結果

問題 No.243 出席番号(2)
ユーザー FF256grhy
提出日時 2019-11-11 23:40:40
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 95 ms / 2,000 ms
コード長 4,704 bytes
コンパイル時間 1,667 ms
コンパイル使用メモリ 172,612 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-09-15 08:16:40
合計ジャッジ時間 3,980 ms
ジャッジサーバーID
（参考情報） 		judge6 / judge1
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 * 30
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 #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
typedef long long   signed int LL;
typedef long long unsigned int LU;
#define incID(i, l, r) for(LL i = (l)    ; i <  (r); ++i)
#define incII(i, l, r) for(LL i = (l)    ; i <= (r); ++i)
#define decID(i, l, r) for(LL i = (r) - 1; i >= (l); --i)
#define decII(i, l, r) for(LL i = (r)    ; i >= (l); --i)
#define inc(i, n)  incID(i, 0, n)
#define inc1(i, n) incII(i, 1, n)
#define dec(i, n)  decID(i, 0, n)
#define dec1(i, n) decII(i, 1, n)
#define inID(v, l, r) ((l) <= (v) && (v) <  (r))
#define inII(v, l, r) ((l) <= (v) && (v) <= (r))
#define PB push_back
#define EB emplace_back
#define MP make_pair
#define FI first
#define SE second
#define  ALL(v)  v.begin(),  v.end()
#define RALL(v) v.rbegin(), v.rend()
template<typename T> bool setmin  (T & a, T b) { if(b <  a) { a = b; return true; } else { return false; } }
template<typename T> bool setmax  (T & a, T b) { if(b >  a) { a = b; return true; } else { return false; } }
template<typename T> bool setmineq(T & a, T b) { if(b <= a) { a = b; return true; } else { return false; } }
template<typename T> bool setmaxeq(T & a, T b) { if(b >= a) { a = b; return true; } else { return false; } }
LL mo(LL a, LL b) { assert(b > 0); a %= b; if(a < 0) { a += b; } return a; }
LL fl(LL a, LL b) { assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); }
LL ce(LL a, LL b) { assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); }
template<typename T> T gcd(T a, T b) { return (b == 0 ? a : gcd(b, a % b)); }
template<typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
#define bit(b, i) (((b) >> (i)) & 1)
#define BC __builtin_popcountll
#define SC static_cast
#define SI(v) SC<int>(v.size())
#define SL(v) SC<LL >(v.size())
#define RF(e, v) for(auto & e: v)
#define ef else if
#define UR assert(false)
// ---- ----
template<LL M> class ModInt {
private:
    LL v = 0;
public:
    ModInt() { }
    ModInt(LL vv) { setval(vv); }
    ModInt & setval(LL vv) { v = vv % M; if(v < 0) { v += M; } return (*this); }
    LL getval() const { return v; }
    ModInt & operator+=(const ModInt & b)       { return setval(v + b.v); }
    ModInt & operator-=(const ModInt & b)       { return setval(v - b.v); }
    ModInt & operator*=(const ModInt & b)       { return setval(v * b.v); }
    ModInt & operator/=(const ModInt & b)       { return setval(v * b.inv()); }
    ModInt & operator^=(            LU b)       { return setval(ex(v, b)); }
    ModInt   operator+ (                ) const { return ModInt(+v); }
    ModInt   operator- (                ) const { return ModInt(-v); }
    ModInt   operator+ (const ModInt & b) const { return ModInt(v + b.v); }
    ModInt   operator- (const ModInt & b) const { return ModInt(v - b.v); }
    ModInt   operator* (const ModInt & b) const { return ModInt(v * b.v); }
    ModInt   operator/ (const ModInt & b) const { return ModInt(v * b.inv()); }
    ModInt   operator^ (            LU b) const { return ModInt(ex(v, b)); }
    LL inv() const {
        LL x = (ex_gcd(v, M).FI + M) % M;
        assert(v * x % M == 1);
        return x;
    }
    LL ex(LL a, LU b) const {
        LL D = 64, x[64], y = 1;
        inc(i, D) { if((b >> i) == 0) { D = i; break; } }
        inc(i, D) { x[i] = (i == 0 ? a : x[i - 1] * x[i - 1]) % M; }
        inc(i, D) { if((b >> i) & 1) { (y *= x[i]) %= M; } }
        return y;
    }
    pair<LL, LL> ex_gcd(LL a, LL b) const {
        if(b == 0) { return MP(1, 0); }
        auto p = ex_gcd(b, a % b);
        return MP(p.SE, p.FI - (a / b) * p.SE);
    }
};
template<LL M> ModInt<M> operator+(LL a, const ModInt<M> & b) { return  b + a; }
template<LL M> ModInt<M> operator-(LL a, const ModInt<M> & b) { return -b + a; }
template<LL M> ModInt<M> operator*(LL a, const ModInt<M> & b) { return  b * a; }
template<LL M> ModInt<M> operator/(LL a, const ModInt<M> & b) { return  a * b.inv(); }
template<LL M> istream & operator>>(istream & is, ModInt<M> & b) { LL v; is >> v; b.setval(v); return is; }
template<LL M> ostream & operator<<(ostream & os, const ModInt<M> & b) { return (os << b.getval()); }
// ---- ----
const int MOD = 1'000'000'007;
int main() {
    int n;
    cin >> n;
    vector<LL> b(n);
    inc(i, n) {
        int a;
        cin >> a;
        if(a < n) { b[a]++; }
    }
    
    vector<LL> f(n + 1), r(n + 1);
    inc(i, n + 1) { f[i] = (i == 0 ? 1 : f[i - 1] * i) % MOD; }
    ModInt<1'000'000'007> F = f[n];
    LL R = F.inv();
    dec(i, n + 1) { r[i] = (i == n ? R : r[i + 1] * (i + 1)) % MOD; }
    auto comb = [&](auto a, auto b) { return f[a] * r[b] % MOD * r[a - b] % MOD; };
    
    vector<LL> x(n + 1);
    x[0] = 1;
    inc(i, n) {
    dec(j, i + 1) {
        (x[j + 1] += x[j] * b[i]) %= MOD;
    }
    }
    
    vector<LL> y(n + 1);
    dec(i, n + 1) {
        y[i] = f[n - i] * x[i] % MOD;
        incII(j, i + 1, n) { (y[i] -= comb(j, i) * y[j]) %= MOD; }
    }
    if(y[0] < 0) { y[0] += MOD; }
    
    cout << y[0] << endl;
    
    return 0;
}
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