DP program: Catalan numbers

[rafi007akhtar]

Program for Catalan numbers

Description

A classic DP problem that is often asked in coding contests and interviews is solving for the nth Catalan number. Catalan numbers have numerous applications, like possible number of expressions with correctly matched parentheses, possible number of BSTs with n keys, and so many more. [Applications of Catalan Numbers - GeeksforGeeks]

In my program

Using the technique of tabulation in dynamic programming, I have written a program that computes and prints the first n+1 Catalan numbers, where n is given by the user.

Although Catalan numbers have a factorial-based definition, the definition I used was a recursive one. This definition is written in the program as comments (shown below), and also available in its Uncyclopedia Page.

* A Catalan number satifies the following two properties:
 * C(0) = C(1) = 1; C(n) = sum(C(i).C(n-i-1)), from i = 0 to n-1

Why should this program be included in this repository

• It is a classic DP problem that was thus far missing from this repository.
• Satisfies all the requirements in the README.
  • Directory structure followed.
  • This PR is fully described.
  • bits/stdc++.h is not used; instead I have used the classic iostream.
  • I have commented the code as much as I could.
  • Didn't need struct or class, so didn't use.
  • Supplied a sample test case in the comments (as I didn't want to put any in the main function).
• Solves the problem correctly using a classic DP technique,

Ending notes

If there is any mistake in my program, please notify in this PR conversation, and I shall try to improve them.

Looking forward to seeing this program in the repository!

[ashwek]

@rafi007akhtar Program works fine for inputs less than 20.
For n = 20, Catalan number = 6564120420 (overflows int's capacity). You can use unsigned int to extend the range.
Accepting PR. 👍