 # C++ Programming Code Examples

## C++ > Mathematics Code Examples

### C++ Program to Perform Partition of an Integer in All Possible Ways

``` C++ Program to Perform Partition of an Integer in All Possible Ways 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. #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; } ``` 