Calculate Stirling numbers which represents the number of ways to arrange r objects around n different circles

// Java program to implement
// above approach
import java.io.*;

class GFG 
{

// Calculating factorial of 
// an integer n.
static long factorial(int n)
{
    // Our base cases of factorial 
    // 0! = 1! = 1
    if (n == 0)
        return 1;

    // n can't be less than 0.
    if (n < 0)
        return -1;
    long res = 1;
    for (int i = 2; i < n + 1; ++i)
        res *= i;
    return res;
}

// Function to compute the number 
// of combination of r objects 
// out of n objects.
static int nCr(int n, int r)
{
    // r cant be more than n so 
    // we'd like the program to 
    // crash if the user entered
    // wrong input.
    if (r > n)
        return -1;

    if (n == r)
        return 1;

    if (r == 0)
        return 1;

    return nCr(n - 1, r - 1) + 
           nCr(n - 1, r);
}

// Function to calculate the Stirling 
// numbers. The base cases which were 
// discussed above are handled to stop
// the recursive calls.
static long stirlingNumber(int r, int n)
{

    // n can't be more than
    // r, s(r, 0) = 0.
    if (n > r)
        return -1;

    if (n == 0)
        return 0;

    if (r == n)
        return 1;

    if (n == 1)
        return factorial(r - 1);

    if (r - n == 1)
        return nCr(r, 2);
    else
        return stirlingNumber(r - 1, n - 1) + 
                                    (r - 1) * 
               stirlingNumber(r - 1, n);
}

// Driver Code
public static void main (String[] args) 
{
    // Calculating the stirling number s(9, 2)
    int r = 9, n = 2;
    
    long val = stirlingNumber(r, n);
    if (val == -1)
        System.out.println(" No stirling number");
    else
        System.out.println( "The Stirling Number s(" + 
                      r + ", " + n + ") is : " + val);
}
}

// This Code is Contributed by anuj_67

import java.util.Arrays;

public class StirlingNumbers {
    // Function to calculate factorial of an integer n
    public static long factorial(int n) {
        // Base case: 0! and 1! = 1
        if (n == 0 || n == 1) {
            return 1;
        }

        // Compute the factorial using a loop
        long res = 1;
        for (int i = 2; i <= n; ++i) {
            res *= i;
        }

        return res;
    }

    // Function to calculate the Stirling numbers using DP
    // tabulation
    public static long stirlingNumber(int r, int n) {
        // Create a 2D array to store the Stirling numbers
        long[][] dp = new long[n + 1][r + 1];

        // Fill in the base cases
        for (int i = 0; i <= n; i++) {
            dp[i][i] = 1;
        }
        for (int i = 1; i <= r; i++) {
            dp[1][i] = factorial(i - 1);
        }

        // Fill in the rest of the table using a loop
        for (int i = 2; i <= n; i++) {
            for (int j = 2; j <= r; j++) {
                dp[i][j] = dp[i - 1][j - 1] + (j - 1) * dp[i][j - 1];
            }
        }

        // Return the computed value
        return dp[n][r];
    }

    // Driver Code
    public static void main(String[] args) {
        // Calculating the Stirling number s(9, 2)
        int r = 9, n = 2;

        long val = stirlingNumber(r, n);
        if (val == -1)
            System.out.println("No Stirling number");
        else
            System.out.println("The Stirling Number s(" + r + ", " + n + ") is : " + val);
    }
}