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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#88764 | #5827. 异或图 | wzh2021 | 20 | 1599ms | 4984kb | C++14 | 3.4kb | 2023-03-17 07:22:47 | 2023-03-17 07:22:50 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 20, S = 1 << 15, L = 61, P = 998244353;
ll c;
ll a[N];
int n, m, ans;
bool ed[N][N];
int f[S], g[S], h0[S];
int dp[L][S], h[N][S];
int p[N], q[N], pw2[N];
#define popc __builtin_popcount
int pls(int x, int y) {
return x + y < P ? x + y : x + y - P;
}
int sub(int x, int y) {
return x < y ? x + P - y : x - y;
}
void dfs(int d, int s, int t, int x, int y, int z) {
if (x > m) {
if (y && !z)
return;
if (!z)
dp[d - 1][t] = pls(dp[d - 1][t], dp[d][s]);
else
dp[d - 1][t] = (dp[d - 1][t] + (ll) dp[d][s] * (1 << (z - 1))) % P;
return;
}
if (!(s & pw2[x - 1]))
return dfs(d, s, t, x + 1, y, z + 1);
if ((a[p[x]] >> (d - 1)) & 1) {
dfs(d, s, t | pw2[x - 1], x + 1, !y, z);
dfs(d, s, t, x + 1, y, z);
return;
}
dfs(d, s, t | pw2[x - 1], x + 1, y, z);
}
int main() {
scanf("%d%d%lld", &n, &m, &c);
for (int i = 1; i <= n; ++i) {
scanf("%lld", &a[i]);
p[i] = i;
}
sort(p + 1, p + n + 1, [] (int i, int j) {
return a[i] < a[j];
});
sort(a + 1, a + n + 1);
for (int i = 1; i <= n; ++i)
q[p[i]] = i;
pw2[0] = 1;
for (int i = 1; i <= n; ++i)
pw2[i] = pw2[i - 1] << 1;
for (int i = 1; i <= m; ++i) {
int u, v;
scanf("%d%d", &u, &v);
if (u == v)
continue;
u = q[u];
v = q[v];
ed[u][v] = ed[v][u] = 1;
}
for (int i = 0; i < pw2[n]; ++i)
for (int j = 1; j <= n; ++j)
if (i & pw2[j - 1])
for (int k = j + 1; k <= n; ++k)
if (ed[j][k] && i & pw2[k - 1])
++f[i];
for (int i = 0; i < 1 << n; ++i) {
g[i] = !f[i];
int t = i & (-i);
for (int j = i; j; j = (j - 1) & i)
if (!f[j] && !(j & t))
g[i] = sub(g[i], g[i ^ j]);
}
h0[0] = 1;
for (int i = 1; i < 1 << n; ++i) {
int t = i & (-i);
for (int j = i; j; j = (j - 1) & i)
if (!(popc(j) & 1) && j & t)
h0[i] = (h0[i] + (a[(int) log2(j & (-j)) + 1] + 1) % P * h0[i ^ j] % P * g[j]) % P;
}
for (int s = 0; s < 1 << n; ++s) {
if ((n - popc(s)) & 1)
continue;
m = 0;
for (int i = 1; i <= n; ++i)
if (s & pw2[i - 1])
p[++m] = i;
for (int i = 0; i < L; ++i)
for (int j = 0; j < pw2[m]; ++j)
dp[i][j] = 0;
dp[L - 1][pw2[m] - 1] = 1;
for (int i = L - 1; i; --i) {
int opt = (c >> (i - 1)) & 1;
for (int j = 0; j < pw2[m]; ++j)
if (dp[i][j])
dfs(i, j, 0, 1, opt, 0);
}
h[0][0] = 1;
for (int i = 1; i <= m; ++i)
for (int j = 0; j < pw2[n - m]; ++j) {
h[i][j] = (ll) h[i - 1][j] * g[pw2[p[i] - 1]] % P;
for (int k = j; k; k = (k - 1) & j) {
if (popc(k) & 1)
continue;
int sta = pw2[p[i] - 1];
for (int l = 1, t = 1; l <= n; ++l)
if (!(s & pw2[l - 1])) {
if (k & pw2[t - 1]) {
if (l < p[i]) {
sta = -1;
break;
}
sta |= pw2[l - 1];
}
++t;
}
if (!~sta)
continue;
h[i][j] = (h[i][j] + (ll) h[i - 1][j ^ k] * g[sta]) % P;
}
}
int t1 = 0;
for (int i = 0; i < 1 << m; ++i)
t1 = pls(t1, dp[0][i]);
int t2 = 0;
for (int i = 0; i < pw2[n - m]; ++i) {
int sta = s;
for (int j = 1, k = 1; j <= n; ++j)
if (!(s & pw2[j - 1])) {
if (i & pw2[k - 1])
sta |= pw2[j - 1];
++k;
}
t2 = (t2 + (ll) h[m][i] * h0[(pw2[n] - 1) ^ sta]) % P;
}
ans = (ans + (ll) t1 * t2) % P;
}
printf("%d", ans);
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Subtask #1:
score: 20
Accepted
Test #1:
score: 20
Accepted
time: 2ms
memory: 4040kb
input:
4 6 2 7 11 14 0 1 2 1 3 2 3 2 4 4 1 4 3
output:
44
result:
ok 1 number(s): "44"
Test #2:
score: 0
Accepted
time: 2ms
memory: 3904kb
input:
4 4 6 12 14 14 5 4 2 1 4 3 2 1 2
output:
798
result:
ok 1 number(s): "798"
Test #3:
score: 0
Accepted
time: 2ms
memory: 3916kb
input:
3 3 2 10 4 11 2 1 3 2 1 3
output:
33
result:
ok 1 number(s): "33"
Test #4:
score: 0
Accepted
time: 2ms
memory: 4028kb
input:
4 0 4 9 8 5 2
output:
148
result:
ok 1 number(s): "148"
Test #5:
score: 0
Accepted
time: 0ms
memory: 4032kb
input:
5 6 14 12 15 13 13 12 3 1 2 4 2 5 2 1 5 3 4 5
output:
21337
result:
ok 1 number(s): "21337"
Test #6:
score: 0
Accepted
time: 2ms
memory: 4048kb
input:
4 5 5 5 2 4 13 2 1 3 4 1 4 4 2 3 2
output:
42
result:
ok 1 number(s): "42"
Test #7:
score: 0
Accepted
time: 2ms
memory: 3916kb
input:
4 4 3 13 7 8 12 4 1 3 1 2 4 4 3
output:
552
result:
ok 1 number(s): "552"
Test #8:
score: 0
Accepted
time: 0ms
memory: 4024kb
input:
4 2 12 1 12 4 11 2 1 3 1
output:
70
result:
ok 1 number(s): "70"
Test #9:
score: 0
Accepted
time: 2ms
memory: 3912kb
input:
5 5 6 10 7 8 2 13 1 5 1 3 2 1 4 3 5 3
output:
1231
result:
ok 1 number(s): "1231"
Test #10:
score: 0
Accepted
time: 2ms
memory: 4048kb
input:
5 7 9 6 7 13 15 12 1 3 5 3 5 2 4 5 4 3 4 1 3 2
output:
6223
result:
ok 1 number(s): "6223"
Test #11:
score: 0
Accepted
time: 0ms
memory: 3920kb
input:
3 0 3 15 7 12
output:
104
result:
ok 1 number(s): "104"
Test #12:
score: 0
Accepted
time: 0ms
memory: 3920kb
input:
3 2 9 10 6 5 1 2 1 3
output:
17
result:
ok 1 number(s): "17"
Test #13:
score: 0
Accepted
time: 2ms
memory: 4052kb
input:
5 5 11 7 9 15 9 9 5 4 5 1 5 2 1 3 3 4
output:
5224
result:
ok 1 number(s): "5224"
Test #14:
score: 0
Accepted
time: 2ms
memory: 4052kb
input:
5 0 12 9 8 14 11 2
output:
3006
result:
ok 1 number(s): "3006"
Test #15:
score: 0
Accepted
time: 0ms
memory: 3872kb
input:
3 1 1 6 10 4 3 1
output:
30
result:
ok 1 number(s): "30"
Subtask #2:
score: 0
Time Limit Exceeded
Dependency #1:
100%
Accepted
Test #16:
score: 50
Accepted
time: 41ms
memory: 3900kb
input:
9 27 705410105529944560 929827299070190972 733413770730537329 473007347105710981 190062421504120247 918561152768663129 196040702922254016 981530663192980241 203295856357272834 337150461958783092 2 8 7 9 8 9 2 3 9 2 2 7 9 5 9 4 4 8 1 7 6 3 6 1 4 1 6 5 2 4 2 1 9 3 9 6 7 3 7 5 5 2 4 5 2 6 3 1 3 8 4 3 8 6
output:
5392583
result:
ok 1 number(s): "5392583"
Test #17:
score: 0
Accepted
time: 41ms
memory: 4060kb
input:
9 7 788762650337246371 605340092851479114 625896945107761227 361131331380167081 572133549445050458 929899192003968010 340514051531987427 690728985364969400 268762741220048006 818120252827139346 5 8 9 6 6 1 1 9 9 8 5 1 4 5
output:
35237078
result:
ok 1 number(s): "35237078"
Test #18:
score: 0
Accepted
time: 4ms
memory: 3888kb
input:
7 8 968166787047166534 945734997493219809 465616677643913237 530128109571749460 717120283671096308 118646732725835921 510958884109370001 797022604947155276 5 2 4 7 1 2 6 5 4 2 4 6 1 6 6 3
output:
133871438
result:
ok 1 number(s): "133871438"
Test #19:
score: 0
Accepted
time: 1599ms
memory: 4984kb
input:
12 21 341964498832651322 422448536649714733 488538974423366199 893293448611252565 879334133559023407 13516625885288091 43377983230712374 263189254162337644 474056776923289355 540904774976211471 103364876621830299 515157013276720499 213857038587555252 12 9 8 3 1 9 1 7 3 1 8 11 11 10 6 10 6 1 10 2 7 9...
output:
296076062
result:
ok 1 number(s): "296076062"
Test #20:
score: 0
Accepted
time: 605ms
memory: 4508kb
input:
11 42 215284372701527433 670445786006000260 969876209382224733 248721347029697734 375741447316879814 840434941395805804 187091598433077755 126574401069916039 764298539206353847 750906714570719526 387387869969339518 713140316419888823 1 10 2 5 1 7 4 11 3 11 2 7 4 5 9 5 1 6 3 4 10 9 11 9 3 7 2 1 8 11 ...
output:
861118590
result:
ok 1 number(s): "861118590"
Test #21:
score: 0
Accepted
time: 0ms
memory: 3928kb
input:
7 20 619868500075052677 653541655679358091 619279335581334164 74945438024390700 772996180610853550 636253173293891586 125935970032544337 454311587629767538 7 3 4 5 6 7 2 7 4 2 5 3 4 6 2 6 7 4 5 7 2 5 6 3 5 1 2 3 3 4 1 7 2 1 1 3 5 6 4 1
output:
396474896
result:
ok 1 number(s): "396474896"
Test #22:
score: -50
Time Limit Exceeded
input:
13 1 655058659126783551 220930961455414900 363602338013759573 443737606888655227 137555247528320912 492558319379424931 930253239754276705 727679308735300884 787033056632957722 29595553176095069 586820353385061840 342786039873677428 141912073483259823 800159879032310691 4 9
output:
result:
Subtask #3:
score: 0
Time Limit Exceeded
Test #47:
score: 0
Time Limit Exceeded
input:
14 0 731833687287532167 157552918690640051 900457311668526045 111217720157614956 84140984111060473 814012186135880499 784848789620248379 958953377683017264 105083874298571687 104921429970878846 44983041675142735 871013110538758030 686733907990421995 98063590462078176 495161493555059993
output:
result:
Subtask #4:
score: 0
Skipped
Dependency #1:
100%
Accepted
Dependency #2:
0%