``````package DynamicProgramming;

/**
* This file contains an implementation of finding the nth CATALAN NUMBER using dynamic programming
* Wikipedia: https://en.wikipedia.org/wiki/Catalan_number
*
* Time Complexity: O(n^2)
* Space Complexity: O(n)
*
* @author AMRITESH ANAND (https://github.com/amritesh19)
*/

import java.util.Scanner;

public class CatalanNumber {

/**
* This method finds the nth Catalan number
*
* @param n input n which determines the nth Catalan number
*          n should be less than equal to 50 as 50th Catalan number is 6,533,841,209,031,609,592
*          for n > 50, BigInteger class should be used instead long
*
* @return catalanArray[n] the nth Catalan number
*/
static long findNthCatalan(int n){

// Array to store the results of subproblems i.e Catalan numbers from [1...n-1]
long catalanArray[] = new long[n + 1];

// Initialising C₀ = 1 and C₁ = 1
catalanArray = 1;
catalanArray = 1;

/**
* The Catalan numbers satisfy the recurrence relation
* C₀=1 and Cn = Σ (Ci * Cn-1-i),  i = 0 to n-1 , n > 0
*/
for(int i = 2; i <= n; i++){
catalanArray[i] = 0;
for(int j = 0; j < i; j++){
catalanArray[i] += catalanArray[j] * catalanArray[i - j - 1];
}
}

return catalanArray[n];
}

// Main method
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);

System.out.println("Enter the number n to find nth Catalan number (n <= 50)");
int n = sc.nextInt();
System.out.println(n + "th Catalan number is " + findNthCatalan(n));

sc.close();
}
}

``````

#### CatalanNumber

A  