C Program to Perform the Unique Factorization of a Given Number

This is a C Program to get all the unique factors of a given integer such that addition of a partition results an integer. Given a positive integer n, generate all possible unique ways to represent n as sum of positive integers.

Here is source code of the C Program to Perform the Unique Factorization of a Given Number. The C program is successfully compiled and run on a Linux system. The program output is also shown below.

```
#include<stdio.h>
```
```
void printarray(int p[], int n) {
```
```
    int i;
```
```
    for (i = 0; i < n; i++)
```
```
        printf("%d ", p[i]);
```
```
    printf("\n");
```
```
}
```
```
void partition(int n) {
```

    int p[n]; // An array to store a partition

    int k = 0; // Index of last element in a partition

    p[k] = n; // Initialize first partition as number itself

```
    int rem_val;
```

    // This loop first prints current partition, then generates next

    // partition. The loop stops when the current partition has all 1s

```
    while (1) {
```
```
        // print current partition
```
```
        printarray(p, k + 1);
```
```
        rem_val = 0;
```
```
        while (k >= 0 && p[k] == 1) {
```
```
            rem_val += p[k];
```
```
            k--;
```
```
        }
```

        // if k < 0, all the values are 1 so there are no more partitions

```
        if (k < 0)
```
```
            return;
```

        // Decrease the p[k] found above and adjust the rem_val

```
        p[k]--;
```
```
        rem_val++;
```

        // If rem_val is more, then the sorted order is violated.  Divide

        // rem_val in different values of size p[k] and copy these values at

        // different positions after p[k]

```
        while (rem_val > p[k]) {
```
```
            p[k + 1] = p[k];
```
```
            rem_val = rem_val - p[k];
```
```
            k++;
```
```
        }
```

        // Copy rem_val to next position and increment position

```
        p[k + 1] = rem_val;
```
```
        k++;
```
```
    }
```
```
}
```
```
int main() {
```
```
    int num;
```

    printf("\nEnter a number to perform integer partition: ");

```
    scanf("%d", &num);
```
```
    partition(num);
```
```
    return 0;
```
```
}
```

Output:

$ gcc UniqueFactors.c
$ ./a.out
 
 
Enter a number to perform integer partition: 4 
4
3 1 
2 2 
2 1 1 
1 1 1 1

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