# C# Program for nth Catalan Number

Catalan numbers are a sequence of natural numbers that occurs in many interesting counting problems like following.

**1)** Count the number of expressions containing n pairs of parentheses which are correctly matched. For n = 3, possible expressions are ((())), ()(()), ()()(), (())(), (()()).

**2)** Count the number of possible Binary Search Trees with n keys (See this)

See this for more applications.

The first few Catalan numbers for n = 0, 1, 2, 3, … are **1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, …**

## Recommended: Please solve it on “__PRACTICE__ ” first, before moving on to the solution.

__PRACTICE__**Recursive Solution**

Catalan numbers satisfy the following recursive formula.

Following is the implementation of above recursive formula.

## C#

`// A recursive C# program to find` `// nth catalan number` `using` `System;` ` ` `class` `GFG {` ` ` ` ` `// A recursive function to find` ` ` `// nth catalan number` ` ` `static` `int` `catalan(` `int` `n)` ` ` `{` ` ` `int` `res = 0;` ` ` ` ` `// Base case` ` ` `if` `(n <= 1) {` ` ` `return` `1;` ` ` `}` ` ` `for` `(` `int` `i = 0; i < n; i++) {` ` ` `res += catalan(i)` ` ` `* catalan(n - i - 1);` ` ` `}` ` ` `return` `res;` ` ` `}` ` ` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `for` `(` `int` `i = 0; i < 10; i++)` ` ` `Console.Write(catalan(i)` ` ` `+ ` `" "` `);` ` ` `}` `}` ` ` `// This code is contributed by` `// nitin mittal.` |

**Output:**

1 1 2 5 14 42 132 429 1430 4862

**Dynamic Programming Solution**

We can observe that the above recursive implementation does a lot of repeated work (we can the same by drawing recursion tree). Since there are overlapping subproblems, we can use dynamic programming for this. Following is a Dynamic programming based implementation in C++.

Please refer complete article on Program for nth Catalan Number for more details!