C++ Programming Code Examples
C++ > Mathematics Code Examples
Program to Perform the Unique Factorization of a Given Number
/* Program to Perform the Unique Factorization of a Given Number
This is a C++ Program to find the unique paritions of a given integer such that addition of a partition result an integer. Given a positive integer n, generate all possible unique ways to represent n as sum of positive integers. */
#include<iostream>
using namespace std;
// A utility function to print an array p[] of size 'n'
void printArray(int p[], int n)
{
for (int i = 0; i < n; i++)
cout << p[i] << " ";
cout << endl;
}
void printAllUniqueParts(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
// This loop first prints current partition, then generates next
// partition. The loop stops when the current partition has all 1s
while (true)
{
// print current partition
printArray(p, k + 1);
// Generate next partition
// Find the rightmost non-one value in p[]. Also, update the
// rem_val so that we know how much value can be accommodated
int 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 violeted. Divide
// rem_val in differnt 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++;
}
}
// Driver program to test above functions
int main()
{
cout << "All Unique Partitions of 2 \n";
printAllUniqueParts(2);
cout << "\nAll Unique Partitions of 3 \n";
printAllUniqueParts(3);
cout << "\nAll Unique Partitions of 4 \n";
printAllUniqueParts(4);
return 0;
}
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