結果
| 問題 | No.2985 May Count Induced C4 Subgraphs |
| ユーザー |
 tko919
|
| 提出日時 | 2024-12-10 02:41:47 |
| 言語 | C++23(gcc13) (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 21,274 bytes |
| コンパイル時間 | 5,126 ms |
| コンパイル使用メモリ | 331,948 KB |
| 実行使用メモリ | 822,892 KB |
| 最終ジャッジ日時 | 2024-12-10 02:43:06 |
| 合計ジャッジ時間 | 71,140 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
429,864 KB |
| testcase_01 | AC | 1 ms
429,812 KB |
| testcase_02 | AC | 2 ms
429,948 KB |
| testcase_03 | AC | 2 ms
10,496 KB |
| testcase_04 | AC | 2 ms
429,672 KB |
| testcase_05 | AC | 2 ms
239,964 KB |
| testcase_06 | TLE | - |
| testcase_07 | MLE | - |
| testcase_08 | TLE | - |
| testcase_09 | TLE | - |
| testcase_10 | TLE | - |
| testcase_11 | MLE | - |
| testcase_12 | AC | 456 ms
35,776 KB |
| testcase_13 | AC | 336 ms
35,608 KB |
| testcase_14 | AC | 375 ms
35,612 KB |
| testcase_15 | AC | 245 ms
35,480 KB |
| testcase_16 | AC | 279 ms
35,604 KB |
| testcase_17 | TLE | - |
| testcase_18 | TLE | - |
| testcase_19 | TLE | - |
| testcase_20 | TLE | - |
| testcase_21 | TLE | - |
ソースコード
#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b)-1; i >= (int)(a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
template <typename T> inline bool chmax(T &a, T b) {
if (a < b) {
a = b;
return 1;
}
return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
if (a > b) {
a = b;
return 1;
}
return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
assert(y != 0);
if (y < 0)
x = -x, y = -y;
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
assert(y != 0);
if (y < 0)
x = -x, y = -y;
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) {
return __builtin_popcountll(x);
}
template <typename T> int topbit(T x) {
return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
return (x == 0 ? -1 : __builtin_ctzll(x));
}
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << "P(" << p.first << ", " << p.second << ")";
return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
os << "{";
for (int i = 0; i < vec.size(); i++) {
os << vec[i] << (i + 1 == vec.size() ? "" : ", ");
}
os << "}";
return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &map_var) {
os << "{";
for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
os << "(" << itr->first << ", " << itr->second << ")";
itr++;
if (itr != map_var.end())
os << ", ";
itr--;
}
os << "}";
return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) {
os << "{";
for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
os << *itr;
++itr;
if (itr != set_var.end())
os << ", ";
itr--;
}
os << "}";
return os;
}
#ifdef LOCAL
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define show(...) true
#endif
template <typename T> void _show(int i, T name) {
cerr << '\n';
}
template <typename T1, typename T2, typename... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
for (; a[i] != ',' && a[i] != '\0'; i++)
cerr << a[i];
cerr << ":" << b << " ";
_show(i + 1, a, c...);
}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memmove(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ)
ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir)
load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir)
load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir)
load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T> void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T> void rd_integer(T &x) {
if (pil + 100 > pir)
load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') {
minus = 1, c = ibuf[pil++];
}
}
x = 0;
while ('0' <= c) {
x = x * 10 + (c & 15), c = ibuf[pil++];
}
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus)
x = -x;
}
}
void rd(int &x) {
rd_integer(x);
}
void rd(ll &x) {
rd_integer(x);
}
void rd(i128 &x) {
rd_integer(x);
}
void rd(uint &x) {
rd_integer(x);
}
void rd(ull &x) {
rd_integer(x);
}
void rd(u128 &x) {
rd_integer(x);
}
void rd(double &x) {
rd_real(x);
}
void rd(long double &x) {
rd_real(x);
}
template <class T, class U> void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T> void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T> void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T> void rd(array<T, N> &x) {
for (auto &d : x)
rd(d);
}
template <class T> void rd(vector<T> &x) {
for (auto &d : x)
rd(d);
}
void read() {}
template <class H, class... T> void read(H &h, T &...t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ)
flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c : s)
wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++)
wt(s[i]);
}
template <typename T> void wt_integer(T x) {
if (por > SZ - 100)
flush();
if (x < 0) {
obuf[por++] = '-', x = -x;
}
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T> void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) {
wt_integer(x);
}
void wt(ll x) {
wt_integer(x);
}
void wt(i128 x) {
wt_integer(x);
}
void wt(uint x) {
wt_integer(x);
}
void wt(ull x) {
wt_integer(x);
}
void wt(u128 x) {
wt_integer(x);
}
void wt(double x) {
wt_real(x);
}
void wt(long double x) {
wt_real(x);
}
template <class T, class U> void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T> void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) {
wt(' ');
}
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T> void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S> void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i)
wt(' ');
wt(val[i]);
}
}
template <class T> void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i)
wt(' ');
wt(val[i]);
}
}
void print() {
wt('\n');
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
wt(head);
if (sizeof...(Tail))
wt(' ');
print(forward<Tail>(tail)...);
}
void __attribute__((destructor)) _d() {
flush();
}
} // namespace fastio
using fastio::flush;
using fastio::print;
using fastio::read;
inline void first(bool i = true) {
print(i ? "first" : "second");
}
inline void Alice(bool i = true) {
print(i ? "Alice" : "Bob");
}
inline void Takahashi(bool i = true) {
print(i ? "Takahashi" : "Aoki");
}
inline void yes(bool i = true) {
print(i ? "yes" : "no");
}
inline void Yes(bool i = true) {
print(i ? "Yes" : "No");
}
inline void No() {
print("No");
}
inline void YES(bool i = true) {
print(i ? "YES" : "NO");
}
inline void NO() {
print("NO");
}
inline void Yay(bool i = true) {
print(i ? "Yay!" : ":(");
}
inline void Possible(bool i = true) {
print(i ? "Possible" : "Impossible");
}
inline void POSSIBLE(bool i = true) {
print(i ? "POSSIBLE" : "IMPOSSIBLE");
}
/**
* @brief Fast IO
*/
#line 3 "sol.cpp"
#line 2 "library/Math/modint.hpp"
template <unsigned mod = 1000000007> struct fp {
unsigned v;
static constexpr int get_mod() {
return mod;
}
constexpr unsigned inv() const {
assert(v != 0);
int x = v, y = mod, p = 1, q = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, p -= t * q;
tmp = x, x = y, y = tmp;
tmp = p, p = q, q = tmp;
}
if (p < 0)
p += mod;
return p;
}
constexpr fp(ll x = 0) : v(x >= 0 ? x % mod : (mod - (-x) % mod) % mod) {}
fp operator-() const {
return fp() - *this;
}
fp pow(ull t) {
fp res = 1, b = *this;
while (t) {
if (t & 1)
res *= b;
b *= b;
t >>= 1;
}
return res;
}
fp &operator+=(const fp &x) {
if ((v += x.v) >= mod)
v -= mod;
return *this;
}
fp &operator-=(const fp &x) {
if ((v += mod - x.v) >= mod)
v -= mod;
return *this;
}
fp &operator*=(const fp &x) {
v = ull(v) * x.v % mod;
return *this;
}
fp &operator/=(const fp &x) {
v = ull(v) * x.inv() % mod;
return *this;
}
fp operator+(const fp &x) const {
return fp(*this) += x;
}
fp operator-(const fp &x) const {
return fp(*this) -= x;
}
fp operator*(const fp &x) const {
return fp(*this) *= x;
}
fp operator/(const fp &x) const {
return fp(*this) /= x;
}
bool operator==(const fp &x) const {
return v == x.v;
}
bool operator!=(const fp &x) const {
return v != x.v;
}
friend istream &operator>>(istream &is, fp &x) {
return is >> x.v;
}
friend ostream &operator<<(ostream &os, const fp &x) {
return os << x.v;
}
};
template <unsigned mod> void rd(fp<mod> &x) {
fastio::rd(x.v);
}
template <unsigned mod> void wt(fp<mod> x) {
fastio::wt(x.v);
}
/**
* @brief Modint
*/
#line 2 "library/Math/comb.hpp"
template <typename T> T Inv(ll n) {
static int md;
static vector<T> buf({0, 1});
if (md != T::get_mod()) {
md = T::get_mod();
buf = vector<T>({0, 1});
}
assert(n > 0);
n %= md;
while (SZ(buf) <= n) {
int k = SZ(buf), q = (md + k - 1) / k;
buf.push_back(buf[k * q - md] * q);
}
return buf[n];
}
template <typename T> T Fact(ll n, bool inv = 0) {
static int md;
static vector<T> buf({1, 1}), ibuf({1, 1});
if (md != T::get_mod()) {
md = T::get_mod();
buf = ibuf = vector<T>({1, 1});
}
assert(n >= 0 and n < md);
while (SZ(buf) <= n) {
buf.push_back(buf.back() * SZ(buf));
ibuf.push_back(ibuf.back() * Inv<T>(SZ(ibuf)));
}
return inv ? ibuf[n] : buf[n];
}
template <typename T> T nPr(int n, int r, bool inv = 0) {
if (n < 0 || n < r || r < 0)
return 0;
return Fact<T>(n, inv) * Fact<T>(n - r, inv ^ 1);
}
template <typename T> T nCr(int n, int r, bool inv = 0) {
if (n < 0 || n < r || r < 0)
return 0;
return Fact<T>(n, inv) * Fact<T>(r, inv ^ 1) * Fact<T>(n - r, inv ^ 1);
}
// sum = n, r tuples
template <typename T> T nHr(int n, int r, bool inv = 0) {
return nCr<T>(n + r - 1, r - 1, inv);
}
// sum = n, a nonzero tuples and b tuples
template <typename T> T choose(int n, int a, int b) {
if (n == 0)
return !a;
return nCr<T>(n + b - 1, a + b - 1);
}
/**
* @brief Combination
*/
#line 6 "sol.cpp"
using Fp = fp<998244353>;
#line 2 "library/Math/matrix.hpp"
template <class T> struct Matrix {
int h, w;
vector<vector<T>> val;
T det;
Matrix() {}
Matrix(int n) : h(n), w(n), val(vector<vector<T>>(n, vector<T>(n))) {}
Matrix(int n, int m)
: h(n), w(m), val(vector<vector<T>>(n, vector<T>(m))) {}
vector<T> &operator[](const int i) {
return val[i];
}
Matrix &operator+=(const Matrix &m) {
assert(h == m.h and w == m.w);
rep(i, 0, h) rep(j, 0, w) val[i][j] += m.val[i][j];
return *this;
}
Matrix &operator-=(const Matrix &m) {
assert(h == m.h and w == m.w);
rep(i, 0, h) rep(j, 0, w) val[i][j] -= m.val[i][j];
return *this;
}
Matrix &operator*=(const Matrix &m) {
assert(w == m.h);
Matrix<T> res(h, m.w);
rep(i, 0, h) rep(j, 0, m.w) rep(k, 0, w) res.val[i][j] +=
val[i][k] * m.val[k][j];
*this = res;
return *this;
}
Matrix operator+(const Matrix &m) const {
return Matrix(*this) += m;
}
Matrix operator-(const Matrix &m) const {
return Matrix(*this) -= m;
}
Matrix operator*(const Matrix &m) const {
return Matrix(*this) *= m;
}
Matrix pow(ll k) {
Matrix<T> res(h, h), c = *this;
rep(i, 0, h) res.val[i][i] = 1;
while (k) {
if (k & 1)
res *= c;
c *= c;
k >>= 1;
}
return res;
}
vector<int> gauss(int c = -1) {
det = 1;
if (val.empty())
return {};
if (c == -1)
c = w;
int cur = 0;
vector<int> res;
rep(i, 0, c) {
if (cur == h)
break;
rep(j, cur, h) if (val[j][i] != 0) {
swap(val[cur], val[j]);
if (cur != j)
det *= -1;
break;
}
det *= val[cur][i];
if (val[cur][i] == 0)
continue;
rep(j, 0, h) if (j != cur) {
T z = val[j][i] / val[cur][i];
rep(k, i, w) val[j][k] -= val[cur][k] * z;
}
res.push_back(i);
cur++;
}
return res;
}
Matrix inv() {
assert(h == w);
Matrix base(h, h * 2), res(h, h);
rep(i, 0, h) rep(j, 0, h) base[i][j] = val[i][j];
rep(i, 0, h) base[i][h + i] = 1;
base.gauss(h);
det = base.det;
rep(i, 0, h) rep(j, 0, h) res[i][j] = base[i][h + j] / base[i][i];
return res;
}
bool operator==(const Matrix &m) {
assert(h == m.h and w == m.w);
rep(i, 0, h) rep(j, 0, w) if (val[i][j] != m.val[i][j]) return false;
return true;
}
bool operator!=(const Matrix &m) {
assert(h == m.h and w == m.w);
rep(i, 0, h) rep(j, 0, w) if (val[i][j] == m.val[i][j]) return false;
return true;
}
friend istream &operator>>(istream &is, Matrix &m) {
rep(i, 0, m.h) rep(j, 0, m.w) is >> m[i][j];
return is;
}
friend ostream &operator<<(ostream &os, Matrix &m) {
rep(i, 0, m.h) {
rep(j, 0, m.w) os << m[i][j]
<< (j == m.w - 1 and i != m.h - 1 ? '\n' : ' ');
}
return os;
}
};
/**
* @brief Matrix
*/
#line 8 "sol.cpp"
using P = pair<int, int>;
using T = pair<int, P>;
vector<T> EnumTriangle(int n, vector<P> &es) {
vector<int> deg(n);
for (auto &[u, v] : es)
deg[u]++, deg[v]++;
vector g(n, vector<int>());
for (auto &[u, v] : es) {
if (P{deg[u], u} > P{deg[v], v})
swap(u, v);
g[u].push_back(v);
}
vector<int> used(n);
vector<T> res;
for (auto &[u, v] : es) {
for (auto &t : g[u])
used[t] = 1;
for (auto &t : g[v])
if (used[t]) {
res.push_back(T{t, P{u, v}});
}
for (auto &t : g[u])
used[t] = 0;
}
return res;
}
class CountingC4 {
private:
int V, threshold;
vector<vector<int>> G;
vector<vector<array<int, 2>>> memo;
vector<int> flag1, flag2;
void process_high_degree(long long &ans) {
for (int i = 0; i < V; ++i) {
if ((int)G[i].size() <= threshold)
continue;
for (const int u : G[i]) {
if (u > i)
flag1[u] = 1;
flag2[u] = 1;
}
for (int j = 0; j < i; ++j) {
if ((int)G[j].size() > threshold)
continue;
long long cnt1 = 0, cnt2 = 0;
for (const int u : G[j]) {
if (u < j || !flag2[u])
continue;
if ((int)G[u].size() > threshold)
++cnt1;
else
++cnt2;
}
ans += (cnt1 + cnt2) * (cnt1 + cnt2 - 1) / 2;
}
for (int j = i + 1; j < V; ++j) {
long long cnt = 0;
for (const int u : G[j]) {
if (flag1[u])
++cnt;
}
ans += cnt * (cnt - 1) / 2;
}
for (const int u : G[i])
flag1[u] = flag2[u] = 0;
}
}
void process_low_degree(long long &ans) {
for (int i = 0; i < V; ++i) {
if ((int)G[i].size() > threshold)
continue;
for (const int u : G[i]) {
for (const int v : G[i]) {
if (v > u)
memo[u].push_back({i, v});
}
}
}
for (int i = 0; i < V; ++i) {
for (const auto &e : memo[i]) {
if (e[0] < i)
++flag1[e[1]];
else
++flag2[e[1]];
}
for (const auto &e : memo[i]) {
ans += (long long)(flag1[e[1]] + 2 * flag2[e[1]] - 1) *
flag1[e[1]] / 2;
flag1[e[1]] = flag2[e[1]] = 0;
}
}
}
public:
CountingC4(const int node_size)
: V(node_size), threshold(0), G(V), memo(V), flag1(V, 0), flag2(V, 0) {}
void add_edge(const int u, const int v) {
G[u].push_back(v), G[v].push_back(u);
++threshold;
}
long long solve() {
threshold = floor(sqrt(2 * threshold)) / 2;
long long ans = 0;
process_high_degree(ans);
process_low_degree(ans);
return ans;
}
};
int main() {
Fp T = Fp(-3).inv();
// coe={1,998244352,1,1,998244352,998244352,998244352,665496236,1,332748117}
int n, m;
read(n, m);
if (n < 4) {
print(T, 0);
return 0;
}
vector<P> es;
vector<int> deg(n);
CountingC4 buf(n);
rep(_, 0, m) {
int x, y;
read(x, y);
x--, y--;
deg[x]++;
deg[y]++;
es.push_back({x, y});
buf.add_edge(x, y);
}
Fp ret = nCr<Fp>(n, 4); // x1
ret += Fp(m) * nCr<Fp>(n - 2, 2) * -1; // x2
{
Fp sum;
rep(v, 0, n) sum += nCr<Fp>(deg[v], 2);
ret += sum * (n - 3); // x3
ret += (nCr<Fp>(m, 2) - sum); // x4
}
{
Fp sum;
rep(v, 0, n) sum += nCr<Fp>(deg[v], 3);
ret += sum * -1; // x5
}
auto tri = EnumTriangle(n, es);
{
Fp sum;
for (auto &[u, v] : es)
sum += Fp(deg[u] - 1) * (deg[v] - 1);
sum -= SZ(tri) * 3;
ret += sum * -1; // x6
}
ret += Fp(n - 3) * SZ(tri) * -1; // x7
ll C4 = buf.solve();
show(C4);
ret += Fp(C4) * 665496236; // x8
vector<int> vcnt(n);
map<P, int> ecnt;
for (auto &[u, vw] : tri) {
auto [v, w] = vw;
vcnt[u]++;
vcnt[v]++;
vcnt[w]++;
int a[3] = {u, v, w};
sort(a, a + 3);
u = a[0], v = a[1], w = a[2];
ecnt[{u, v}]++;
ecnt[{v, w}]++;
ecnt[{u, w}]++;
}
{
Fp sum;
rep(v, 0, n) sum += Fp(deg[v] - 2) * vcnt[v];
ret += sum; // x9
}
{
Fp sum;
for (auto &[e, c] : ecnt)
sum += nCr<Fp>(c, 2);
ret += sum * 332748117; // x10
}
print(T, ret);
// {
// Fp A, B;
// read(A, B);
// print(A + T * B);
// }
return 0;
}