結果

問題 No.329 全射
ユーザー minami
提出日時 2019-03-28 05:30:32
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,766 ms / 2,000 ms
コード長 3,800 bytes
コンパイル時間 1,949 ms
コンパイル使用メモリ 176,896 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-10-12 00:16:24
合計ジャッジ時間 18,253 ms
ジャッジサーバーID
（参考情報） 		judge4 / 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;
#ifdef _DEBUG
#include "dump.hpp"
#else
#define dump(...)
#endif

//#define int long long
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--)
#define all(c) begin(c),end(c)
const int INF = sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = 1'000'000'007;
template<class T> bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; }
template<class T> bool chmin(T &a, const T &b) { if (b < a) { a = b; return true; } return false; }

template<int MOD>
struct ModInt {
	static const int kMod = MOD;
	unsigned x;
	ModInt() :x(0) {}
	ModInt(signed x_) { x_ %= MOD; if (x_ < 0)x_ += MOD; x = x_; }
	ModInt(signed long long x_) { x_ %= MOD; if (x_ < 0)x_ += MOD; x = x_; }
	int get()const { return (int)x; }
	ModInt &operator+=(ModInt m) { if ((x += m.x) >= MOD)x -= MOD; return *this; }
	ModInt &operator-=(ModInt m) { if ((x += MOD - m.x) >= MOD)x -= MOD; return *this; }
	ModInt &operator*=(ModInt m) { x = (unsigned long long)x*m.x%MOD; return *this; }
	ModInt &operator/=(ModInt m) { return *this *= m.inverse(); }
	ModInt operator+(ModInt m)const { return ModInt(*this) += m; }
	ModInt operator-(ModInt m)const { return ModInt(*this) -= m; }
	ModInt operator*(ModInt m)const { return ModInt(*this) *= m; }
	ModInt operator/(ModInt m)const { return ModInt(*this) /= m; }
	ModInt operator-()const { return ModInt(kMod - x); }
	bool operator==(ModInt m)const { return x == m.x; }
	bool operator!=(ModInt m)const { return x != m.x; }
	ModInt inverse()const {
		signed a = x, b = MOD, u = 1, v = 0;
		while (b) {
			signed t = a / b;
			a -= t * b; swap(a, b);
			u -= t * v; swap(u, v);
		}
		if (u < 0)u += MOD;
		return ModInt(u);
	}
};
template<int MOD>
ostream &operator<<(ostream &os, const ModInt<MOD> &m) { return os << m.x; }
template<int MOD>
istream &operator>>(istream &is, ModInt<MOD> &m) { signed long long s; is >> s; m = ModInt<MOD>(s); return is; };

using mint = ModInt<MOD>;

template<int MOD>
ModInt<MOD> pow(ModInt<MOD> a, unsigned long long k) {
	ModInt<MOD> r = 1;
	while (k) {
		if (k & 1)r *= a;
		a *= a;
		k >>= 1;
	}
	return r;
}

// n < 10^7
// 前計算 O(n)
// 計算 O(1)
vector<mint> fact, factinv;
void precomputeFact(int n) {
	n = min(n, mint::kMod - 1); //  N >= kMod  =>  N! = 0 (mod kMod)
	fact.resize(n + 1); factinv.resize(n + 1);
	fact[0] = 1;
	for (int i = 1; i < n + 1; i++)
		fact[i] = fact[i - 1] * i;
	factinv[n] = fact[n].inverse();
	for (int i = n; i >= 1; i--)
		factinv[i - 1] = factinv[i] * i; // ((i-1)!)^(-1) = (i!)^(-1) * i
}
mint binom(int n, int r) {
	if (n >= mint::kMod)
		return binom(n % mint::kMod, r % mint::kMod) * binom(n / mint::kMod, r / mint::kMod);
	return r > n ? 0 : fact[n] * factinv[n - r] * factinv[r];
}


signed main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	int N, M; cin >> N >> M;
	vector<int> w(N); rep(i, 0, N) {
		cin >> w[i];
	}
	vector<int> I(M), J(M); rep(i, 0, M) {
		cin >> I[i] >> J[i];
		I[i]--, J[i]--;
	}

	vector<vector<int>> wf(N, vector<int>(N, INF));
	rep(i, 0, N)wf[i][i] = 0;

	rep(i, 0, M) {
		int s = I[i], d = J[i], w = 1;
		wf[s][d] = min(wf[s][d], w); // 有向
	}

	int L = ceil(log2(N));
	rep(l, 0, L)rep(k, 0, N)rep(i, 0, N)rep(j, 0, N) {
		if (wf[i][k] != INF && wf[k][j] != INF && w[i] >= w[j] && w[k] >= w[j])
			wf[i][j] = min(wf[i][j], wf[i][k] + wf[k][j]);
	}

	dump(wf);

	precomputeFact(*max_element(all(w)));

	mint ans = 0;
	rep(i, 0, N)rep(j, 0, N) {
		if (w[i] >= w[j]) {
			if (wf[i][j] == INF)continue;
			mint s = 0;
			rep(k, 1, w[j] + 1) {
				mint t = 1;
				t *= pow(mint(-1), w[j] - k);
				t *= binom(w[j], k);
				t *= pow(mint(k), w[i]);
				s += t;
			}
			dump(i, j, s);
			ans += s;
		}
	}
	cout << ans << endl;
	return 0;
}
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