diff --git a/DynamicProgramming/CatalanNumber.java b/DynamicProgramming/CatalanNumber.java new file mode 100644 index 000000000..156654cec --- /dev/null +++ b/DynamicProgramming/CatalanNumber.java @@ -0,0 +1,60 @@ +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[0] = 1; + catalanArray[1] = 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(); + } +} +