kth permutation recursive solution

kth-permutation-recursive.cpp

int factorial(int n) {
    if (n > 12) return INT_MAX;
    int f = 1;
    for (int i = 2; i <= n; i++)
        f *= i;
    return f;
}

void getPermutationHelper(vector<int>& num, int k, stringstream& ss) {
    if (num.size() == 0) return;
    int f = factorial(num.size() - 1);
    int incr = k / f;
    ss << to_string(num[incr]);
    num.erase(num.begin() + incr);
    getPermutationHelper(num, k % f, ss);
}

string getPermutation(int n, int k) {
    k--; // 0-based indexing
    if (k >= factorial(n)) return ""; // error
    vector<int> num(n);
    for (int i = 0; i < n; ++i)
        num[i] = i+1;
    stringstream ss;
    getPermutationHelper(num, k, ss);
    return ss.str();
}