結果
問題 | No.329 全射 |
ユーザー |
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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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 40 |
ソースコード
#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;}