C Program to Perform the Unique Factorization of a Given Number

This is a C Program to get all the unique partitions 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 the source code of the C program to partition an integer in all possible ways. The C program is successfully compiled and run on a Linux system. The program output is also shown below.

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

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

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

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

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

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        p[k]--;
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        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]

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

        // Copy rem_val to next position and increment position

```
        p[k+1] = rem_val;
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        k++;
```
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    }
```
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}
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int main()
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{
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    int num;
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    printf("\nEnter a number to perform integer partition: ");

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

$ gcc partition.c -o partition
$ ./partition
 
Enter a number to perform integer partition: 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