Submission #868308

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
868308	2023-10-31T03:29:12 Z	ND0322	Amusement Park (CEOI19_amusementpark)	C++17	100 / 100	1727 ms	4180 KB

amusementpark

#include <bits/stdc++.h>
#include <iostream>

using namespace std;

const int MAXN = 18;
const int MOD = 998244353;


//if you find a dag that works reversing all edges creates a new dag
//ans would be edges * (#dag/2)
//the dags differ by their nodes

int n, m, popcount[1<<MAXN];

long long dp[1<<MAXN];

bool indep[1<<MAXN];

//dp = num dags using nodes in the mask
//indep is if a mask is an independant subset (no two nodes are connected)
//all submasks of independant submasks are independant as well
//for all independant subsets of mask:
//if(number of nodes in subset is odd) dp[mask] += dp[the rest of the mask]
//and because we overcount some
//if(number of nodes in subset is even) dp[mask] -= dp[the rest of the mask]



//every subset of an independant set is independant
//if it isnt then the whole thing isnt independant



int main(){
    
    scanf("%d %d", &n, &m);

    fill(indep, indep + (1<<n), 1);

    for(int i = 0; i < m; i++){
        int x,y; scanf("%d %d", &x, &y);

        indep[1<<(x-1) | 1<<(y-1)] = 0;
       
    }

    //same thing as the function
    for(int i = 0; i < n; i++){
        for(int j = (1<<n)-1; j >= 0; j--) if(j & (1<<i)) indep[j] &= indep[j ^ (1<<i)];
    }

    for(int i = 0; i < (1<<n); i++){
        popcount[i] = popcount[i>>1] + (i&1);
    }
    

    dp[0] = 1;

    for(int i = 0; i < (1<<n); i++){
        for(int j = i; j >= 1; j = (j-1) & i ){
            if(indep[j]){
                if(popcount[j] & 1) dp[i] = (dp[i] + dp[i^j]) % MOD;
                else dp[i] = (dp[i] - dp[i^j]) % MOD;
            }
        }
    }

    //https://math.stackexchange.com/questions/3361647/finding-inverse-of-2-mod-m
    int minv = ((1+MOD)/2);
    dp[(1 << n) - 1] = (dp[(1 << n) - 1] + MOD) % MOD;
    

    printf("%lld\n", dp[(1<<n)-1] * m % MOD * minv % MOD);

    

  


}

Compilation message

amusementpark.cpp: In function 'int main()':
amusementpark.cpp:37:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   37 |     scanf("%d %d", &n, &m);
      |     ~~~~~^~~~~~~~~~~~~~~~~
amusementpark.cpp:42:23: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   42 |         int x,y; scanf("%d %d", &x, &y);
      |                  ~~~~~^~~~~~~~~~~~~~~~~

Subtask #1
7.0 / 7.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	2392 KB	Output is correct
2	Correct	1 ms	2392 KB	Output is correct
3	Correct	0 ms	2396 KB	Output is correct
4	Correct	0 ms	2396 KB	Output is correct
5	Correct	0 ms	2396 KB	Output is correct
6	Correct	0 ms	2396 KB	Output is correct
7	Correct	0 ms	2396 KB	Output is correct
8	Correct	0 ms	2396 KB	Output is correct

Subtask #2
12.0 / 12.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	2392 KB	Output is correct
2	Correct	1 ms	2392 KB	Output is correct
3	Correct	0 ms	2396 KB	Output is correct
4	Correct	0 ms	2396 KB	Output is correct
5	Correct	0 ms	2396 KB	Output is correct
6	Correct	0 ms	2396 KB	Output is correct
7	Correct	0 ms	2396 KB	Output is correct
8	Correct	0 ms	2396 KB	Output is correct
9	Correct	0 ms	2396 KB	Output is correct
10	Correct	0 ms	2396 KB	Output is correct
11	Correct	1 ms	2392 KB	Output is correct
12	Correct	1 ms	2396 KB	Output is correct
13	Correct	1 ms	2396 KB	Output is correct
14	Correct	1 ms	2396 KB	Output is correct
15	Correct	0 ms	2396 KB	Output is correct
16	Correct	0 ms	2392 KB	Output is correct
17	Correct	0 ms	2396 KB	Output is correct
18	Correct	0 ms	2396 KB	Output is correct
19	Correct	0 ms	2396 KB	Output is correct
20	Correct	1 ms	2392 KB	Output is correct
21	Correct	0 ms	2500 KB	Output is correct
22	Correct	1 ms	2396 KB	Output is correct
23	Correct	1 ms	2396 KB	Output is correct
24	Correct	1 ms	2396 KB	Output is correct

Subtask #3
23.0 / 23.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	2392 KB	Output is correct
2	Correct	1 ms	2392 KB	Output is correct
3	Correct	0 ms	2396 KB	Output is correct
4	Correct	0 ms	2396 KB	Output is correct
5	Correct	0 ms	2396 KB	Output is correct
6	Correct	0 ms	2396 KB	Output is correct
7	Correct	0 ms	2396 KB	Output is correct
8	Correct	0 ms	2396 KB	Output is correct
9	Correct	0 ms	2396 KB	Output is correct
10	Correct	0 ms	2396 KB	Output is correct
11	Correct	1 ms	2392 KB	Output is correct
12	Correct	1 ms	2396 KB	Output is correct
13	Correct	1 ms	2396 KB	Output is correct
14	Correct	1 ms	2396 KB	Output is correct
15	Correct	0 ms	2396 KB	Output is correct
16	Correct	0 ms	2392 KB	Output is correct
17	Correct	0 ms	2396 KB	Output is correct
18	Correct	0 ms	2396 KB	Output is correct
19	Correct	0 ms	2396 KB	Output is correct
20	Correct	1 ms	2392 KB	Output is correct
21	Correct	0 ms	2500 KB	Output is correct
22	Correct	1 ms	2396 KB	Output is correct
23	Correct	1 ms	2396 KB	Output is correct
24	Correct	1 ms	2396 KB	Output is correct
25	Correct	1 ms	2392 KB	Output is correct
26	Correct	1 ms	2396 KB	Output is correct
27	Correct	0 ms	2396 KB	Output is correct
28	Correct	1 ms	2396 KB	Output is correct
29	Correct	1 ms	2396 KB	Output is correct
30	Correct	0 ms	2396 KB	Output is correct
31	Correct	1 ms	2396 KB	Output is correct
32	Correct	0 ms	2396 KB	Output is correct
33	Correct	0 ms	2396 KB	Output is correct
34	Correct	0 ms	2396 KB	Output is correct
35	Correct	0 ms	2396 KB	Output is correct
36	Correct	1 ms	2396 KB	Output is correct
37	Correct	0 ms	2396 KB	Output is correct
38	Correct	0 ms	2396 KB	Output is correct
39	Correct	0 ms	2396 KB	Output is correct
40	Correct	1 ms	2396 KB	Output is correct
41	Correct	0 ms	2396 KB	Output is correct
42	Correct	0 ms	2396 KB	Output is correct
43	Correct	1 ms	2396 KB	Output is correct
44	Correct	1 ms	2392 KB	Output is correct
45	Correct	0 ms	2396 KB	Output is correct
46	Correct	0 ms	2396 KB	Output is correct
47	Correct	0 ms	2396 KB	Output is correct
48	Correct	1 ms	2396 KB	Output is correct
49	Correct	1 ms	2396 KB	Output is correct
50	Correct	0 ms	2396 KB	Output is correct
51	Correct	0 ms	2396 KB	Output is correct
52	Correct	1 ms	2396 KB	Output is correct
53	Correct	1 ms	2396 KB	Output is correct
54	Correct	1 ms	2396 KB	Output is correct
55	Correct	1 ms	2396 KB	Output is correct
56	Correct	1 ms	2396 KB	Output is correct
57	Correct	1 ms	2396 KB	Output is correct
58	Correct	1 ms	2396 KB	Output is correct
59	Correct	0 ms	2396 KB	Output is correct
60	Correct	1 ms	2392 KB	Output is correct
61	Correct	1 ms	2396 KB	Output is correct
62	Correct	1 ms	2396 KB	Output is correct
63	Correct	1 ms	2396 KB	Output is correct
64	Correct	1 ms	2396 KB	Output is correct

Subtask #4
21.0 / 21.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	2392 KB	Output is correct
2	Correct	1 ms	2392 KB	Output is correct
3	Correct	0 ms	2396 KB	Output is correct
4	Correct	0 ms	2396 KB	Output is correct
5	Correct	0 ms	2396 KB	Output is correct
6	Correct	0 ms	2396 KB	Output is correct
7	Correct	0 ms	2396 KB	Output is correct
8	Correct	0 ms	2396 KB	Output is correct
9	Correct	0 ms	2396 KB	Output is correct
10	Correct	0 ms	2396 KB	Output is correct
11	Correct	1 ms	2392 KB	Output is correct
12	Correct	1 ms	2396 KB	Output is correct
13	Correct	1 ms	2396 KB	Output is correct
14	Correct	1 ms	2396 KB	Output is correct
15	Correct	0 ms	2396 KB	Output is correct
16	Correct	0 ms	2392 KB	Output is correct
17	Correct	0 ms	2396 KB	Output is correct
18	Correct	0 ms	2396 KB	Output is correct
19	Correct	0 ms	2396 KB	Output is correct
20	Correct	1 ms	2392 KB	Output is correct
21	Correct	0 ms	2500 KB	Output is correct
22	Correct	1 ms	2396 KB	Output is correct
23	Correct	1 ms	2396 KB	Output is correct
24	Correct	1 ms	2396 KB	Output is correct
25	Correct	1 ms	2392 KB	Output is correct
26	Correct	1 ms	2396 KB	Output is correct
27	Correct	0 ms	2396 KB	Output is correct
28	Correct	1 ms	2396 KB	Output is correct
29	Correct	1 ms	2396 KB	Output is correct
30	Correct	0 ms	2396 KB	Output is correct
31	Correct	1 ms	2396 KB	Output is correct
32	Correct	0 ms	2396 KB	Output is correct
33	Correct	0 ms	2396 KB	Output is correct
34	Correct	0 ms	2396 KB	Output is correct
35	Correct	0 ms	2396 KB	Output is correct
36	Correct	1 ms	2396 KB	Output is correct
37	Correct	0 ms	2396 KB	Output is correct
38	Correct	0 ms	2396 KB	Output is correct
39	Correct	0 ms	2396 KB	Output is correct
40	Correct	1 ms	2396 KB	Output is correct
41	Correct	0 ms	2396 KB	Output is correct
42	Correct	0 ms	2396 KB	Output is correct
43	Correct	1 ms	2396 KB	Output is correct
44	Correct	1 ms	2392 KB	Output is correct
45	Correct	0 ms	2396 KB	Output is correct
46	Correct	0 ms	2396 KB	Output is correct
47	Correct	0 ms	2396 KB	Output is correct
48	Correct	1 ms	2396 KB	Output is correct
49	Correct	1 ms	2396 KB	Output is correct
50	Correct	0 ms	2396 KB	Output is correct
51	Correct	0 ms	2396 KB	Output is correct
52	Correct	1 ms	2396 KB	Output is correct
53	Correct	1 ms	2396 KB	Output is correct
54	Correct	1 ms	2396 KB	Output is correct
55	Correct	1 ms	2396 KB	Output is correct
56	Correct	1 ms	2396 KB	Output is correct
57	Correct	1 ms	2396 KB	Output is correct
58	Correct	1 ms	2396 KB	Output is correct
59	Correct	0 ms	2396 KB	Output is correct
60	Correct	1 ms	2392 KB	Output is correct
61	Correct	1 ms	2396 KB	Output is correct
62	Correct	1 ms	2396 KB	Output is correct
63	Correct	1 ms	2396 KB	Output is correct
64	Correct	1 ms	2396 KB	Output is correct
65	Correct	7 ms	2396 KB	Output is correct
66	Correct	7 ms	2580 KB	Output is correct
67	Correct	6 ms	2572 KB	Output is correct
68	Correct	6 ms	2392 KB	Output is correct
69	Correct	12 ms	2396 KB	Output is correct
70	Correct	9 ms	2396 KB	Output is correct
71	Correct	9 ms	2572 KB	Output is correct
72	Correct	10 ms	2396 KB	Output is correct
73	Correct	8 ms	2568 KB	Output is correct
74	Correct	7 ms	2396 KB	Output is correct
75	Correct	8 ms	2576 KB	Output is correct
76	Correct	8 ms	2392 KB	Output is correct
77	Correct	24 ms	2900 KB	Output is correct
78	Correct	20 ms	2652 KB	Output is correct
79	Correct	19 ms	2656 KB	Output is correct
80	Correct	17 ms	2652 KB	Output is correct
81	Correct	16 ms	2652 KB	Output is correct
82	Correct	15 ms	2652 KB	Output is correct
83	Correct	16 ms	2652 KB	Output is correct
84	Correct	14 ms	2656 KB	Output is correct
85	Correct	39 ms	2396 KB	Output is correct
86	Correct	25 ms	2648 KB	Output is correct
87	Correct	27 ms	2652 KB	Output is correct
88	Correct	28 ms	2656 KB	Output is correct
89	Correct	22 ms	2652 KB	Output is correct
90	Correct	20 ms	2652 KB	Output is correct
91	Correct	21 ms	2652 KB	Output is correct
92	Correct	23 ms	2656 KB	Output is correct

Subtask #5
37.0 / 37.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	2392 KB	Output is correct
2	Correct	1 ms	2392 KB	Output is correct
3	Correct	0 ms	2396 KB	Output is correct
4	Correct	0 ms	2396 KB	Output is correct
5	Correct	0 ms	2396 KB	Output is correct
6	Correct	0 ms	2396 KB	Output is correct
7	Correct	0 ms	2396 KB	Output is correct
8	Correct	0 ms	2396 KB	Output is correct
9	Correct	0 ms	2396 KB	Output is correct
10	Correct	0 ms	2396 KB	Output is correct
11	Correct	1 ms	2392 KB	Output is correct
12	Correct	1 ms	2396 KB	Output is correct
13	Correct	1 ms	2396 KB	Output is correct
14	Correct	1 ms	2396 KB	Output is correct
15	Correct	0 ms	2396 KB	Output is correct
16	Correct	0 ms	2392 KB	Output is correct
17	Correct	0 ms	2396 KB	Output is correct
18	Correct	0 ms	2396 KB	Output is correct
19	Correct	0 ms	2396 KB	Output is correct
20	Correct	1 ms	2392 KB	Output is correct
21	Correct	0 ms	2500 KB	Output is correct
22	Correct	1 ms	2396 KB	Output is correct
23	Correct	1 ms	2396 KB	Output is correct
24	Correct	1 ms	2396 KB	Output is correct
25	Correct	1 ms	2392 KB	Output is correct
26	Correct	1 ms	2396 KB	Output is correct
27	Correct	0 ms	2396 KB	Output is correct
28	Correct	1 ms	2396 KB	Output is correct
29	Correct	1 ms	2396 KB	Output is correct
30	Correct	0 ms	2396 KB	Output is correct
31	Correct	1 ms	2396 KB	Output is correct
32	Correct	0 ms	2396 KB	Output is correct
33	Correct	0 ms	2396 KB	Output is correct
34	Correct	0 ms	2396 KB	Output is correct
35	Correct	0 ms	2396 KB	Output is correct
36	Correct	1 ms	2396 KB	Output is correct
37	Correct	0 ms	2396 KB	Output is correct
38	Correct	0 ms	2396 KB	Output is correct
39	Correct	0 ms	2396 KB	Output is correct
40	Correct	1 ms	2396 KB	Output is correct
41	Correct	0 ms	2396 KB	Output is correct
42	Correct	0 ms	2396 KB	Output is correct
43	Correct	1 ms	2396 KB	Output is correct
44	Correct	1 ms	2392 KB	Output is correct
45	Correct	0 ms	2396 KB	Output is correct
46	Correct	0 ms	2396 KB	Output is correct
47	Correct	0 ms	2396 KB	Output is correct
48	Correct	1 ms	2396 KB	Output is correct
49	Correct	1 ms	2396 KB	Output is correct
50	Correct	0 ms	2396 KB	Output is correct
51	Correct	0 ms	2396 KB	Output is correct
52	Correct	1 ms	2396 KB	Output is correct
53	Correct	1 ms	2396 KB	Output is correct
54	Correct	1 ms	2396 KB	Output is correct
55	Correct	1 ms	2396 KB	Output is correct
56	Correct	1 ms	2396 KB	Output is correct
57	Correct	1 ms	2396 KB	Output is correct
58	Correct	1 ms	2396 KB	Output is correct
59	Correct	0 ms	2396 KB	Output is correct
60	Correct	1 ms	2392 KB	Output is correct
61	Correct	1 ms	2396 KB	Output is correct
62	Correct	1 ms	2396 KB	Output is correct
63	Correct	1 ms	2396 KB	Output is correct
64	Correct	1 ms	2396 KB	Output is correct
65	Correct	7 ms	2396 KB	Output is correct
66	Correct	7 ms	2580 KB	Output is correct
67	Correct	6 ms	2572 KB	Output is correct
68	Correct	6 ms	2392 KB	Output is correct
69	Correct	12 ms	2396 KB	Output is correct
70	Correct	9 ms	2396 KB	Output is correct
71	Correct	9 ms	2572 KB	Output is correct
72	Correct	10 ms	2396 KB	Output is correct
73	Correct	8 ms	2568 KB	Output is correct
74	Correct	7 ms	2396 KB	Output is correct
75	Correct	8 ms	2576 KB	Output is correct
76	Correct	8 ms	2392 KB	Output is correct
77	Correct	24 ms	2900 KB	Output is correct
78	Correct	20 ms	2652 KB	Output is correct
79	Correct	19 ms	2656 KB	Output is correct
80	Correct	17 ms	2652 KB	Output is correct
81	Correct	16 ms	2652 KB	Output is correct
82	Correct	15 ms	2652 KB	Output is correct
83	Correct	16 ms	2652 KB	Output is correct
84	Correct	14 ms	2656 KB	Output is correct
85	Correct	39 ms	2396 KB	Output is correct
86	Correct	25 ms	2648 KB	Output is correct
87	Correct	27 ms	2652 KB	Output is correct
88	Correct	28 ms	2656 KB	Output is correct
89	Correct	22 ms	2652 KB	Output is correct
90	Correct	20 ms	2652 KB	Output is correct
91	Correct	21 ms	2652 KB	Output is correct
92	Correct	23 ms	2656 KB	Output is correct
93	Correct	798 ms	3672 KB	Output is correct
94	Correct	905 ms	3676 KB	Output is correct
95	Correct	876 ms	3672 KB	Output is correct
96	Correct	668 ms	3676 KB	Output is correct
97	Correct	578 ms	3920 KB	Output is correct
98	Correct	621 ms	3676 KB	Output is correct
99	Correct	70 ms	2652 KB	Output is correct
100	Correct	58 ms	2652 KB	Output is correct
101	Correct	54 ms	2652 KB	Output is correct
102	Correct	49 ms	2652 KB	Output is correct
103	Correct	540 ms	3108 KB	Output is correct
104	Correct	280 ms	2904 KB	Output is correct
105	Correct	199 ms	2904 KB	Output is correct
106	Correct	168 ms	3116 KB	Output is correct
107	Correct	1727 ms	3676 KB	Output is correct
108	Correct	679 ms	3672 KB	Output is correct
109	Correct	487 ms	3676 KB	Output is correct
110	Correct	404 ms	3676 KB	Output is correct
111	Correct	45 ms	2652 KB	Output is correct
112	Correct	41 ms	2648 KB	Output is correct
113	Correct	40 ms	2648 KB	Output is correct
114	Correct	102 ms	2796 KB	Output is correct
115	Correct	99 ms	2792 KB	Output is correct
116	Correct	79 ms	2788 KB	Output is correct
117	Correct	83 ms	2796 KB	Output is correct
118	Correct	72 ms	2792 KB	Output is correct
119	Correct	73 ms	2648 KB	Output is correct
120	Correct	65 ms	2904 KB	Output is correct
121	Correct	65 ms	2792 KB	Output is correct
122	Correct	151 ms	3108 KB	Output is correct
123	Correct	128 ms	3108 KB	Output is correct
124	Correct	118 ms	3116 KB	Output is correct
125	Correct	116 ms	2904 KB	Output is correct
126	Correct	111 ms	3112 KB	Output is correct
127	Correct	103 ms	3108 KB	Output is correct
128	Correct	100 ms	3116 KB	Output is correct
129	Correct	94 ms	3160 KB	Output is correct
130	Correct	90 ms	2904 KB	Output is correct
131	Correct	394 ms	3108 KB	Output is correct
132	Correct	310 ms	2908 KB	Output is correct
133	Correct	316 ms	2908 KB	Output is correct
134	Correct	311 ms	3156 KB	Output is correct
135	Correct	182 ms	2904 KB	Output is correct
136	Correct	204 ms	2908 KB	Output is correct
137	Correct	249 ms	2908 KB	Output is correct
138	Correct	240 ms	2904 KB	Output is correct
139	Correct	171 ms	2904 KB	Output is correct
140	Correct	178 ms	2904 KB	Output is correct
141	Correct	157 ms	2908 KB	Output is correct
142	Correct	353 ms	3676 KB	Output is correct
143	Correct	326 ms	3680 KB	Output is correct
144	Correct	312 ms	3692 KB	Output is correct
145	Correct	295 ms	3692 KB	Output is correct
146	Correct	282 ms	3676 KB	Output is correct
147	Correct	268 ms	3928 KB	Output is correct
148	Correct	366 ms	3672 KB	Output is correct
149	Correct	347 ms	3680 KB	Output is correct
150	Correct	356 ms	3672 KB	Output is correct
151	Correct	466 ms	3928 KB	Output is correct
152	Correct	405 ms	3684 KB	Output is correct
153	Correct	624 ms	3696 KB	Output is correct
154	Correct	661 ms	3928 KB	Output is correct
155	Correct	746 ms	3672 KB	Output is correct
156	Correct	719 ms	3680 KB	Output is correct
157	Correct	709 ms	3932 KB	Output is correct
158	Correct	734 ms	3748 KB	Output is correct
159	Correct	537 ms	3688 KB	Output is correct
160	Correct	467 ms	3924 KB	Output is correct
161	Correct	557 ms	3676 KB	Output is correct
162	Correct	453 ms	3680 KB	Output is correct
163	Correct	444 ms	4180 KB	Output is correct
164	Correct	432 ms	3676 KB	Output is correct
165	Correct	428 ms	3924 KB	Output is correct
166	Correct	397 ms	3676 KB	Output is correct
167	Correct	401 ms	3920 KB	Output is correct

Submission #868308

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