ordered_unordered_n_partition.cpp

#include<iostream>                                                                                                                                                         
#include<vector>

using namespace std;

typedef vector<int> VI; 

int ordered_partitons(int n, VI& ni) {
        int res = 0;
        for (int i : ni) {
                int t = n- i;
                if (t == 0)
                        ++res;
                else if (t > 0)
                        res += ordered_partitons(t, ni);
        }
        return res;
}

int unordered_partitions(int n, VI& ni, int j) { // expected ordered ni passed
        if (j < 0)
                return 0;
        int t = n - ni[j];
        if (t == 0)
                return 1;
        if (t < 0)
                return 0;
        return unordered_partitions(n, ni, j-1) +
                unordered_partitions(t, ni, j); 
}

int main(int argc, char ** argv) {
        VI ni({1,2,3});
        cout << "F(7; 1,2,3): " << ordered_partitons(7, ni) << endl;
        cout << "P(7; 1,2,3): " << unordered_partitions(7, ni, (int)ni.size() - 1) << endl;
        return 0;
}