結果

問題 No.2068 Restricted Permutation
ユーザー rniyarniya
提出日時 2022-09-02 22:24:22
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 20 ms / 2,000 ms
コード長 8,160 bytes
コンパイル時間 2,632 ms
コンパイル使用メモリ 212,160 KB
実行使用メモリ 7,020 KB
最終ジャッジ日時 2024-11-16 04:19:02
合計ジャッジ時間 3,442 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 23
権限があれば一括ダウンロードができます

ソースコード

diff # 

#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (size_t i = 0; i < v.size(); i++) {
        os << v[i] << (i + 1 == v.size() ? "" : " ");
    }
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
    for (size_t i = 0; i < v.size(); i++) {
        os << v[i] << (i + 1 == v.size() ? "" : " ");
    }
    return os;
}
template <typename T, size_t N> ostream& operator<<(ostream& os, const array<T, N>& v) {
    for (size_t i = 0; i < N; i++) {
        os << v[i] << (i + 1 == N ? "" : " ");
    }
    return os;
}

template <int i, typename T> void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {
    if (i) os << ',';
    os << get<i>(t);
    print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {
    os << '{';
    print_tuple<0, tuple<Args...>, Args...>(os, t);
    return os << '}';
}

void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                                   \
    cerr << " ";                                                                     \
    cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
    cerr << " ";                                                                     \
    debug_out(__VA_ARGS__)
#else
#define debug(...) void(0)
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
long long MSK(int n) { return (1LL << n) - 1; }

template <class T> T ceil(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? x / y : (x - y + 1) / y);
}

template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <typename T> void mkuni(vector<T>& v) {
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
}
template <typename T> int lwb(const vector<T>& v, const T& x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); }
#pragma endregion

#include <iostream>
#include "atcoder/modint"

namespace atcoder {

template <int MOD> std::istream& operator>>(std::istream& is, static_modint<MOD>& x) {
    int64_t v;
    x = static_modint<MOD>{(is >> v, v)};
    return is;
}

template <int MOD> std::ostream& operator<<(std::ostream& os, const static_modint<MOD>& x) { return os << x.val(); }

template <int ID> std::ostream& operator<<(std::ostream& os, const dynamic_modint<ID>& x) { return os << x.val(); }

}  // namespace atcoder

#include <cassert>
#include <vector>

template <typename T> struct Binomial {
    Binomial(int MAX = 0) : n(1), facs(1, T(1)), finvs(1, T(1)), invs(1, T(1)) {
        while (n <= MAX) extend();
    }

    T fac(int i) {
        assert(i >= 0);
        while (n <= i) extend();
        return facs[i];
    }

    T finv(int i) {
        assert(i >= 0);
        while (n <= i) extend();
        return finvs[i];
    }

    T inv(int i) {
        assert(i >= 0);
        while (n <= i) extend();
        return invs[i];
    }

    T P(int n, int r) {
        if (n < 0 || n < r || r < 0) return T(0);
        return fac(n) * finv(n - r);
    }

    T C(int n, int r) {
        if (n < 0 || n < r || r < 0) return T(0);
        return fac(n) * finv(n - r) * finv(r);
    }

    T H(int n, int r) {
        if (n < 0 || r < 0) return T(0);
        return r == 0 ? 1 : C(n + r - 1, r);
    }

    T C_naive(int n, int r) {
        if (n < 0 || n < r || r < 0) return T(0);
        T res = 1;
        r = std::min(r, n - r);
        for (int i = 1; i <= r; i++) res *= inv(i) * (n--);
        return res;
    }

private:
    int n;
    std::vector<T> facs, finvs, invs;

    inline void extend() {
        int m = n << 1;
        facs.resize(m);
        finvs.resize(m);
        invs.resize(m);
        for (int i = n; i < m; i++) facs[i] = facs[i - 1] * i;
        finvs[m - 1] = T(1) / facs[m - 1];
        invs[m - 1] = finvs[m - 1] * facs[m - 2];
        for (int i = m - 2; i >= n; i--) {
            finvs[i] = finvs[i + 1] * (i + 1);
            invs[i] = finvs[i] * facs[i - 1];
        }
        n = m;
    }
};

const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;

using mint = atcoder::modint998244353;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    Binomial<mint> BINOM;
    int N, K, X;
    cin >> N >> K >> X;
    K--, X--;

    mint ans = 0;
    // i 項目で大小が確定するような順列 A と B (b_K = X) の個数
    for (int i = 0; i < N; i++) {
        if (i == K) {
            ans += BINOM.P(N - 2, i) * X * BINOM.fac(N - 1 - i) * BINOM.fac(N - 1 - i);
        } else if (i < K) {
            ans +=
                BINOM.C(N - 1, i + 2) * BINOM.C(i + 2, 2) * BINOM.fac(i) * BINOM.fac(N - 2 - i) * BINOM.fac(N - 1 - i);
            ans += BINOM.P(N - 2, i) * (N - 1 - X) * BINOM.fac(N - 2 - i) * BINOM.fac(N - 1 - i);  // b_i = X
        } else {
            ans += BINOM.C(N - 1, i + 1) * BINOM.C(i + 1, 2) * BINOM.fac(i - 1) * BINOM.fac(N - 1 - i) *
                   BINOM.fac(N - 1 - i);
        }
    }

    cout << ans << '\n';
    return 0;
}
0