61 lines
1.7 KiB
Java
61 lines
1.7 KiB
Java
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package DynamicProgramming;
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/**
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* This file contains an implementation of finding the nth CATALAN NUMBER using dynamic programming
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* Wikipedia: https://en.wikipedia.org/wiki/Catalan_number
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*
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* Time Complexity: O(n^2)
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* Space Complexity: O(n)
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*
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* @author AMRITESH ANAND (https://github.com/amritesh19)
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*/
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import java.util.Scanner;
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public class CatalanNumber {
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/**
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* This method finds the nth Catalan number
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*
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* @param n input n which determines the nth Catalan number
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* n should be less than equal to 50 as 50th Catalan number is 6,533,841,209,031,609,592
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* for n > 50, BigInteger class should be used instead long
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*
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* @return catalanArray[n] the nth Catalan number
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*/
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static long findNthCatalan(int n){
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// Array to store the results of subproblems i.e Catalan numbers from [1...n-1]
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long catalanArray[] = new long[n + 1];
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// Initialising C₀ = 1 and C₁ = 1
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catalanArray[0] = 1;
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catalanArray[1] = 1;
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/**
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* The Catalan numbers satisfy the recurrence relation
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* C₀=1 and Cn = Σ (Ci * Cn-1-i), i = 0 to n-1 , n > 0
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*/
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for(int i = 2; i <= n; i++){
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catalanArray[i] = 0;
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for(int j = 0; j < i; j++){
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catalanArray[i] += catalanArray[j] * catalanArray[i - j - 1];
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}
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}
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return catalanArray[n];
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}
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// Main method
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public static void main(String[] args) {
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Scanner sc = new Scanner(System.in);
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System.out.println("Enter the number n to find nth Catalan number (n <= 50)");
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int n = sc.nextInt();
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System.out.println(n + "th Catalan number is " + findNthCatalan(n));
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sc.close();
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}
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}
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