Kortit II

#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <iterator>
#include <iomanip>
#include <list>
#include <numeric>

using namespace std;


int mod_factorial(int n) {
    long long result = 1;
    for (int i = 2; i <= n; ++i) {
        result = (result * i) % 1000000007;
    }
    return result;
}
long long factorial(int n) {
    long long result = 1;
    for (int i = 2; i <= n; ++i) {
        result *= i;
    }
    return result;
}

long long nCr(int n, int k) {
    long long result = mod_factorial(n)/(mod_factorial(k)*mod_factorial(n-k));
    return result;
}

vector<int> ith_permutation(const vector<int>& l, int i) {
    int n = l.size();
    vector<long long> fact(n, 1);
    vector<int> perm(n, 0);

    for (int k = 1; k < n; ++k) {
        fact[k] = fact[k - 1] * k;
    }

    for (int k = 0; k < n; ++k) {
        perm[k] = i / fact[n - 1 - k];
        i = i % fact[n - 1 - k];
    }

    for (int k = n - 1; k > 0; --k) {
        for (int j = k - 1; j >= 0; --j) {
            if (perm[j] <= perm[k]) {
                perm[k]++;
            }
        }
    }

    vector<int> result;
    for (int x : perm) {
        result.push_back(l[x]);
    }
    return result;
}

int main() {
    int t;
    cin >> t;

    vector<vector<int>> vals(t);
    for (int test = 0; test < t; ++test) {
        int n, a, b;
        cin >> n >> a >> b;
        vals[test] = {n, a, b};
    }

    for (const auto& test : vals) {
        int n = test[0], a = test[1], b = test[2];
        if (a + b == 1 || a + b > n) {
            cout << 0 << endl;
            continue;
        }
        if (a+b==0) {
            cout << mod_factorial(n) << "\n";
            continue;
        }
        if (b>a) {
            int temp=a;
            a=b;
            b=temp;
        }
        int possibles = 0;
        int apb = a + b;
        int c = n-apb;
        int _fac = factorial(apb) - 1;
        vector<int> draws(n - apb);
        iota(draws.begin(), draws.end(), apb);
        vector<int> pairs(n);
        iota(pairs.begin(), pairs.end(), 0);

        sort(draws.rbegin(), draws.rend());
        for (int draw : draws) {
            pairs.erase(pairs.begin() + draw);
        }

        int i = _fac;
        while (i >= 0) {
            vector<int> perm = ith_permutation(pairs, i);
            int A = 0, B = 0, C = 0;
            for (int j = 0; j < apb; j++) {
                if (perm[j] < pairs[j]) {
                    A++;
                } else if (perm[j] > pairs[j]) {
                    B++;
                } else {
                    C++;
                }

                if (A > a || B > b || C > c || (A <= a && B <= b && j == apb - 1)) {
                    i -= factorial(apb - j - 1);
                    break;
                }
            }

            if (A == a && B == b) {
                possibles++;
            }
        }
        

        possibles = (((possibles * mod_factorial(n)) % 1000000007) * nCr(n, c)) % 1000000007;
        cout << possibles << "\n";
    }

    return 0;
}

Test 1

Group: 1, 2, 3, 4, 5

Verdict: ACCEPTED

Test 2

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 3

Group: 3, 4, 5

Verdict: TIME LIMIT EXCEEDED

Test 4

Group: 4, 5

Verdict: TIME LIMIT EXCEEDED

Test 5

Group: 5

Verdict: TIME LIMIT EXCEEDED

Test 6

Group: 5

Verdict: WRONG ANSWER