QOJ.ac
QOJ
| ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
|---|---|---|---|---|---|---|---|---|---|
| #369087 | #1839. Joke | crsfaa | AC ✓ | 1ms | 3732kb | C++14 | 2.4kb | 2024-03-27 20:24:36 | 2024-03-27 20:24:38 |
Judging History
answer
#include<bits/stdc++.h>
#define Yukinoshita namespace
#define Yukino std
using Yukinoshita Yukino;
int read()
{
int s=0,w=1;
char ch=getchar();
while(ch<'0'||ch>'9') w=ch=='-'?-1:1,ch=getchar();
while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
return s*w;
}
/*
草了我看错题了。。。所以我赛时其实在想什么问题？我也记不起来了。
问题是计数可以被生成的 s 数量
先把 p 扔了，就是把 q 归位。
然后考虑检验一个 s 是否合法！
先不考虑 q 的问号，考虑一个 q？
考虑一个有趣的从小到大填数的过程
如是 q 必须按某个顺序填，p 只能从前往后填
设先填 q 的位置是 1，先填 p 的位置是 0
可以发现一个性质：填 q 的地方是递增的！
就是说 s 的个数就是 q 的上升子序列数量！！！
开始传统 dp。
发现。这个。不是。很好做。不是。很好做。
因为上升-子序列是对偶的。所以是按数值还是序列 dp 无所谓，
然而可以发现一些显然的转移。
明确一下，我们现在是要计数所有子序列的贡献。
dp i j 表示，以第 i 个数为结尾，有 j 个数不在上升子序列的方案数
*/
const int mod=998244353;
int qpow(int a,int p)
{
int mul=1;
for(;p;p>>=1)
{
if(p&1) mul=1ll*mul*a%mod;
a=1ll*a*a%mod;
}
return mul;
}
int p[105],q[105];
int dp[105][105];
int pre[105];
int fac[105],inv[105];
int pres[105];
void init(int n)
{
fac[0]=1;
int i;
for(i=1;i<=n;i++)
fac[i]=1ll*fac[i-1]*i%mod;
inv[n]=qpow(fac[n],mod-2);
for(i=n;i;i--)
inv[i-1]=1ll*inv[i]*i%mod;
}
int C(int n,int m)
{
return 1ll*fac[n]*inv[m]%mod*inv[n-m]%mod;
}
int main()
{
int n=read(),i,j,k,l;
for(i=1;i<=n;i++)
p[i]=read();
for(i=1;i<=n;i++)
q[p[i]]=read();
for(i=1;i<=n;i++)
pre[q[i]]=1;
for(i=1;i<=n;i++)
pre[i]=pre[i-1]+!pre[i];
for(i=1;i<=n;i++)
pres[i]=pres[i-1]+!q[i];
init(n);
dp[0][0]=1;
q[n+1]=n+1;
for(i=1;i<=n+1;i++)
if(q[i])
{
for(j=0;j<i;j++)
if(!j||q[j]&&q[j]<q[i])
{
int cnt1=pres[i-1]-pres[j],cnt2=pre[q[i]-1]-pre[q[j]];
for(k=0;k<=cnt1&&k<=cnt2;k++)
for(l=0;l<=j;l++)
dp[i][cnt1-k+l]=(dp[i][cnt1-k+l]+1ll*dp[j][l]*C(cnt2,k)%mod*C(cnt1,k))%mod;
}
}
int sum=0;
for(i=0;i<=n;i++)
sum=(sum+1ll*dp[n+1][i]*fac[i])%mod;
cout<<sum;
}
/*
6
1 6 2 5 3 4
0 1 0 2 0 3
*/
详细
Test #1:
score: 100
Accepted
time: 0ms
memory: 3624kb
input:
2 1 2 2 1
output:
3
result:
ok 1 number(s): "3"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3648kb
input:
4 4 3 2 1 4 3 2 1
output:
16
result:
ok 1 number(s): "16"
Test #3:
score: 0
Accepted
time: 0ms
memory: 3672kb
input:
5 1 2 3 4 5 0 0 0 0 0
output:
1546
result:
ok 1 number(s): "1546"
Test #4:
score: 0
Accepted
time: 0ms
memory: 3604kb
input:
6 1 6 2 5 3 4 0 1 0 2 0 3
output:
52
result:
ok 1 number(s): "52"
Test #5:
score: 0
Accepted
time: 0ms
memory: 3644kb
input:
10 8 2 10 3 4 6 1 7 9 5 0 0 0 0 0 0 0 0 0 0
output:
234662231
result:
ok 1 number(s): "234662231"
Test #6:
score: 0
Accepted
time: 0ms
memory: 3596kb
input:
10 5 8 4 9 6 1 2 7 3 10 8 3 0 5 0 9 0 0 6 0
output:
5294
result:
ok 1 number(s): "5294"
Test #7:
score: 0
Accepted
time: 1ms
memory: 3540kb
input:
10 4 2 6 9 5 3 8 1 10 7 0 9 8 0 7 3 4 2 1 10
output:
166
result:
ok 1 number(s): "166"
Test #8:
score: 0
Accepted
time: 1ms
memory: 3604kb
input:
10 8 2 7 1 5 9 3 4 10 6 7 0 2 9 5 1 8 4 3 6
output:
26
result:
ok 1 number(s): "26"
Test #9:
score: 0
Accepted
time: 0ms
memory: 3544kb
input:
10 10 1 6 7 9 8 4 3 5 2 2 5 1 3 9 10 4 8 6 7
output:
47
result:
ok 1 number(s): "47"
Test #10:
score: 0
Accepted
time: 1ms
memory: 3572kb
input:
50 41 15 17 1 5 31 7 38 30 39 43 35 2 26 20 42 48 25 19 32 50 4 8 10 44 12 9 18 13 36 28 6 27 23 40 24 3 14 29 11 49 47 45 46 34 21 37 16 22 33 0 0 0 0 0 0 0 0 0 33 34 0 0 0 0 0 0 0 0 0 0 2 0 0 0 20 0 0 28 0 0 0 9 0 0 0 48 0 0 0 50 0 0 0 0 5 0 0 32 0
output:
976189245
result:
ok 1 number(s): "976189245"
Test #11:
score: 0
Accepted
time: 0ms
memory: 3572kb
input:
50 36 35 13 14 45 44 22 10 30 23 15 17 6 42 8 49 21 46 5 32 25 34 38 4 48 50 28 3 9 24 43 47 20 2 40 37 29 41 26 7 39 33 31 19 27 16 11 12 1 18 0 0 0 19 20 42 0 18 9 0 27 0 38 0 0 45 0 33 0 0 0 0 0 7 0 0 37 41 0 2 0 1 0 0 5 13 8 0 0 0 0 0 0 15 17 0 12 0 0 0
output:
861991745
result:
ok 1 number(s): "861991745"
Test #12:
score: 0
Accepted
time: 1ms
memory: 3552kb
input:
50 24 4 17 27 45 5 8 33 7 23 19 42 11 2 39 38 48 37 32 29 18 47 6 36 25 15 31 50 12 3 44 28 30 41 40 16 14 21 46 22 34 9 43 26 49 35 10 1 20 13 15 0 0 19 0 0 0 0 0 5 3 0 31 0 25 26 41 7 9 0 22 0 11 49 24 0 43 13 14 35 16 0 27 0 0 0 47 0 0 18 20 23 33 42 36 8 0 30 44 0
output:
231982952
result:
ok 1 number(s): "231982952"
Test #13:
score: 0
Accepted
time: 1ms
memory: 3712kb
input:
50 37 9 29 2 13 35 7 16 12 42 34 47 14 46 27 6 21 32 15 49 20 10 31 48 18 4 23 40 25 30 50 41 24 26 11 5 33 36 8 22 39 3 17 43 44 1 45 28 19 38 50 33 0 0 14 10 13 15 16 0 35 12 5 9 34 6 0 38 21 22 45 0 0 28 31 36 0 43 29 37 7 1 20 44 11 4 40 2 0 17 27 39 0 3 30 0 24 26 25 18
output:
31263262
result:
ok 1 number(s): "31263262"
Test #14:
score: 0
Accepted
time: 0ms
memory: 3572kb
input:
50 24 47 6 19 1 25 42 38 18 2 7 3 13 27 23 48 28 36 45 39 37 29 16 12 15 10 8 46 33 34 43 14 50 9 31 32 44 20 26 4 40 22 17 49 35 41 11 21 5 30 7 47 5 19 31 9 48 14 32 11 12 13 33 36 42 29 26 24 39 46 28 15 50 8 30 22 35 3 4 43 10 38 41 6 21 20 2 27 16 37 23 17 45 34 49 40 25 18 44 1
output:
78388
result:
ok 1 number(s): "78388"
Test #15:
score: 0
Accepted
time: 0ms
memory: 3604kb
input:
100 11 9 35 34 51 74 16 67 26 21 14 80 84 79 7 61 28 3 53 43 42 5 56 36 69 30 22 88 1 27 65 91 46 31 59 50 17 96 25 18 64 55 78 2 63 24 95 48 93 13 38 76 89 94 15 90 45 81 52 87 83 73 44 49 23 82 85 75 86 33 47 19 58 97 37 20 40 10 92 4 6 68 77 54 71 12 62 60 100 39 41 99 72 29 57 8 70 32 66 98 0 0 ...
output:
452312947
result:
ok 1 number(s): "452312947"
Test #16:
score: 0
Accepted
time: 0ms
memory: 3544kb
input:
100 78 52 95 76 96 49 53 59 77 100 64 11 9 48 15 17 44 46 21 54 39 68 43 4 32 28 73 6 16 62 72 84 65 86 98 75 33 45 25 3 91 82 2 92 63 88 7 50 97 93 14 22 20 42 60 55 80 85 29 34 56 71 83 38 26 47 90 70 51 41 40 31 37 12 35 99 67 94 1 87 57 8 61 19 23 79 36 18 66 74 5 27 81 69 24 58 13 10 89 30 0 0 ...
output:
366370216
result:
ok 1 number(s): "366370216"
Test #17:
score: 0
Accepted
time: 0ms
memory: 3476kb
input:
100 62 70 29 14 12 87 94 78 39 92 84 91 61 49 60 33 69 37 19 82 42 8 45 97 81 43 54 67 1 22 77 58 65 17 18 28 25 57 16 90 40 13 4 21 68 35 15 76 73 93 56 95 79 47 74 75 30 71 66 99 41 24 88 83 5 6 31 96 38 80 27 46 51 53 2 86 32 9 20 100 26 36 63 7 52 55 23 3 50 59 48 89 85 44 34 64 10 72 11 98 0 0 ...
output:
351981437
result:
ok 1 number(s): "351981437"
Test #18:
score: 0
Accepted
time: 0ms
memory: 3656kb
input:
100 100 6 41 33 5 32 39 58 95 48 27 17 90 73 10 81 56 87 79 91 43 42 47 75 57 98 22 49 67 28 94 86 89 60 65 96 11 46 13 23 85 61 9 99 63 52 15 66 40 31 12 72 93 20 77 44 88 55 16 54 38 7 26 19 97 36 14 92 3 4 1 24 2 8 50 76 82 34 51 53 64 45 70 37 18 62 25 21 69 35 74 30 71 84 59 80 83 29 78 68 0 0 ...
output:
195404592
result:
ok 1 number(s): "195404592"
Test #19:
score: 0
Accepted
time: 1ms
memory: 3688kb
input:
100 80 78 96 22 39 21 74 48 61 16 55 32 27 52 34 51 98 4 72 47 42 46 28 90 43 33 44 99 91 11 29 85 92 19 58 73 65 12 87 97 54 59 75 15 9 63 24 67 71 84 36 6 60 94 82 89 70 95 31 5 10 3 37 49 45 18 83 53 64 17 100 1 81 86 88 38 20 40 66 77 50 7 30 69 14 13 79 35 23 68 57 25 8 93 41 62 56 2 76 26 0 48...
output:
119407737
result:
ok 1 number(s): "119407737"
Test #20:
score: 0
Accepted
time: 1ms
memory: 3624kb
input:
100 73 72 15 88 11 48 18 17 52 10 75 99 71 80 97 57 47 32 31 12 64 45 85 26 41 14 21 66 27 84 82 6 29 38 37 62 91 65 92 3 40 1 4 13 42 63 44 68 67 46 87 5 9 50 93 36 7 51 79 58 98 70 56 81 83 96 35 54 74 20 55 2 49 43 59 53 30 94 16 89 19 39 61 22 77 23 90 28 34 8 78 100 76 24 33 69 95 25 60 86 0 0 ...
output:
916702910
result:
ok 1 number(s): "916702910"
Test #21:
score: 0
Accepted
time: 1ms
memory: 3616kb
input:
100 53 38 68 92 52 62 98 90 50 29 20 56 69 89 85 66 12 13 4 57 34 88 73 32 22 44 26 7 55 2 75 6 21 96 25 46 28 58 40 72 19 24 59 37 91 63 10 77 84 3 67 14 9 70 93 97 48 17 80 43 27 100 35 87 8 95 83 33 47 54 18 65 78 36 60 30 23 42 79 15 86 71 1 41 49 64 39 16 31 82 45 5 81 76 99 51 74 94 11 61 0 0 ...
output:
379434745
result:
ok 1 number(s): "379434745"
Test #22:
score: 0
Accepted
time: 1ms
memory: 3624kb
input:
100 96 67 6 71 66 85 72 38 11 47 13 59 17 40 58 39 7 48 28 95 53 42 49 19 33 64 68 5 84 51 97 12 18 43 76 44 89 27 62 88 4 65 74 79 32 70 25 3 20 23 60 98 50 91 26 93 54 21 31 45 73 92 10 29 14 82 37 83 16 77 90 80 56 75 24 61 63 55 99 57 78 9 100 87 41 36 69 30 86 15 22 2 35 81 34 52 94 1 8 46 0 0 ...
output:
831372413
result:
ok 1 number(s): "831372413"
Test #23:
score: 0
Accepted
time: 1ms
memory: 3560kb
input:
100 28 4 61 67 32 97 47 10 53 87 46 35 33 54 45 48 1 77 75 52 8 81 42 14 9 44 92 94 26 43 74 3 50 55 18 40 49 80 70 25 56 98 82 90 69 13 31 84 6 68 34 57 100 39 5 38 93 12 20 89 21 91 99 96 58 78 2 16 83 71 41 95 62 37 7 59 24 60 86 19 22 85 17 23 15 27 73 29 64 63 72 51 88 30 66 79 11 65 76 36 30 3...
output:
842694516
result:
ok 1 number(s): "842694516"
Test #24:
score: 0
Accepted
time: 1ms
memory: 3544kb
input:
100 9 33 80 5 79 68 56 12 17 3 58 39 1 48 76 52 23 74 38 15 82 87 51 78 34 95 26 72 60 64 96 61 43 7 36 44 25 18 75 77 62 22 70 86 50 20 99 73 45 55 66 94 49 90 57 37 53 93 16 24 13 46 6 41 63 71 84 67 54 91 83 8 85 100 88 29 32 81 31 47 42 69 35 89 92 65 98 21 10 2 27 19 40 4 14 30 11 28 97 59 0 0 ...
output:
982762140
result:
ok 1 number(s): "982762140"
Test #25:
score: 0
Accepted
time: 0ms
memory: 3636kb
input:
100 19 55 91 50 31 23 60 84 38 1 22 51 27 76 28 98 11 44 61 63 15 93 52 3 66 16 53 36 18 62 35 85 78 37 73 64 87 74 46 26 82 69 49 33 83 89 56 67 71 25 39 94 96 17 21 6 47 68 34 42 57 81 13 10 54 2 48 80 20 77 4 5 59 30 90 95 45 75 8 88 24 41 40 14 97 32 7 9 65 70 100 99 72 58 92 29 79 12 86 43 0 0 ...
output:
66690913
result:
ok 1 number(s): "66690913"
Test #26:
score: 0
Accepted
time: 1ms
memory: 3656kb
input:
100 38 39 59 95 16 6 33 55 11 10 100 43 77 52 34 1 90 5 37 24 28 22 35 63 71 49 97 79 19 54 21 85 56 13 40 17 57 76 91 99 53 88 20 29 65 81 94 96 89 47 30 80 84 58 9 31 51 61 42 60 73 23 4 74 3 78 8 67 86 14 87 66 2 45 26 70 48 46 72 44 82 69 27 12 92 36 50 62 41 64 75 7 98 15 25 68 18 32 83 93 0 0 ...
output:
899036040
result:
ok 1 number(s): "899036040"
Test #27:
score: 0
Accepted
time: 1ms
memory: 3576kb
input:
100 17 97 68 44 14 16 38 4 29 52 55 93 62 34 96 41 80 40 66 71 47 81 85 99 57 73 5 39 53 9 70 24 86 49 77 50 54 13 7 21 83 25 3 23 42 10 91 79 67 35 92 12 95 26 48 56 27 30 88 1 8 69 20 15 2 76 72 31 19 94 11 89 61 64 28 60 59 18 37 100 63 75 98 36 78 51 22 82 84 32 65 74 46 58 33 43 45 87 6 90 0 0 ...
output:
517437875
result:
ok 1 number(s): "517437875"
Test #28:
score: 0
Accepted
time: 1ms
memory: 3692kb
input:
100 90 100 46 75 59 41 89 99 95 35 5 11 93 85 24 92 87 47 26 4 64 63 70 37 25 39 68 57 52 98 31 45 40 82 30 28 36 19 83 12 21 29 97 54 14 96 43 73 72 49 10 17 33 2 44 91 7 77 78 3 23 80 56 34 22 13 79 27 48 32 15 65 50 60 86 53 88 9 20 42 38 18 74 66 55 6 76 58 84 67 61 71 81 94 69 62 16 51 8 1 0 83...
output:
958635644
result:
ok 1 number(s): "958635644"
Test #29:
score: 0
Accepted
time: 1ms
memory: 3708kb
input:
100 26 67 2 42 77 85 88 49 45 50 71 82 73 96 62 93 78 97 12 34 35 92 94 61 69 74 31 70 87 89 86 10 79 58 3 1 59 41 30 16 83 4 23 25 76 20 75 40 65 68 54 5 6 51 32 64 13 95 21 24 39 66 43 91 18 47 22 15 81 56 100 57 19 98 80 9 53 28 46 37 52 14 27 11 33 29 55 48 36 7 90 63 99 44 60 17 38 8 72 84 63 1...
output:
735454002
result:
ok 1 number(s): "735454002"
Test #30:
score: 0
Accepted
time: 1ms
memory: 3524kb
input:
100 30 14 58 67 48 84 15 16 26 35 47 19 74 9 95 93 60 34 1 98 52 50 63 88 8 64 28 77 25 40 6 55 4 24 73 27 90 31 45 2 80 87 23 10 3 53 94 51 62 56 7 78 89 36 12 13 42 57 5 46 81 29 22 18 49 61 75 59 37 82 39 91 76 86 32 20 99 65 66 92 43 85 21 68 72 44 83 38 79 97 54 69 100 71 11 41 33 70 96 17 45 2...
output:
477087154
result:
ok 1 number(s): "477087154"
Test #31:
score: 0
Accepted
time: 1ms
memory: 3524kb
input:
100 2 4 82 12 47 63 52 91 87 45 53 1 17 25 64 50 9 13 22 54 21 30 43 24 38 33 68 11 41 78 99 23 28 18 58 67 79 10 71 56 49 61 26 29 59 20 90 74 5 75 89 8 39 95 72 42 66 98 44 32 88 35 92 3 97 55 65 51 77 27 81 76 84 69 73 85 19 46 62 100 60 37 7 36 57 6 14 83 40 48 16 70 96 15 31 93 80 86 94 34 0 37...
output:
316550008
result:
ok 1 number(s): "316550008"
Test #32:
score: 0
Accepted
time: 1ms
memory: 3640kb
input:
100 45 56 48 36 81 10 94 70 86 92 90 1 82 2 5 31 17 98 57 53 100 14 16 55 11 59 61 39 77 44 26 65 79 46 66 21 40 23 64 72 76 38 58 30 71 74 52 20 47 78 18 49 68 8 91 60 12 15 87 4 89 19 13 80 42 96 32 63 67 37 84 7 6 24 34 85 54 83 93 50 3 97 51 43 35 29 27 25 99 75 28 95 9 41 33 69 22 88 73 62 71 8...
output:
104300725
result:
ok 1 number(s): "104300725"
Test #33:
score: 0
Accepted
time: 1ms
memory: 3704kb
input:
100 70 5 29 43 3 84 78 68 64 73 31 49 18 69 60 92 48 15 35 58 13 90 22 66 12 55 8 27 14 80 94 65 96 74 10 88 23 38 41 44 25 52 19 47 26 45 11 28 95 9 86 77 79 37 4 61 97 51 59 6 53 98 91 24 33 46 50 85 76 67 34 30 99 2 36 32 62 72 93 75 21 71 63 89 56 16 83 54 57 1 100 39 87 17 40 42 7 81 82 20 87 8...
output:
131305690
result:
ok 1 number(s): "131305690"
Test #34:
score: 0
Accepted
time: 1ms
memory: 3592kb
input:
100 97 23 19 13 87 95 35 46 98 6 1 100 66 39 48 86 51 89 67 49 76 22 21 62 61 84 29 9 41 69 16 68 30 65 7 36 4 52 25 24 47 55 80 64 5 58 28 82 53 20 57 26 88 94 43 44 99 45 85 42 2 72 70 15 60 50 27 59 56 32 17 91 92 33 18 77 74 54 14 93 63 73 78 40 90 3 71 81 8 10 79 75 83 11 38 96 12 31 34 37 83 1...
output:
121844310
result:
ok 1 number(s): "121844310"
Test #35:
score: 0
Accepted
time: 1ms
memory: 3640kb
input:
100 78 66 37 31 84 90 17 80 40 14 1 38 79 64 26 34 87 75 3 41 67 77 58 6 50 82 8 81 27 9 13 22 16 52 42 65 53 46 92 44 99 18 11 33 55 45 23 21 76 85 48 56 98 61 95 70 62 86 39 43 57 15 47 96 32 60 10 24 5 73 88 30 97 4 35 12 29 94 83 91 93 100 51 2 54 19 20 71 28 69 74 7 72 59 68 25 49 63 89 36 22 3...
output:
18919311
result:
ok 1 number(s): "18919311"
Test #36:
score: 0
Accepted
time: 1ms
memory: 3708kb
input:
100 88 31 100 15 92 44 94 22 24 51 95 41 30 86 34 37 38 12 4 81 60 69 45 40 99 62 6 46 35 27 96 36 59 47 73 78 65 87 3 9 85 57 2 77 26 20 55 97 64 58 63 21 80 19 42 54 49 79 66 70 75 17 16 13 89 28 72 48 90 74 61 71 1 23 5 76 43 32 29 83 18 93 8 7 14 10 39 91 50 67 82 53 52 11 68 33 98 25 84 56 18 8...
output:
8454871
result:
ok 1 number(s): "8454871"
Test #37:
score: 0
Accepted
time: 1ms
memory: 3732kb
input:
100 70 54 10 72 81 84 56 15 27 19 43 100 49 44 52 33 63 40 95 17 58 2 51 39 22 18 82 1 16 99 32 29 24 94 9 98 5 37 47 14 42 73 41 31 79 64 12 6 53 26 68 67 89 13 90 4 21 93 46 74 75 88 66 57 23 7 25 48 92 62 30 8 50 61 38 87 71 34 97 28 80 11 60 91 3 35 86 96 36 20 59 65 83 45 76 77 78 69 85 55 29 7...
output:
42741099
result:
ok 1 number(s): "42741099"