#include <bits/stdc++.h>
#define int long long
using namespace std;
string to_string(string s) { return s; }
template <typename T> string to_string(T v) {
bool first = true;
string res = "[";
for (const auto &x : v) {
if (!first)
res += ", ";
first = false;
res += to_string(x);
}
res += "]";
return res;
}
void dbg_out() { cout << endl; }
template <typename Head, typename... Tail> void dbg_out(Head H, Tail... T) {
cout << ' ' << to_string(H);
dbg_out(T...);
}
#ifdef DEBUG
#define dbg(...) cout << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif
template <const int32_t MOD> struct ModInt {
int32_t x;
ModInt() : x(0) {}
ModInt(long long u) : x(u % MOD) {
if (x < 0)
x += MOD;
}
friend bool operator==(const ModInt &a, const ModInt &b) {
return a.x == b.x;
}
friend bool operator!=(const ModInt &a, const ModInt &b) {
return a.x != b.x;
}
friend bool operator<(const ModInt &a, const ModInt &b) { return a.x < b.x; }
friend bool operator>(const ModInt &a, const ModInt &b) { return a.x > b.x; }
friend bool operator<=(const ModInt &a, const ModInt &b) {
return a.x <= b.x;
}
friend bool operator>=(const ModInt &a, const ModInt &b) {
return a.x >= b.x;
}
static ModInt sign(long long k) {
return ((k & 1) ? ModInt(MOD - 1) : ModInt(1));
}
ModInt &operator+=(const ModInt &m) {
x += m.x;
if (x >= MOD)
x -= MOD;
return *this;
}
ModInt &operator-=(const ModInt &m) {
x -= m.x;
if (x < 0LL)
x += MOD;
return *this;
}
ModInt &operator*=(const ModInt &m) {
x = (1LL * x * m.x) % MOD;
return *this;
}
friend ModInt operator-(const ModInt &a) {
ModInt res(a);
if (res.x)
res.x = MOD - res.x;
return res;
}
friend ModInt operator+(const ModInt &a, const ModInt &b) {
return ModInt(a) += ModInt(b);
}
friend ModInt operator-(const ModInt &a, const ModInt &b) {
return ModInt(a) -= ModInt(b);
}
friend ModInt operator*(const ModInt &a, const ModInt &b) {
return ModInt(a) *= ModInt(b);
}
static long long fp(long long u, long long k) {
long long res = 1LL;
while (k > 0LL) {
if (k & 1LL)
res = (res * u) % MOD;
u = (u * u) % MOD;
k /= 2LL;
}
return res;
}
static constexpr int mod() { return MOD; }
ModInt fastpow(long long k) { return ModInt(fp(x, k)); }
ModInt inv() {
assert(x);
return ModInt(fp(x, MOD - 2));
}
ModInt &operator/=(const ModInt &m) { return *this *= ModInt(m).inv(); }
friend ModInt operator/(const ModInt &a, const ModInt &b) {
return ModInt(a) *= ModInt(b).inv();
}
friend ostream &operator<<(ostream &out, const ModInt &a) {
return out << a.x;
}
friend istream &operator>>(istream &in, ModInt &a) { return in >> a.x; }
friend string to_string(ModInt u) { return to_string(u.x); }
};
// const int MOD = 1e9 + 7;
const int MOD = 998244353;
using Mint = ModInt<MOD>;
signed main(void) {
ios_base::sync_with_stdio(false);
cin.tie(0);
int n, m;
cin >> n >> m;
vector<int> adj(n);
vector<int> bitAdj(n);
for (int i = 0; i < m; ++i) {
int u, v;
cin >> u >> v;
--u, --v;
adj[u] |= 1 << v;
bitAdj[u] |= 1 << v;
bitAdj[v] |= 1 << u;
}
vector<int> areBad(n);
for (int u = 0; u < n; ++u)
for (int v = 0; v < u; ++v)
if (!((1 << v) & bitAdj[u]))
areBad[u] |= 1 << v;
vector<vector<int>> inComplement(1 << n);
for (int msk = 0; msk < (1 << n); ++msk) {
int c = (1 << n) - 1 - msk;
int complement = c;
while (true) {
inComplement[msk].push_back(c);
if (!c)
break;
c = (c - 1) & complement;
}
sort(inComplement[msk].begin(), inComplement[msk].end());
}
auto getId = [&](int msk, int c) {
return lower_bound(inComplement[msk].begin(), inComplement[msk].end(), c) -
inComplement[msk].begin();
};
vector<vector<Mint>> dpBack(1 << n);
vector<vector<Mint>> dpForward(1 << n);
for (int msk = 0; msk < (1 << n); ++msk) {
dpBack[msk].resize(inComplement[msk].size());
dpForward[msk].resize(inComplement[msk].size());
}
dpBack[0][0] = 1;
for (int added = 0; added < (1 << n); ++added) {
int complement = (1 << n) - 1 - added;
for (int i = 0; i < (int)inComplement[added].size(); ++i) {
int bad = inComplement[added][i];
assert((bad & added) == 0);
for (int nxt = 0; nxt < n; ++nxt)
if (!((1 << nxt) & added) and !((1 << nxt) & bad)) {
int nxtBad = bad & (bad ^ bitAdj[nxt]);
nxtBad |= areBad[nxt] & complement;
assert((nxtBad & (added ^ (1 << nxt))) == 0);
int j = getId(added ^ (1 << nxt), nxtBad);
assert(j < (int)inComplement[added ^ (1 << nxt)].size());
dpBack[added ^ (1 << nxt)][j] += dpBack[added][i];
}
}
}
dpForward[(1 << n) - 1][0] = 1;
for (int added = (1 << n) - 2; added >= 0; --added) {
for (int i = 0; i < (int)inComplement[added].size(); ++i) {
int bad = inComplement[added][i];
for (int nxt = 0; nxt < n; ++nxt)
if (!((1 << nxt) & added) and !((1 << nxt) & bad)) {
int nxtBad = bad & (bad ^ bitAdj[nxt]);
nxtBad |= areBad[nxt] & inComplement[added].back();
dpForward[added][i] +=
dpForward[added ^ (1 << nxt)][getId(added ^ (1 << nxt), nxtBad)];
}
}
}
Mint sol = 0;
for (int added = 0; added < (1 << n); ++added) {
int complement = (1 << n) - 1 - added;
for (int i = 0; i < (int)inComplement[added].size(); ++i) {
int bad = inComplement[added][i];
for (int nxt = 0; nxt < n; ++nxt)
if (!((1 << nxt) & added) and !((1 << nxt) & bad)) {
int nxtBad = bad & (bad ^ bitAdj[nxt]);
nxtBad |= areBad[nxt] & complement;
Mint cnt =
dpForward[added ^ (1 << nxt)][getId(added ^ (1 << nxt), nxtBad)] *
dpBack[added][i];
int cntFlip = __builtin_popcount(adj[nxt] & added);
sol += cnt * cntFlip;
}
if (!bad)
break;
bad = (bad - 1) & complement;
}
}
cout << sol << endl;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
1 ms |
212 KB |
Output is correct |
| 4 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 5 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
1 ms |
212 KB |
Output is correct |
| 4 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 5 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
1 ms |
212 KB |
Output is correct |
| 4 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 5 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
1 ms |
212 KB |
Output is correct |
| 4 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 5 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
1 ms |
212 KB |
Output is correct |
| 4 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 5 |
Halted |
0 ms |
0 KB |
- |
