Partition Finding

#include <bits/stdc++.h>
using namespace std;

int op(int i, int j){
    return (i + j - 2 * __gcd(i, j));
}

bool check(vector<int> v, int limit){
    //calculates sum (i + j - 2gcd(i, j))
    vector<int> k;
    for (int i = 0; i < v.size(); i++){
        if (v[i]) k.push_back(i);
    }
    int ans = 0;

    for (int i = 0; i < k.size(); i++){
        for (int j = i + 1; j < k.size(); j++){
            ans += v[k[i]]*v[k[j]]*op(k[i] + 1, k[j] + 1);
            if (ans > (4*limit - 4)){
                return false;
            }
        }
    }
    for (int i = 0; i < k.size(); i++){
        if (k[i] % 2){
            ans += v[k[i]] * (k[i] - 1);
        }
        else{
            ans += v[k[i]] * (k[i] - 2);
        }
    }
    int val = 0; int r = k.size();
    for (int i = 0; i < min(6, r); i++){
        val += v[i];
    }
    if (val < 10) return false;
    if (ans > (4*limit - 4)){
        return false;
    }
    return true;
}
void print(vector<int> v){
    for (int i = 0; i < v.size(); i++){
        if (v[i] != 0){
            printf("%d^^%d ", i+1, v[i]);
        }
    }
    printf("\n");
}
void solve(vector<int> v, int limit, int gcdterm, int sum, int no, int paritycounter){
    //no terms can go in which exceed limit
    //limit is equal to N.
    if (sum == limit){
        if (check(v, limit)){
            print(v);
        }
        return;
    }
    int k = v.size() + 1; //all ones, twos, and threes have been added into the set, if k = 4.
    if (k == 7){
        if (no < 10) return;
    }
    if (k > (limit - sum)){ //clearly this isn't going to work, is it?
        return;
    }

    //if q_k = 0...
    vector<int> q(v);
    q.push_back(0);
    solve(q, limit, gcdterm, sum, no, paritycounter);
    for (int q_k = 1; q_k <= (limit - sum)/k; q_k++){
        int tempg = gcdterm;
        int temps = sum;
        int tempn = no;
        int tempp = paritycounter;
        temps += q_k*k;
        tempn += q_k;
        if (k % 2 == 0){
            tempp += (k - 2)*q_k;
        }
        else{
            tempp += (k - 1)*q_k;
        }
        if (((tempn)*(limit - temps))/2 + tempg + tempp > (4*limit-4)) continue;
        for (int i = 0; i < k - 1; i++){
            tempg += v[i]*q_k*op(i + 1, k);
        }
        if (((tempn)*(limit - temps))/2 + tempg + tempp > (4*limit-4)) continue;
        vector<int> q(v);
        q.push_back(q_k);
        solve(q, limit, tempg, temps, tempn, tempp);
    }
}

int main(){
    //Possible partitions were Q_k <= 4N - 4
    freopen("answersCi.out", "w", stdout);
    for (int i = 1; i < 300; i++){
        printf("This is the answer for case %d:\n", i);
        cerr << i << endl;
        vector<int> v;
        solve(v, i, 0, 0, 0, 0);
    }
}