結果
| 問題 | No.2985 May Count Induced C4 Subgraphs |
| ユーザー |
👑  hos.lyric
|
| 提出日時 | 2024-12-10 00:46:24 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2,388 ms / 5,000 ms |
| コード長 | 7,297 bytes |
| コンパイル時間 | 1,800 ms |
| コンパイル使用メモリ | 133,704 KB |
| 実行使用メモリ | 30,592 KB |
| 最終ジャッジ日時 | 2024-12-10 00:46:52 |
| 合計ジャッジ時間 | 24,510 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 22 |
ソースコード
#include <cassert>#include <cmath>#include <cstdint>#include <cstdio>#include <cstdlib>#include <cstring>#include <algorithm>#include <bitset>#include <complex>#include <deque>#include <functional>#include <iostream>#include <limits>#include <map>#include <numeric>#include <queue>#include <random>#include <set>#include <sstream>#include <string>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>using namespace std;using Int = long long;template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i>= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }#define COLOR(s) ("\x1b[" s "m")////////////////////////////////////////////////////////////////////////////////template <unsigned M_> struct ModInt {static constexpr unsigned M = M_;unsigned x;constexpr ModInt() : x(0U) {}constexpr ModInt(unsigned x_) : x(x_ % M) {}constexpr ModInt(unsigned long long x_) : x(x_ % M) {}constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }ModInt pow(long long e) const {if (e < 0) return inv().pow(-e);ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;}ModInt inv() const {unsigned a = M, b = x; int y = 0, z = 1;for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }assert(a == 1U); return ModInt(y);}ModInt operator+() const { return *this; }ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }explicit operator bool() const { return x; }bool operator==(const ModInt &a) const { return (x == a.x); }bool operator!=(const ModInt &a) const { return (x != a.x); }friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }};////////////////////////////////////////////////////////////////////////////////constexpr unsigned MO = 998244353;using Mint = ModInt<MO>;// https://x.com/NachiaVivias/status/1863300035263553791/photo/1int N, M;vector<int> A, B;vector<vector<int>> graph;vector<vector<pair<int, int>>> graphI;int main() {for (; ~scanf("%d%d", &N, &M); ) {A.resize(M);B.resize(M);for (int i = 0; i < M; ++i) {scanf("%d%d", &A[i], &B[i]);--A[i];--B[i];}graph.assign(N, {});graphI.assign(N, {});for (int i = 0; i < M; ++i) {graph[A[i]].push_back(B[i]);graph[B[i]].push_back(A[i]);graphI[A[i]].emplace_back(B[i], i);graphI[B[i]].emplace_back(A[i], i);}vector<int> deg(N);for (int u = 0; u < N; ++u) deg[u] = graph[u].size();vector<int> us(N);for (int u = 0; u < N; ++u) us[u] = u;sort(us.begin(), us.end(), [&](int u, int v) -> bool {return (deg[u] > deg[v]);});vector<int> ord(N, -1);for (int j = 0; j < N; ++j) ord[us[j]] = j;// cerr<<"us = "<<us<<endl;Mint Y[10] = {};vector<int> tri(M, 0);// \sum[u] min{deg(u)^2, M} <= \sum[u] deg[u] sqrt(M) = O(M sqrt(M)){vector<int> fs(N, 0);for (int j = 0; j < N; ++j) {const int u = us[j];for (const auto &vi : graphI[u]) if (ord[u] < ord[vi.first]) {fs[vi.first] = ~vi.second;}for (const auto &vi : graphI[u]) if (ord[u] < ord[vi.first]) {const int v = vi.first;for (const auto &wi : graphI[v]) if (ord[v] < ord[wi.first]) {const int w = wi.first;if (fs[w]) {// C[3]// cerr<<"C3 "<<u<<" "<<v<<" "<<w<<endl;Y[5] -= 3;Y[6] += 1;Y[8] += (deg[u] + deg[v] + deg[w] - 6);++tri[vi.second];++tri[wi.second];++tri[~fs[w]];}}}for (const int v : graph[u]) if (ord[u] < ord[v]) {fs[v] = 0;}for (const int v : graph[u]) if (ord[u] < ord[v]) {for (const int w : graph[v]) if (ord[u] < ord[w]) {// C[4]Y[7] += fs[w];++fs[w];}}for (const int v : graph[u]) if (ord[u] < ord[v]) {for (const int w : graph[v]) if (ord[u] < ord[w]) {--fs[w];}}}}// cerr<<"tri = "<<tri<<endl;for (int i = 0; i < M; ++i) {const Int t = tri[i];Y[9] += t*(t-1)/2;}for (int u = 0; u < N; ++u) {const Int d = deg[u];const Int d2 = d*(d-1)/2;const Int d3 = d*(d-1)*(d-2)/6;Y[2] += d2;Y[3] -= d2;Y[4] += d3;}Y[0] += (unsigned)((__int128)N*(N-1)*(N-2)*(N-3)/24 % MO);Y[1] += Mint(M) * Mint((Int)(N-2)*(N-3)/2);Y[2] *= (N-3);Y[3] += (Int)M*(M-1)/2;for (int i = 0; i < M; ++i) Y[5] += (Int)(deg[A[i]] - 1) * (deg[B[i]] - 1);Y[6] *= (N-3);cerr<<"Y = ";pv(Y,Y+10);const Mint T = Mint(-1)/3;const Mint COEF[10] = {1, -1, 1, 1, -1, -1, -1, Mint(2)/3, 1, Mint(-2)/3};cerr<<"sample: "<<(2+T*1)<<" "<<(13+T*2)<<endl;Mint ans = 0;for (int i = 0; i < 10; ++i) ans += COEF[i] * Y[i];printf("%u %u\n", T.x, ans.x);#ifdef LOCALmap<vector<int>,int>brt;for(int p=0;p<1<<N;++p)if(__builtin_popcount(p)==4){vector<int>ds;for(int u=0;u<N;++u)if(p>>u&1){int d=0;for(const int v:graph[u])if(p>>v&1)++d;ds.push_back(d);}sort(ds.begin(),ds.end(),greater<int>{});++brt[ds];}for(const auto&kv:brt)cerr<<kv<<endl;#endif}return 0;}