Add nth Catalan number (fixes #2402) (#2518)

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Amritesh Anand 2021-10-11 16:33:40 +05:30 committed by GitHub
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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 C = 1 and C = 1
catalanArray[0] = 1;
catalanArray[1] = 1;
/**
* The Catalan numbers satisfy the recurrence relation
* C=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();
}
}