kth permutation iterative solution

kth-permutation-iterative.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;
}

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 perm;
    for (int i = 0; i < n; i++) {
        int fact = factorial(n-i-1);
        int incr = k / fact;
        int t = num[i+incr];
        for (int j = i+incr; j > i; j--)
            num[j] = num[j-1];
        num[i] = t;
        k %= fact;
        perm << to_string(num[i]);
    }
    return perm.str();
}