# C++ program to perform unique factorization of a Given Number

Here is a C++ Program to get all the unique factorization of a given integer such that addition of a partition results an integer. In this program, a positive integer n is given, and we shall generate all possible unique ways to represent n as sum of positive integers.

## Algorithm

Begin
function displayAllUniqueParts(int m):
1) Set Index of last element k in a partition to 0
2) Initialize first partition as number itself, p[k]=m
3) Create a while loop which first prints current partition, then generates next partition. The loop stops when the current partition has all 1s.
4) Display current partition as displayArray(p, k + 1)
5) Generate next partition:
6) Initialize val = 0.
Find the rightmost non-one value in p[]. Also, update the val
so that we know how much value can be accommodated.
If k < 0,
all the values are 1 so there are no more partitions
Decrease the p[k] found above and adjust the val.
7) If val is more, then the sorted order is violated. Divide val in different
values of size p[k] and copy these values at different positions
after p[k].
Copy val to next position and increment position.
End

## Example

#include<iostream>
using namespace std;
void displayArray(int p[], int m) //to print the array
{
for (int i = 0; i < m; i++)
cout << p[i] << " ";
cout << endl;
}
void displayAllUniqueParts(int m)
{
int p[m];
int k = 0;
p[k] = m;
while (true)
{
displayArray(p, k + 1);
int val = 0; //initialize val
while (k >= 0 && p[k] == 1)
{
val += p[k]; //update val
k--;
}
if (k < 0)
return;
p[k]--;
val++;
while (val > p[k]) //if val is more
{
p[k + 1] = p[k];
val = val - p[k];
k++;
}
p[k + 1] = val;
k++;
}
}
int main()
{
cout << "Display All Unique Partitions of 3\n";
displayAllUniqueParts(3);
cout << "\nDisplay All Unique Partitions of 4\n";
displayAllUniqueParts(4);
cout << "\nDisplay All Unique Partitions of 5\n";
displayAllUniqueParts(5);
return 0;
}

## Output

Display All Unique Partitions of 3
3
2 1
1 1 1
Display All Unique Partitions of 4
4
3 1
2 2
2 1 1
1 1 1 1
Display All Unique Partitions of 5
5
4 1
3 2
3 1 1
2 2 1
2 1 1 1
1 1 1 1 1