cplib-cpp
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graph/test/enumerate_cliques.test.cpp
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- Last update: 2023-12-26 21:26:22+09:00
- Problem: https://judge.yosupo.jp/problem/enumerate_cliques
Depends on
Code
#include "../enumerate_cliques.hpp"
#include "../../modint.hpp"
#include <iostream>
#include <vector>
using namespace std;
#define PROBLEM "https://judge.yosupo.jp/problem/enumerate_cliques"
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
int N, M;
cin >> N >> M;
using mint = ModInt998244353;
vector<mint> X(N);
for (auto &x : X) cin >> x;
enumerate_cliques ec(N);
while (M--) {
int u, v;
cin >> u >> v;
ec.add_bi_edge(u, v);
}
mint ret = mint();
auto op = [&](const std::vector<int> &clique) -> void {
mint tmp = 1;
for (int x : clique) tmp *= X.at(x);
ret += tmp;
};
ec.run(op);
cout << ret << endl;
}#line 2 "graph/enumerate_cliques.hpp"
/**
* @file enumerate_cliques.hpp
* @brief Enumerate all cliques of given undirected graph
* @author hitonanode
* @date 2023/03/10
*/
#include <algorithm>
#include <cassert>
#include <numeric>
#include <queue>
#include <utility>
#include <vector>
// Complexity: O(2^sqrt(2m) * n)
// Verify: https://judge.yosupo.jp/problem/enumerate_cliques (~1ms for n <= 100, m <= 100)
// p.15, https://www.slideshare.net/wata_orz/ss-12131479
struct enumerate_cliques {
std::vector<std::vector<int>> to;
std::vector<std::pair<int, int>> edges;
int n() const { return to.size(); }
int m() const { return edges.size(); }
enumerate_cliques(int n_) : to(n_) {}
void add_bi_edge(int u, int v) {
assert(0 <= u and u < n());
assert(0 <= v and v < n());
if (u != v) edges.emplace_back(std::minmax(u, v));
}
// Build `to`
void precalc() {
std::sort(edges.begin(), edges.end());
edges.erase(std::unique(edges.begin(), edges.end()), edges.end());
for (auto &vec : to) vec.clear();
for (auto [u, v] : edges) to.at(u).push_back(v), to.at(v).push_back(u);
for (auto &vec : to) std::sort(vec.begin(), vec.end());
}
template <class F>
void bruteforce(const std::vector<int> &cand_vs, int prefix_use, F op) const {
const int k = cand_vs.size();
const int mask_all = (1 << k) - 1;
std::vector<int> ok_masks(k, mask_all);
for (int i = 0; i < k; ++i) {
for (int j = 0; j < i; ++j) {
int u = cand_vs.at(i), v = cand_vs.at(j);
if (!std::binary_search(to.at(u).cbegin(), to.at(u).cend(), v)) {
ok_masks.at(i) &= ~(1 << j), ok_masks.at(j) &= ~(1 << i);
}
}
}
std::vector<int> seq;
if (prefix_use >= 0) seq.push_back(prefix_use);
seq.reserve(seq.size() + k);
auto rec = [&](auto &&self, int now, const int last_mask) -> void {
op(seq);
seq.push_back(-1);
for (int i = now; i < k; ++i) {
if ((last_mask >> i) & 1) {
seq.back() = cand_vs.at(i);
self(self, i + 1, last_mask & ok_masks.at(i));
}
}
seq.pop_back();
};
rec(rec, 0, mask_all);
return;
}
template <class F> void run(F op) {
precalc();
std::vector<int> deg(n()), is_alive(n(), 1);
using P = std::pair<int, int>;
std::priority_queue<P, std::vector<P>, std::greater<P>> pq;
for (int i = 0; i < n(); ++i) deg.at(i) = to.at(i).size(), pq.emplace(deg.at(i), i);
int rem_n = n(), rem_m = m();
std::vector<int> cand_vs;
while (!pq.empty()) {
auto [di, i] = pq.top();
pq.pop();
if (deg.at(i) != di) continue;
cand_vs.clear();
if (di * di > rem_m * 2) { // Avoid "deg[i] = 0" case
for (int i = 0; i < n(); ++i) {
if (is_alive.at(i)) cand_vs.push_back(i);
}
bruteforce(cand_vs, -1, op);
break;
}
for (int j : to.at(i)) {
if (is_alive.at(j)) cand_vs.push_back(j);
}
bruteforce(cand_vs, i, op);
--rem_n, deg.at(i) = 0, is_alive.at(i) = 0;
for (int j : cand_vs) --rem_m, --deg.at(j), pq.emplace(deg.at(j), j);
}
}
};
#line 3 "modint.hpp"
#include <iostream>
#include <set>
#line 6 "modint.hpp"
template <int md> struct ModInt {
using lint = long long;
constexpr static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val_;
int val() const noexcept { return val_; }
constexpr ModInt() : val_(0) {}
constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }
constexpr ModInt(lint v) { _setval(v % md + md); }
constexpr explicit operator bool() const { return val_ != 0; }
constexpr ModInt operator+(const ModInt &x) const {
return ModInt()._setval((lint)val_ + x.val_);
}
constexpr ModInt operator-(const ModInt &x) const {
return ModInt()._setval((lint)val_ - x.val_ + md);
}
constexpr ModInt operator*(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.val_ % md);
}
constexpr ModInt operator/(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.inv().val() % md);
}
constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }
constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; }
friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; }
friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; }
friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; }
constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }
constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }
constexpr bool operator<(const ModInt &x) const {
return val_ < x.val_;
} // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {
return os << x.val_;
}
constexpr ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static constexpr int cache_limit = std::min(md, 1 << 21);
static std::vector<ModInt> facs, facinvs, invs;
constexpr static void _precalculation(int N) {
const int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
constexpr ModInt inv() const {
if (this->val_ < cache_limit) {
if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val_];
} else {
return this->pow(md - 2);
}
}
constexpr ModInt fac() const {
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[this->val_];
}
constexpr ModInt facinv() const {
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[this->val_];
}
constexpr ModInt doublefac() const {
lint k = (this->val_ + 1) / 2;
return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac())
: ModInt(k).fac() * ModInt(2).pow(k);
}
constexpr ModInt nCr(int r) const {
if (r < 0 or this->val_ < r) return ModInt(0);
return this->fac() * (*this - r).facinv() * ModInt(r).facinv();
}
constexpr ModInt nPr(int r) const {
if (r < 0 or this->val_ < r) return ModInt(0);
return this->fac() * (*this - r).facinv();
}
static ModInt binom(int n, int r) {
static long long bruteforce_times = 0;
if (r < 0 or n < r) return ModInt(0);
if (n <= bruteforce_times or n < (int)facs.size()) return ModInt(n).nCr(r);
r = std::min(r, n - r);
ModInt ret = ModInt(r).facinv();
for (int i = 0; i < r; ++i) ret *= n - i;
bruteforce_times += r;
return ret;
}
// Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)
// Complexity: O(sum(ks))
template <class Vec> static ModInt multinomial(const Vec &ks) {
ModInt ret{1};
int sum = 0;
for (int k : ks) {
assert(k >= 0);
ret *= ModInt(k).facinv(), sum += k;
}
return ret * ModInt(sum).fac();
}
// Catalan number, C_n = binom(2n, n) / (n + 1)
// C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...
// https://oeis.org/A000108
// Complexity: O(n)
static ModInt catalan(int n) {
if (n < 0) return ModInt(0);
return ModInt(n * 2).fac() * ModInt(n + 1).facinv() * ModInt(n).facinv();
}
ModInt sqrt() const {
if (val_ == 0) return 0;
if (md == 2) return val_;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val_, md - x.val_));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
using ModInt998244353 = ModInt<998244353>;
// using mint = ModInt<998244353>;
// using mint = ModInt<1000000007>;
#line 5 "graph/test/enumerate_cliques.test.cpp"
using namespace std;
#define PROBLEM "https://judge.yosupo.jp/problem/enumerate_cliques"
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
int N, M;
cin >> N >> M;
using mint = ModInt998244353;
vector<mint> X(N);
for (auto &x : X) cin >> x;
enumerate_cliques ec(N);
while (M--) {
int u, v;
cin >> u >> v;
ec.add_bi_edge(u, v);
}
mint ret = mint();
auto op = [&](const std::vector<int> &clique) -> void {
mint tmp = 1;
for (int x : clique) tmp *= X.at(x);
ret += tmp;
};
ec.run(op);
cout << ret << endl;
}