結果

問題 No.329 全射
ユーザー paruki
提出日時 2016-06-22 08:04:03
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 308 ms / 2,000 ms
コード長 3,692 bytes
コンパイル時間 1,950 ms
コンパイル使用メモリ 184,712 KB
実行使用メモリ 7,680 KB
最終ジャッジ日時 2024-10-11 19:15:55
合計ジャッジ時間 5,538 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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 * 40
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 # 

#include "bits/stdc++.h"
using namespace std;
#define FOR(i,j,k) for(int (i)=(j);(i)<(int)(k);++(i))
#define rep(i,j) FOR(i,0,j)
#define each(x,y) for(auto &(x):(y))
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define debug(x) cout<<#x<<": "<<(x)<<endl
#define smax(x,y) (x)=max((x),(y))
#define smin(x,y) (x)=min((x),(y))
#define MEM(x,y) memset((x),(y),sizeof (x))
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<ll> vll;

template<int MOD>
class ModInt{
public:
    ModInt():value(0){}
    ModInt(int val):value(val<0?MOD+val%MOD:val%MOD){ }
    
    ModInt& operator+=(ModInt that){
        value = value+that.value;
        if(value>=MOD)value-=MOD;
        return *this;
    }
    ModInt& operator-=(ModInt that){
        value -= that.value;
        if(value<0)value+=MOD;
        return *this;
    }
    ModInt& operator*=(ModInt that){
        value = (int)((long long)value * that.value % MOD);
        return *this;
    }
    ModInt &operator/=(ModInt that){
        return *this *= that.inverse();
    }
    ModInt operator+(ModInt that) const{
        return ModInt(*this)+=that;
    }
    ModInt operator-(ModInt that) const{
        return ModInt(*this)-=that;
    }
    ModInt operator*(ModInt that) const{
        return ModInt(*this)*=that;
    }
    ModInt operator/(ModInt that) const {
        return ModInt(*this) /= that;
    }
    ModInt operator^(long long k) const{
        ModInt n = *this, res = 1;
        while(k){
            if(k & 1)res *= n;
            n *= n;
            k >>= 1;
        }
        return res;
    }
    ModInt inverse() const {
        long long a = value, b = MOD, u = 1, v = 0;
        while(b) {
            long long t = a / b;
            a -= t * b;
            swap(a, b);
            u -= t * v;
            swap(u, v);
        }
        return ModInt((int)u);
    }
    int toi() const{ return value; }

private:
    int value;
};
typedef ModInt<1000000007> mint;
ostream& operator<<(ostream& os, const mint& x){
    os << x.toi();
    return os;
}

template <class Val>
vector<Val> factorials(int n){
    vector<Val> res(n + 1);
    res[0] = res[1] = 1;
    for(int i = 2; i <= n; ++i)
        res[i] = res[i - 1] * i;
    return res;
}

mint nCr(int n, int r, const vector<mint> &fact){
    return fact[n] / (fact[r] * fact[n - r]);
}

template<class Val>
vector<vector<Val>> StirlingSecond(int n){
    vector<vector<Val>> res(n + 1, vector<Val>(n + 1));
    for(int i = 1; i <= n; ++i)res[i][i] = res[i][1] = 1;
    for(int m = 3; m <= n; ++m)
        for(int k = 2; k < m; ++k)
            res[m][k] = res[m - 1][k - 1] + res[m - 1][k] * k;
    return res;
}

const int MAX = 1000;

mint solve(vector<vector<int>> G, vi &num, vector<mint> &fact){
    auto S = StirlingSecond<mint>(MAX);
    int V = (int)G.size();
    mint res = 0;
    for(int u = 0; u < V; ++u){
        priority_queue<pii> que;
        vi vis(V);
        que.push(mp(num[u], u));
        while(que.size()){
            int mini, v;
            tie(mini, v) = que.top();
            que.pop();
            if(vis[v]++)continue;
            if(mini >= num[v])res += S[num[u]][num[v]] * fact[num[v]];
            for(int w : G[v])if(!vis[w])
                que.push(mp(min(mini, num[v]), w));
        }
    }
    return res;
}

int main(){
    ios::sync_with_stdio(0);
    cin.tie(0);
    int N, M;
    auto fact = factorials<mint>(MAX);

    cin >> N >> M;
    vi w(N);
    rep(i, N)cin >> w[i];
    vector<vi> G(N);
    rep(i, M){
        int u, v;
        cin >> u >> v;
        --u;
        --v;
        G[u].push_back(v);
    }
    cout << solve(G, w, fact) << endl;
}
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