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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#142068 | #6736. Alice and Bob | OvO_Zuo | AC ✓ | 119ms | 81828kb | C++14 | 1.0kb | 2023-08-18 13:37:15 | 2023-08-18 13:37:18 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=1e7+5,mo=998244353;
int n,frac[N],inv[N];
int mi(int x,int y)
{
int res=1;
for(;y;y>>=1,x=(ll)x*x%mo)
if(y&1) res=(ll)res*x%mo;
return res;
}
int C(int x,int y)
{
if(x<y) return 0;
return (ll)frac[x]*inv[y]%mo*inv[x-y]%mo;
}
void init()
{
int i,j;
frac[0]=1;
for(i=1;i<=n;i++) frac[i]=(ll)frac[i-1]*i%mo;
inv[n]=mi(frac[n],mo-2);
for(i=n-1;i>=0;--i) inv[i]=(ll)inv[i+1]*(i+1)%mo;
}
ll ans=0;
int main()
{
scanf("%d",&n);
int i,j;
init();
for(i=1;i<=n;i++)
ans+=(ll)C(n-i,i-1)*frac[i-1]%mo*frac[n-i]%mo;
ans%=mo;
printf("%lld\n",ans);
return 0;
}
/*
当 p[1]~p[p[1]] 中所有数都>=p[1] 时,后手一定能将p[1]再次调到序列首,先手必败
若存在小于的,则将最小的挪到 p[1] 的位置
设新的排列为 p',此时一定有 p'[1]~p'[p'[1]] 均 >=p'[1]
此时原先的后手必败
于是后手Bob胜利的充要条件就是p[1]~p[p[1]]之间所有数都>=p[1]
*/
Details
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Test #1:
score: 100
Accepted
time: 1ms
memory: 5924kb
input:
1
output:
1
result:
ok 1 number(s): "1"
Test #2:
score: 0
Accepted
time: 1ms
memory: 5888kb
input:
2
output:
1
result:
ok 1 number(s): "1"
Test #3:
score: 0
Accepted
time: 1ms
memory: 5704kb
input:
10
output:
997920
result:
ok 1 number(s): "997920"
Test #4:
score: 0
Accepted
time: 1ms
memory: 5760kb
input:
100
output:
188898954
result:
ok 1 number(s): "188898954"
Test #5:
score: 0
Accepted
time: 0ms
memory: 5928kb
input:
4
output:
10
result:
ok 1 number(s): "10"
Test #6:
score: 0
Accepted
time: 1ms
memory: 5700kb
input:
8
output:
12336
result:
ok 1 number(s): "12336"
Test #7:
score: 0
Accepted
time: 0ms
memory: 5776kb
input:
16
output:
373118483
result:
ok 1 number(s): "373118483"
Test #8:
score: 0
Accepted
time: 1ms
memory: 5672kb
input:
32
output:
314585464
result:
ok 1 number(s): "314585464"
Test #9:
score: 0
Accepted
time: 1ms
memory: 5760kb
input:
64
output:
627827331
result:
ok 1 number(s): "627827331"
Test #10:
score: 0
Accepted
time: 1ms
memory: 5712kb
input:
128
output:
828497685
result:
ok 1 number(s): "828497685"
Test #11:
score: 0
Accepted
time: 2ms
memory: 7980kb
input:
256
output:
65697890
result:
ok 1 number(s): "65697890"
Test #12:
score: 0
Accepted
time: 1ms
memory: 5684kb
input:
512
output:
854187619
result:
ok 1 number(s): "854187619"
Test #13:
score: 0
Accepted
time: 0ms
memory: 5696kb
input:
1024
output:
513823539
result:
ok 1 number(s): "513823539"
Test #14:
score: 0
Accepted
time: 16ms
memory: 19104kb
input:
1361956
output:
617368199
result:
ok 1 number(s): "617368199"
Test #15:
score: 0
Accepted
time: 90ms
memory: 63608kb
input:
7579013
output:
827172636
result:
ok 1 number(s): "827172636"
Test #16:
score: 0
Accepted
time: 82ms
memory: 67804kb
input:
8145517
output:
710624331
result:
ok 1 number(s): "710624331"
Test #17:
score: 0
Accepted
time: 66ms
memory: 52320kb
input:
6140463
output:
707600568
result:
ok 1 number(s): "707600568"
Test #18:
score: 0
Accepted
time: 45ms
memory: 33164kb
input:
3515281
output:
698302413
result:
ok 1 number(s): "698302413"
Test #19:
score: 0
Accepted
time: 79ms
memory: 59880kb
input:
6969586
output:
69470392
result:
ok 1 number(s): "69470392"
Test #20:
score: 0
Accepted
time: 30ms
memory: 26628kb
input:
2888636
output:
433579983
result:
ok 1 number(s): "433579983"
Test #21:
score: 0
Accepted
time: 113ms
memory: 81828kb
input:
9999998
output:
758172780
result:
ok 1 number(s): "758172780"
Test #22:
score: 0
Accepted
time: 110ms
memory: 81776kb
input:
9999999
output:
605195495
result:
ok 1 number(s): "605195495"
Test #23:
score: 0
Accepted
time: 119ms
memory: 81792kb
input:
10000000
output:
866813682
result:
ok 1 number(s): "866813682"