Submission #885518

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
885518	2023-12-09T22:44:29 Z	beaboss	Amusement Park (CEOI19_amusementpark)	C++14	100 / 100	2173 ms	6828 KB

amusementpark

// Source: https://oj.uz/problem/view/CEOI19_amusementpark
// 

#include "bits/stdc++.h"

using namespace std;

#define s second
#define f first
#define pb push_back

typedef long long ll;

typedef pair<ll, ll> pii;
typedef vector<pii> vpii;

typedef vector<ll> vi;

#define FOR(i, a, b) for (ll i = (a); i<b; i++)

const ll N = 18;

ll indep[1 << N];
ll dp[1 << N];
ll sz[1 << N];
vi adj[N];
const ll MOD = 998244353;

ll binpow(ll x, ll n) {
	assert(n >= 0);
	x %= MOD;  // note: m * m must be less than 2^63 to avoid ll overflow
	ll res = 1;
	while (n > 0) {
		if (n % 2 == 1) { res = res * x % MOD; }
		x = x * x % MOD;
		n /= 2;
	}
	return res;
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);

	ll n, m;
	cin >> n >> m;


	FOR(i, 0, m) {
		ll a, b;
		cin >> a >> b;
		a--;b--;
		adj[a].pb(b);
		adj[b].pb(a);

	}

	FOR(i, 0, 1 << n) {
		dp[i]=0;
		indep[i]=true;
		sz[i] = 0;
		FOR(j, 0, n) {
			if ((1 << j) & i) {
				for (auto val: adj[j]) {
					if ((1 << val) & i) indep[i]=false;
				}

				sz[i] ++;
			}
		}

		// cout << i << ' ' << indep[i] << endl;

		if (sz[i] % 2 == 1) sz[i] = 1;
		else sz[i] = -1;
	}

	dp[0] = 1;


	FOR(i, 1, 1 << n) {
		dp[i] = 0;
		for (ll j = i; j; j = (j - 1) & i) {
			// cout << ' ' << j << dp[i ^ j] << dp[i] << sz[j] << indep[j] << endl;
			if (indep[j]) dp[i] = ((dp[i] + dp[i ^ j] * sz[j])) % MOD;

		}

		// cout << i << ' ' << dp[i] << endl;	
	}
	dp[(1 << n) - 1] = (dp[(1 << n) - 1] + MOD) % MOD;
	cout << ((dp[(1 << n) - 1] * m) % MOD * binpow(2, MOD - 2)) % MOD << endl;


}

Subtask #1
7.0 / 7.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	4444 KB	Output is correct
2	Correct	1 ms	4444 KB	Output is correct
3	Correct	1 ms	4444 KB	Output is correct
4	Correct	1 ms	4444 KB	Output is correct
5	Correct	1 ms	4444 KB	Output is correct
6	Correct	1 ms	4444 KB	Output is correct
7	Correct	1 ms	4444 KB	Output is correct
8	Correct	1 ms	4444 KB	Output is correct

Subtask #2
12.0 / 12.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	4444 KB	Output is correct
2	Correct	1 ms	4444 KB	Output is correct
3	Correct	1 ms	4444 KB	Output is correct
4	Correct	1 ms	4444 KB	Output is correct
5	Correct	1 ms	4444 KB	Output is correct
6	Correct	1 ms	4444 KB	Output is correct
7	Correct	1 ms	4444 KB	Output is correct
8	Correct	1 ms	4444 KB	Output is correct
9	Correct	1 ms	4444 KB	Output is correct
10	Correct	1 ms	4444 KB	Output is correct
11	Correct	1 ms	4444 KB	Output is correct
12	Correct	1 ms	4444 KB	Output is correct
13	Correct	1 ms	4444 KB	Output is correct
14	Correct	1 ms	4444 KB	Output is correct
15	Correct	1 ms	4444 KB	Output is correct
16	Correct	1 ms	4444 KB	Output is correct
17	Correct	1 ms	4444 KB	Output is correct
18	Correct	1 ms	4444 KB	Output is correct
19	Correct	2 ms	4444 KB	Output is correct
20	Correct	1 ms	4444 KB	Output is correct
21	Correct	1 ms	4444 KB	Output is correct
22	Correct	1 ms	4444 KB	Output is correct
23	Correct	1 ms	4444 KB	Output is correct
24	Correct	1 ms	4444 KB	Output is correct

Subtask #3
23.0 / 23.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	4444 KB	Output is correct
2	Correct	1 ms	4444 KB	Output is correct
3	Correct	1 ms	4444 KB	Output is correct
4	Correct	1 ms	4444 KB	Output is correct
5	Correct	1 ms	4444 KB	Output is correct
6	Correct	1 ms	4444 KB	Output is correct
7	Correct	1 ms	4444 KB	Output is correct
8	Correct	1 ms	4444 KB	Output is correct
9	Correct	1 ms	4444 KB	Output is correct
10	Correct	1 ms	4444 KB	Output is correct
11	Correct	1 ms	4444 KB	Output is correct
12	Correct	1 ms	4444 KB	Output is correct
13	Correct	1 ms	4444 KB	Output is correct
14	Correct	1 ms	4444 KB	Output is correct
15	Correct	1 ms	4444 KB	Output is correct
16	Correct	1 ms	4444 KB	Output is correct
17	Correct	1 ms	4444 KB	Output is correct
18	Correct	1 ms	4444 KB	Output is correct
19	Correct	2 ms	4444 KB	Output is correct
20	Correct	1 ms	4444 KB	Output is correct
21	Correct	1 ms	4444 KB	Output is correct
22	Correct	1 ms	4444 KB	Output is correct
23	Correct	1 ms	4444 KB	Output is correct
24	Correct	1 ms	4444 KB	Output is correct
25	Correct	1 ms	4444 KB	Output is correct
26	Correct	3 ms	4556 KB	Output is correct
27	Correct	1 ms	4444 KB	Output is correct
28	Correct	1 ms	4444 KB	Output is correct
29	Correct	1 ms	4444 KB	Output is correct
30	Correct	1 ms	4444 KB	Output is correct
31	Correct	1 ms	4448 KB	Output is correct
32	Correct	1 ms	4448 KB	Output is correct
33	Correct	1 ms	4448 KB	Output is correct
34	Correct	1 ms	4448 KB	Output is correct
35	Correct	1 ms	4448 KB	Output is correct
36	Correct	1 ms	4448 KB	Output is correct
37	Correct	1 ms	4448 KB	Output is correct
38	Correct	1 ms	4448 KB	Output is correct
39	Correct	1 ms	4444 KB	Output is correct
40	Correct	1 ms	4444 KB	Output is correct
41	Correct	1 ms	4444 KB	Output is correct
42	Correct	1 ms	4448 KB	Output is correct
43	Correct	1 ms	4448 KB	Output is correct
44	Correct	1 ms	4448 KB	Output is correct
45	Correct	1 ms	4448 KB	Output is correct
46	Correct	1 ms	4452 KB	Output is correct
47	Correct	1 ms	4444 KB	Output is correct
48	Correct	1 ms	4444 KB	Output is correct
49	Correct	1 ms	4452 KB	Output is correct
50	Correct	1 ms	4444 KB	Output is correct
51	Correct	1 ms	4560 KB	Output is correct
52	Correct	1 ms	4440 KB	Output is correct
53	Correct	1 ms	4444 KB	Output is correct
54	Correct	1 ms	4448 KB	Output is correct
55	Correct	1 ms	4440 KB	Output is correct
56	Correct	1 ms	4444 KB	Output is correct
57	Correct	1 ms	4444 KB	Output is correct
58	Correct	1 ms	4444 KB	Output is correct
59	Correct	1 ms	4444 KB	Output is correct
60	Correct	1 ms	4444 KB	Output is correct
61	Correct	1 ms	4444 KB	Output is correct
62	Correct	1 ms	4444 KB	Output is correct
63	Correct	1 ms	4444 KB	Output is correct
64	Correct	1 ms	4564 KB	Output is correct

Subtask #4
21.0 / 21.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	4444 KB	Output is correct
2	Correct	1 ms	4444 KB	Output is correct
3	Correct	1 ms	4444 KB	Output is correct
4	Correct	1 ms	4444 KB	Output is correct
5	Correct	1 ms	4444 KB	Output is correct
6	Correct	1 ms	4444 KB	Output is correct
7	Correct	1 ms	4444 KB	Output is correct
8	Correct	1 ms	4444 KB	Output is correct
9	Correct	1 ms	4444 KB	Output is correct
10	Correct	1 ms	4444 KB	Output is correct
11	Correct	1 ms	4444 KB	Output is correct
12	Correct	1 ms	4444 KB	Output is correct
13	Correct	1 ms	4444 KB	Output is correct
14	Correct	1 ms	4444 KB	Output is correct
15	Correct	1 ms	4444 KB	Output is correct
16	Correct	1 ms	4444 KB	Output is correct
17	Correct	1 ms	4444 KB	Output is correct
18	Correct	1 ms	4444 KB	Output is correct
19	Correct	2 ms	4444 KB	Output is correct
20	Correct	1 ms	4444 KB	Output is correct
21	Correct	1 ms	4444 KB	Output is correct
22	Correct	1 ms	4444 KB	Output is correct
23	Correct	1 ms	4444 KB	Output is correct
24	Correct	1 ms	4444 KB	Output is correct
25	Correct	1 ms	4444 KB	Output is correct
26	Correct	3 ms	4556 KB	Output is correct
27	Correct	1 ms	4444 KB	Output is correct
28	Correct	1 ms	4444 KB	Output is correct
29	Correct	1 ms	4444 KB	Output is correct
30	Correct	1 ms	4444 KB	Output is correct
31	Correct	1 ms	4448 KB	Output is correct
32	Correct	1 ms	4448 KB	Output is correct
33	Correct	1 ms	4448 KB	Output is correct
34	Correct	1 ms	4448 KB	Output is correct
35	Correct	1 ms	4448 KB	Output is correct
36	Correct	1 ms	4448 KB	Output is correct
37	Correct	1 ms	4448 KB	Output is correct
38	Correct	1 ms	4448 KB	Output is correct
39	Correct	1 ms	4444 KB	Output is correct
40	Correct	1 ms	4444 KB	Output is correct
41	Correct	1 ms	4444 KB	Output is correct
42	Correct	1 ms	4448 KB	Output is correct
43	Correct	1 ms	4448 KB	Output is correct
44	Correct	1 ms	4448 KB	Output is correct
45	Correct	1 ms	4448 KB	Output is correct
46	Correct	1 ms	4452 KB	Output is correct
47	Correct	1 ms	4444 KB	Output is correct
48	Correct	1 ms	4444 KB	Output is correct
49	Correct	1 ms	4452 KB	Output is correct
50	Correct	1 ms	4444 KB	Output is correct
51	Correct	1 ms	4560 KB	Output is correct
52	Correct	1 ms	4440 KB	Output is correct
53	Correct	1 ms	4444 KB	Output is correct
54	Correct	1 ms	4448 KB	Output is correct
55	Correct	1 ms	4440 KB	Output is correct
56	Correct	1 ms	4444 KB	Output is correct
57	Correct	1 ms	4444 KB	Output is correct
58	Correct	1 ms	4444 KB	Output is correct
59	Correct	1 ms	4444 KB	Output is correct
60	Correct	1 ms	4444 KB	Output is correct
61	Correct	1 ms	4444 KB	Output is correct
62	Correct	1 ms	4444 KB	Output is correct
63	Correct	1 ms	4444 KB	Output is correct
64	Correct	1 ms	4564 KB	Output is correct
65	Correct	10 ms	4444 KB	Output is correct
66	Correct	12 ms	4700 KB	Output is correct
67	Correct	10 ms	4700 KB	Output is correct
68	Correct	10 ms	4608 KB	Output is correct
69	Correct	14 ms	4700 KB	Output is correct
70	Correct	14 ms	4444 KB	Output is correct
71	Correct	15 ms	4444 KB	Output is correct
72	Correct	12 ms	4444 KB	Output is correct
73	Correct	10 ms	4444 KB	Output is correct
74	Correct	10 ms	4560 KB	Output is correct
75	Correct	11 ms	4444 KB	Output is correct
76	Correct	11 ms	4692 KB	Output is correct
77	Correct	26 ms	4700 KB	Output is correct
78	Correct	25 ms	4696 KB	Output is correct
79	Correct	26 ms	4700 KB	Output is correct
80	Correct	25 ms	4696 KB	Output is correct
81	Correct	27 ms	4696 KB	Output is correct
82	Correct	25 ms	4696 KB	Output is correct
83	Correct	28 ms	4700 KB	Output is correct
84	Correct	26 ms	4732 KB	Output is correct
85	Correct	55 ms	4696 KB	Output is correct
86	Correct	40 ms	4808 KB	Output is correct
87	Correct	42 ms	4700 KB	Output is correct
88	Correct	42 ms	4696 KB	Output is correct
89	Correct	26 ms	4808 KB	Output is correct
90	Correct	32 ms	4660 KB	Output is correct
91	Correct	30 ms	4696 KB	Output is correct
92	Correct	37 ms	4816 KB	Output is correct

Subtask #5
37.0 / 37.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	4444 KB	Output is correct
2	Correct	1 ms	4444 KB	Output is correct
3	Correct	1 ms	4444 KB	Output is correct
4	Correct	1 ms	4444 KB	Output is correct
5	Correct	1 ms	4444 KB	Output is correct
6	Correct	1 ms	4444 KB	Output is correct
7	Correct	1 ms	4444 KB	Output is correct
8	Correct	1 ms	4444 KB	Output is correct
9	Correct	1 ms	4444 KB	Output is correct
10	Correct	1 ms	4444 KB	Output is correct
11	Correct	1 ms	4444 KB	Output is correct
12	Correct	1 ms	4444 KB	Output is correct
13	Correct	1 ms	4444 KB	Output is correct
14	Correct	1 ms	4444 KB	Output is correct
15	Correct	1 ms	4444 KB	Output is correct
16	Correct	1 ms	4444 KB	Output is correct
17	Correct	1 ms	4444 KB	Output is correct
18	Correct	1 ms	4444 KB	Output is correct
19	Correct	2 ms	4444 KB	Output is correct
20	Correct	1 ms	4444 KB	Output is correct
21	Correct	1 ms	4444 KB	Output is correct
22	Correct	1 ms	4444 KB	Output is correct
23	Correct	1 ms	4444 KB	Output is correct
24	Correct	1 ms	4444 KB	Output is correct
25	Correct	1 ms	4444 KB	Output is correct
26	Correct	3 ms	4556 KB	Output is correct
27	Correct	1 ms	4444 KB	Output is correct
28	Correct	1 ms	4444 KB	Output is correct
29	Correct	1 ms	4444 KB	Output is correct
30	Correct	1 ms	4444 KB	Output is correct
31	Correct	1 ms	4448 KB	Output is correct
32	Correct	1 ms	4448 KB	Output is correct
33	Correct	1 ms	4448 KB	Output is correct
34	Correct	1 ms	4448 KB	Output is correct
35	Correct	1 ms	4448 KB	Output is correct
36	Correct	1 ms	4448 KB	Output is correct
37	Correct	1 ms	4448 KB	Output is correct
38	Correct	1 ms	4448 KB	Output is correct
39	Correct	1 ms	4444 KB	Output is correct
40	Correct	1 ms	4444 KB	Output is correct
41	Correct	1 ms	4444 KB	Output is correct
42	Correct	1 ms	4448 KB	Output is correct
43	Correct	1 ms	4448 KB	Output is correct
44	Correct	1 ms	4448 KB	Output is correct
45	Correct	1 ms	4448 KB	Output is correct
46	Correct	1 ms	4452 KB	Output is correct
47	Correct	1 ms	4444 KB	Output is correct
48	Correct	1 ms	4444 KB	Output is correct
49	Correct	1 ms	4452 KB	Output is correct
50	Correct	1 ms	4444 KB	Output is correct
51	Correct	1 ms	4560 KB	Output is correct
52	Correct	1 ms	4440 KB	Output is correct
53	Correct	1 ms	4444 KB	Output is correct
54	Correct	1 ms	4448 KB	Output is correct
55	Correct	1 ms	4440 KB	Output is correct
56	Correct	1 ms	4444 KB	Output is correct
57	Correct	1 ms	4444 KB	Output is correct
58	Correct	1 ms	4444 KB	Output is correct
59	Correct	1 ms	4444 KB	Output is correct
60	Correct	1 ms	4444 KB	Output is correct
61	Correct	1 ms	4444 KB	Output is correct
62	Correct	1 ms	4444 KB	Output is correct
63	Correct	1 ms	4444 KB	Output is correct
64	Correct	1 ms	4564 KB	Output is correct
65	Correct	10 ms	4444 KB	Output is correct
66	Correct	12 ms	4700 KB	Output is correct
67	Correct	10 ms	4700 KB	Output is correct
68	Correct	10 ms	4608 KB	Output is correct
69	Correct	14 ms	4700 KB	Output is correct
70	Correct	14 ms	4444 KB	Output is correct
71	Correct	15 ms	4444 KB	Output is correct
72	Correct	12 ms	4444 KB	Output is correct
73	Correct	10 ms	4444 KB	Output is correct
74	Correct	10 ms	4560 KB	Output is correct
75	Correct	11 ms	4444 KB	Output is correct
76	Correct	11 ms	4692 KB	Output is correct
77	Correct	26 ms	4700 KB	Output is correct
78	Correct	25 ms	4696 KB	Output is correct
79	Correct	26 ms	4700 KB	Output is correct
80	Correct	25 ms	4696 KB	Output is correct
81	Correct	27 ms	4696 KB	Output is correct
82	Correct	25 ms	4696 KB	Output is correct
83	Correct	28 ms	4700 KB	Output is correct
84	Correct	26 ms	4732 KB	Output is correct
85	Correct	55 ms	4696 KB	Output is correct
86	Correct	40 ms	4808 KB	Output is correct
87	Correct	42 ms	4700 KB	Output is correct
88	Correct	42 ms	4696 KB	Output is correct
89	Correct	26 ms	4808 KB	Output is correct
90	Correct	32 ms	4660 KB	Output is correct
91	Correct	30 ms	4696 KB	Output is correct
92	Correct	37 ms	4816 KB	Output is correct
93	Correct	949 ms	6584 KB	Output is correct
94	Correct	989 ms	6736 KB	Output is correct
95	Correct	933 ms	6588 KB	Output is correct
96	Correct	673 ms	6768 KB	Output is correct
97	Correct	671 ms	6600 KB	Output is correct
98	Correct	767 ms	6736 KB	Output is correct
99	Correct	72 ms	5056 KB	Output is correct
100	Correct	78 ms	4960 KB	Output is correct
101	Correct	74 ms	5192 KB	Output is correct
102	Correct	67 ms	4952 KB	Output is correct
103	Correct	688 ms	5564 KB	Output is correct
104	Correct	311 ms	5468 KB	Output is correct
105	Correct	265 ms	5564 KB	Output is correct
106	Correct	199 ms	5468 KB	Output is correct
107	Correct	2173 ms	6584 KB	Output is correct
108	Correct	775 ms	6596 KB	Output is correct
109	Correct	548 ms	6584 KB	Output is correct
110	Correct	512 ms	6592 KB	Output is correct
111	Correct	73 ms	4952 KB	Output is correct
112	Correct	64 ms	5056 KB	Output is correct
113	Correct	63 ms	4944 KB	Output is correct
114	Correct	165 ms	5052 KB	Output is correct
115	Correct	104 ms	5212 KB	Output is correct
116	Correct	120 ms	4936 KB	Output is correct
117	Correct	127 ms	5056 KB	Output is correct
118	Correct	73 ms	5060 KB	Output is correct
119	Correct	93 ms	5060 KB	Output is correct
120	Correct	98 ms	5056 KB	Output is correct
121	Correct	100 ms	4956 KB	Output is correct
122	Correct	187 ms	5568 KB	Output is correct
123	Correct	173 ms	5520 KB	Output is correct
124	Correct	187 ms	5572 KB	Output is correct
125	Correct	171 ms	5572 KB	Output is correct
126	Correct	168 ms	5580 KB	Output is correct
127	Correct	177 ms	5568 KB	Output is correct
128	Correct	171 ms	5460 KB	Output is correct
129	Correct	176 ms	5764 KB	Output is correct
130	Correct	171 ms	5456 KB	Output is correct
131	Correct	422 ms	5568 KB	Output is correct
132	Correct	248 ms	5464 KB	Output is correct
133	Correct	367 ms	5568 KB	Output is correct
134	Correct	356 ms	5568 KB	Output is correct
135	Correct	251 ms	5468 KB	Output is correct
136	Correct	232 ms	5568 KB	Output is correct
137	Correct	290 ms	5564 KB	Output is correct
138	Correct	305 ms	5468 KB	Output is correct
139	Correct	211 ms	5568 KB	Output is correct
140	Correct	248 ms	5480 KB	Output is correct
141	Correct	202 ms	5712 KB	Output is correct
142	Correct	503 ms	6452 KB	Output is correct
143	Correct	464 ms	6736 KB	Output is correct
144	Correct	474 ms	6592 KB	Output is correct
145	Correct	457 ms	6480 KB	Output is correct
146	Correct	487 ms	6588 KB	Output is correct
147	Correct	474 ms	6356 KB	Output is correct
148	Correct	504 ms	6480 KB	Output is correct
149	Correct	480 ms	6596 KB	Output is correct
150	Correct	498 ms	6512 KB	Output is correct
151	Correct	569 ms	6560 KB	Output is correct
152	Correct	547 ms	6736 KB	Output is correct
153	Correct	701 ms	6592 KB	Output is correct
154	Correct	734 ms	6592 KB	Output is correct
155	Correct	730 ms	6484 KB	Output is correct
156	Correct	816 ms	6728 KB	Output is correct
157	Correct	792 ms	6828 KB	Output is correct
158	Correct	857 ms	6464 KB	Output is correct
159	Correct	595 ms	6588 KB	Output is correct
160	Correct	673 ms	6588 KB	Output is correct
161	Correct	734 ms	6592 KB	Output is correct
162	Correct	601 ms	6588 KB	Output is correct
163	Correct	580 ms	6408 KB	Output is correct
164	Correct	556 ms	6484 KB	Output is correct
165	Correct	551 ms	6736 KB	Output is correct
166	Correct	593 ms	6588 KB	Output is correct
167	Correct	614 ms	6740 KB	Output is correct

Submission #885518

Compilation message

Subtask #1 7.0 / 7.0

Subtask #2 12.0 / 12.0

Subtask #3 23.0 / 23.0

Subtask #4 21.0 / 21.0

Subtask #5 37.0 / 37.0

Subtask #1
7.0 / 7.0

Subtask #2
12.0 / 12.0

Subtask #3
23.0 / 23.0

Subtask #4
21.0 / 21.0

Subtask #5
37.0 / 37.0