# Java Program to Find the Number of Ways to Write a Number as the Sum of Numbers Smaller than Itself

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.

Here is the source code of the Java Program to Find the Number of Ways to Write a Number as the Sum of Numbers Smaller than Itself. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

1. //This is a java program to find the number of ways to write a number as a sum of smaller than the number itself
2. import java.util.Scanner;
3.
4. public class NumberOf_Unique_Partitions
5. {
6.     public static void print(int[] p, int n, int count)
7.     {
8.         for (int i = 0; i < n; i++)
9.             System.out.print(p[i] + " ");
10.         System.out.println();
11.         int j;
12.         for (j = 0; j < n; j++)
13.         {
14.             if (p[j] == 1)
15.                 continue;
16.             else
17.                 break;
18.         }
19.         if (j == n)
20.             System.out
21.                     .println("The number of ways to write a number as a sum of number smaller than itself is :"
22.                             + (count - 1));
23.     }
24.
25.     public static void generateUniquePartition(int n)
26.     {
27.         int[] p = new int[n];
28.         int k = 0, count = 0;
29.         p[k] = n;
30.         while (true)
31.         {
32.             count++;
33.             print(p, k + 1, count);
34.             int rem_value = 0;
35.             while (k >= 0 && p[k] == 1)
36.             {
37.                 rem_value += p[k];
38.                 k--;
39.             }
40.             if (k < 0)
41.                 return;
42.
43.             p[k]--;
44.             rem_value++;
45.
46.             while (rem_value > p[k])
47.             {
48.                 p[k + 1] = p[k];
49.                 rem_value -= p[k];
50.                 k++;
51.             }
52.             p[k + 1] = rem_value;
53.             k++;
54.         }
55.     }
56.
57.     public static void main(String args[])
58.     {
59.         System.out.println("Unique Partitioning of a given number");
60.         System.out.println("Enter the number:");
61.         Scanner sc = new Scanner(System.in);
62.         int n = sc.nextInt();
63.         generateUniquePartition(n);
64.         sc.close();
65.     }
66. }

Output:

\$ javac NumberOf_Unique_Partitions.java
\$ java NumberOf_Unique_Partitions

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

Sanfoundry Global Education & Learning Series – 1000 Java Programs.