// Build DAG by adding single vertices.
// If we add vertex i, we can't add any vertex < i
// until there is an edge to it from vertex i or any later added vertex.
// States of DP: (added vertices, candidates for next added). O(4^N).
#include <bits/stdc++.h>
using namespace std;
long long pow(long long a, long long e, long long mod) {
if(e <= 0) return 1;
long long x = pow(a, e/2, mod);
x = x * x % mod;
return (e&1) ? (a * x % mod) : x;
}
struct state {
int candidates;
int cnt;
// long long sum;
constexpr static int mod = 998244353;
inline state & operator+=(const state & S) {
cnt += S.cnt;
if(cnt >= mod) cnt -= mod;
// sum += S.sum;
return *this;
}
bool operator<(const state & S) const {
return candidates < S.candidates;
}
};
int main() {
cin.sync_with_stdio(0);
cin.tie(0);
int N, M;
cin >> N >> M;
vector<int> E(N, 0), Ei(N, 0), E_all(N, 0);
for(int i = 0; i < M; i++) {
int u, v;
/* rand */
// static mt19937_64 rng(std::chrono::steady_clock::now().time_since_epoch().count());
// u = rng()%N, v = rng()%N;
// while(u == v || (E_all[u]>>v)&1)
// u = rng()%N, v = rng()%N;
/* rand */
/* input */
cin >> u >> v;
u--, v--;
/* input */
E[u] |= 1<<v;
Ei[v] |= 1<<u;
E_all[u] |= 1<<v;
E_all[v] |= 1<<u;
}
vector< vector<state> > dp(1<<N);
dp[0].push_back({(1<<N)-1, 1});
// dp[0].push_back({(1<<N)-1, 1, 0});
for(int used = 0; used < (1<<N); used++) {
sort(begin(dp[used]), end(dp[used]));
int pos = 0;
for(int i = 1; i < (int)dp[used].size(); i++) {
if(dp[used][i].candidates == dp[used][pos].candidates) {
dp[used][pos] += dp[used][i];
continue;
}
// dp[used][pos].sum %= state::mod;
pos++;
dp[used][pos] = dp[used][i];
}
if(!dp[used].empty()) {
// dp[used][pos].sum %= state::mod;
dp[used].resize(pos+1);
}
for(state & st : dp[used]) {
int suf = (1<<N)-1;
for(int j = 0; j < N; j++) {
suf ^= (1<<j);
if(((st.candidates)>>j)&1) {
int next_used = used | (1<<j);
int next_candidates = (st.candidates & suf) | E_all[j];
next_candidates ^= (next_candidates & next_used);
dp[next_used].push_back({next_candidates, st.cnt});
}
}
}
}
int num_states = 0;
for(int i = 0; i < (1<<N); i++) num_states += dp[i].size();
cerr << num_states << "\n";
long long ans_sum = 0, ans_cnt = 0;
for(state & st : dp[(1<<N)-1]) {
ans_cnt += st.cnt;
// ans_sum += st.sum;
}
ans_cnt %= state::mod;
// ans_sum %= state::mod;
ans_sum = ans_cnt * M % state::mod;
ans_sum = ans_sum * pow(2, state::mod-2, state::mod) % state::mod;
// cout << ans_cnt << "\n";
cout << ans_sum << "\n";
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
2 ms |
376 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
2 ms |
376 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
2 ms |
376 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
2 ms |
376 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
2 ms |
376 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
