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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#547740 | #8211. Enumerating Substrings | HuTao | AC ✓ | 29ms | 48760kb | C++14 | 2.9kb | 2024-09-05 09:00:00 | 2024-09-05 09:00:00 |
Judging History
answer
/*
1. min{F(i, j), F(j, k)} <= F(i, k):考虑对于任意一组大小小于 min{F(i, j), F(j, k)} 的割,都会保留一条 i -> j,j -> k 的通路。
2. 将所有流至少为 1 的边,分别讨论连通块;将所有流至少为 2 的边,分别讨论连通块,这些连通块外部连边构成连。
3. 对所有流至少为 3 的边,构成团,若团大小:
- 至少为 4 的偶数:连成环之后,相对的两个点连边。
- 至少为 4 的奇数:除去最后一个点之外连成环之后,与最后一个点连边。
- 上面两种其中一个点作为代表连到环内。
- 2:
* 只有一个这样的团,这两个点不能相邻,之间额外连边。
* 若连通块内点数不超过 3,无解。
* 存在更多这样的团无解。
- 3:
* 只有一个这样的团,这三个点之间额外连任意两条边,相连边的两个点不能相邻。
* 连通块的点个数不超过 4,无解。
4. 按团的数量连外部边:
- 1:不用管。
- 2:若大小都为 1,无解;否则将其中一个不为 1 的团中任意两个点向另一个团的点连边。
- 3:否则可以连成环。
5. 听说上面这样搞出来有反例的,但是不知道是什么。
*/
#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int N = 1e6 + 5, P = 1e9 + 7;
int n, m, k;
LL fact[N], invf[N], ck[N], s2[N], pk[N];
LL f[N];
inline LL ksm(LL a, LL n)
{
LL res = 1;
while(n)
{
if(n & 1) res = res * a % P;
a = a * a % P;
n >>= 1;
}
return res;
}
inline void Init(int n)
{
fact[0] = 1;
for(int i = 1; i <= n; i ++ ) fact[i] = fact[i - 1] * i % P;
invf[n] = ksm(fact[n], P - 2);
for(int i = n; i >= 1; i -- ) invf[i - 1] = invf[i] * i % P;
ck[0] = 1;
for(int i = 1; i <= n; i ++ ) ck[i] = ck[i - 1] * (k - i + 1) % P;
s2[0] = 1;
for(int i = 1; i <= n / 2; i ++ ) s2[i] = s2[i - 1] * (i * 2 - 1) % P;
for(int i = 1; i <= n / 2; i ++ ) s2[i] = s2[i] * invf[i * 2] % P;
pk[0] = 1;
for(int i = 1; i <= n; i ++ ) pk[i] = pk[i - 1] * k % P;
}
int main()
{
scanf("%d%d%d", &n, &m, &k);
Init(n);
LL s0 = 0;
for(int i = m / 2; i >= 0; i -- )
{
LL s = 0;
for(int j = 0; j <= m / 2 - i; j ++ )
s = (s + ck[m - i - j] * invf[m - i * 2 - j * 2] % P * s2[j]) % P;
s = s * fact[m - i * 2] % P;
if(i == 0)
{
s -= s0;
f[m] += s;
}
else
{
(s0 += s) >= P && (s0 -= P);
for(int j = m, k = 1; j <= n; j += m - i, k = -k) f[j] += s * k;
}
}
LL ans = 0;
for(int i = m; i <= n; i ++ ) ans = (ans + (f[i] % P + P) * (n - i + 1) % P * pk[n - i]) % P;
printf("%lld\n", ans);
return 0;
}
这程序好像有点Bug,我给组数据试试?
Details
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Test #1:
score: 100
Accepted
time: 0ms
memory: 14152kb
input:
4 2 3
output:
228
result:
ok 1 number(s): "228"
Test #2:
score: 0
Accepted
time: 23ms
memory: 48760kb
input:
999999 1999 12345678
output:
52352722
result:
ok 1 number(s): "52352722"
Test #3:
score: 0
Accepted
time: 2ms
memory: 14020kb
input:
7 4 2
output:
182
result:
ok 1 number(s): "182"
Test #4:
score: 0
Accepted
time: 2ms
memory: 14020kb
input:
4 3 4
output:
480
result:
ok 1 number(s): "480"
Test #5:
score: 0
Accepted
time: 0ms
memory: 14148kb
input:
3 1 1
output:
3
result:
ok 1 number(s): "3"
Test #6:
score: 0
Accepted
time: 1ms
memory: 14096kb
input:
5 5 1
output:
0
result:
ok 1 number(s): "0"
Test #7:
score: 0
Accepted
time: 1ms
memory: 14060kb
input:
7 4 3
output:
5784
result:
ok 1 number(s): "5784"
Test #8:
score: 0
Accepted
time: 1ms
memory: 14024kb
input:
5 2 4
output:
3932
result:
ok 1 number(s): "3932"
Test #9:
score: 0
Accepted
time: 2ms
memory: 14160kb
input:
8 2 2
output:
1522
result:
ok 1 number(s): "1522"
Test #10:
score: 0
Accepted
time: 0ms
memory: 14148kb
input:
8 1 2
output:
2048
result:
ok 1 number(s): "2048"
Test #11:
score: 0
Accepted
time: 1ms
memory: 14144kb
input:
7 5 3
output:
2430
result:
ok 1 number(s): "2430"
Test #12:
score: 0
Accepted
time: 2ms
memory: 14164kb
input:
10 4 3
output:
272004
result:
ok 1 number(s): "272004"
Test #13:
score: 0
Accepted
time: 11ms
memory: 45936kb
input:
675978 614 2
output:
0
result:
ok 1 number(s): "0"
Test #14:
score: 0
Accepted
time: 4ms
memory: 25640kb
input:
244613 38 1
output:
0
result:
ok 1 number(s): "0"
Test #15:
score: 0
Accepted
time: 4ms
memory: 23472kb
input:
186293 1462 1
output:
0
result:
ok 1 number(s): "0"
Test #16:
score: 0
Accepted
time: 3ms
memory: 16400kb
input:
24867 886 1
output:
0
result:
ok 1 number(s): "0"
Test #17:
score: 0
Accepted
time: 26ms
memory: 48568kb
input:
976164 1014 2
output:
0
result:
ok 1 number(s): "0"
Test #18:
score: 0
Accepted
time: 8ms
memory: 23728kb
input:
179356 2 716844809
output:
577866092
result:
ok 1 number(s): "577866092"
Test #19:
score: 0
Accepted
time: 18ms
memory: 40640kb
input:
621001 130 310625363
output:
892869197
result:
ok 1 number(s): "892869197"
Test #20:
score: 0
Accepted
time: 16ms
memory: 43044kb
input:
678862 850 754662812
output:
582264789
result:
ok 1 number(s): "582264789"
Test #21:
score: 0
Accepted
time: 11ms
memory: 42968kb
input:
650845 978 348443366
output:
825425732
result:
ok 1 number(s): "825425732"
Test #22:
score: 0
Accepted
time: 11ms
memory: 42680kb
input:
669914 402 87448112
output:
318098088
result:
ok 1 number(s): "318098088"
Test #23:
score: 0
Accepted
time: 18ms
memory: 48732kb
input:
998593 530 681228665
output:
408255654
result:
ok 1 number(s): "408255654"
Test #24:
score: 0
Accepted
time: 16ms
memory: 29700kb
input:
369361 1954 125266115
output:
509912384
result:
ok 1 number(s): "509912384"
Test #25:
score: 0
Accepted
time: 27ms
memory: 48244kb
input:
900226 1378 424079373
output:
406320917
result:
ok 1 number(s): "406320917"
Test #26:
score: 0
Accepted
time: 4ms
memory: 29808kb
input:
334887 1506 17859926
output:
503264679
result:
ok 1 number(s): "503264679"
Test #27:
score: 0
Accepted
time: 23ms
memory: 48240kb
input:
936048 544 53978328
output:
548647866
result:
ok 1 number(s): "548647866"
Test #28:
score: 0
Accepted
time: 7ms
memory: 20576kb
input:
152789 1264 792983073
output:
839541707
result:
ok 1 number(s): "839541707"
Test #29:
score: 0
Accepted
time: 18ms
memory: 46672kb
input:
714493 1392 91796331
output:
721071046
result:
ok 1 number(s): "721071046"
Test #30:
score: 0
Accepted
time: 11ms
memory: 25360kb
input:
269571 816 830801077
output:
330064211
result:
ok 1 number(s): "330064211"
Test #31:
score: 0
Accepted
time: 20ms
memory: 45700kb
input:
845120 944 424581630
output:
348960190
result:
ok 1 number(s): "348960190"
Test #32:
score: 0
Accepted
time: 7ms
memory: 38076kb
input:
533990 368 163586376
output:
522092095
result:
ok 1 number(s): "522092095"
Test #33:
score: 0
Accepted
time: 8ms
memory: 22924kb
input:
181707 1792 462399634
output:
373795106
result:
ok 1 number(s): "373795106"
Test #34:
score: 0
Accepted
time: 13ms
memory: 32876kb
input:
417349 1920 761212891
output:
587051329
result:
ok 1 number(s): "587051329"
Test #35:
score: 0
Accepted
time: 15ms
memory: 37760kb
input:
526583 1344 500217637
output:
108767800
result:
ok 1 number(s): "108767800"
Test #36:
score: 0
Accepted
time: 29ms
memory: 48084kb
input:
867054 769 93998191
output:
239123369
result:
ok 1 number(s): "239123369"
Extra Test:
score: 0
Extra Test Passed