i] += arr[j] * arr[k] reflects the recursive formula (Cn = \sumCi*C(n-i)).

All of the mentioned methods can be used to find the nth Catalan number.

Counting the number of Dyck words, Counting the number of expressions containing n pairs of parenthesis, Counting the number of ways in which a convex polygon can be cut into triangles by connecting vertices with straight lines are the applications of Catalan numbers where as creation of head and tails for a given number of tosses is an application of Pascal's triangle.

Catalan numbers are given by: (2n!)/((n+1)!n!).

First Catalan number is given by n = 0.

So the 6th Catalan number will be given by n = 5, which is 42.

Catalan numbers are given by: (2n!)/((n+1)!n!).

For n = 0, we get C0 = 1.

For n = 3, we get C3 = 5.

For n = 4, we get C4 = 14.

For n = 5, we get C3 = 42.