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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