/*This is a java program to find the number of ways to write a given number as sum of numbers less than the number itself. We start with the number, number minus one is the next partition and so on, till all one’s are the last partition where we stop.*/

//This is a java program to find the number of ways to write a number as a sum of smaller than the number itself
import java.util.Scanner;

public class NumberOf_Unique_Partitions
{
    public static void print(int[] p, int n, int count)
    {
        for (int i = 0; i < n; i++)
            System.out.print(p[i] + " ");
        System.out.println();
        int j;
        for (j = 0; j < n; j++)
            {
                if (p[j] == 1)
                    continue;
                else
                    break;
            }
        if (j == n)
            System.out
            .println("The number of ways to write a number as a sum of number smaller than itself is :"
                     + (count - 1));
    }

    public static void generateUniquePartition(int n)
    {
        int[] p = new int[n];
        int k = 0, count = 0;
        p[k] = n;
        while (true)
            {
                count++;
                print(p, k + 1, count);
                int rem_value = 0;
                while (k >= 0 && p[k] == 1)
                    {
                        rem_value += p[k];
                        k--;
                    }
                if (k < 0)
                    return;
                p[k]--;
                rem_value++;
                while (rem_value > p[k])
                    {
                        p[k + 1] = p[k];
                        rem_value -= p[k];
                        k++;
                    }
                p[k + 1] = rem_value;
                k++;
            }
    }

    public static void main(String args[])
    {
        System.out.println("Unique Partitioning of a given number");
        System.out.println("Enter the number:");
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        generateUniquePartition(n);
        sc.close();
    }
}

/*
Unique Partitioning of a given number
Enter the number:
6
6
5 1
4 2
4 1 1
3 3
3 2 1
3 1 1 1
2 2 2
2 2 1 1
2 1 1 1 1
1 1 1 1 1 1
The number of ways to write as a sum of number smaller than itself is :10