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 |
---|---|---|---|---|---|---|---|---|---|
#810649 | #6137. Sub-cycle Graph | hotdogseller | AC ✓ | 241ms | 7104kb | C++14 | 1.9kb | 2024-12-12 07:52:13 | 2024-12-12 07:52:14 |
Judging History
answer
#include<bits/stdc++.h>
#define maxn 100005
#define int long long
#define mod 1000000007
using namespace std;
inline int read(){
int lre=0,f=1;
char c=getchar();
while(!isdigit(c)){
if(c=='-'){
f=-1;
}
c=getchar();
}
while(isdigit(c)){
lre=(lre<<3)+(lre<<1)+(c-'0');
c=getchar();
}
return lre*f;
}
inline int slowpow(int a,int b){
__int128 x=a,y=b;
return (x*y)%mod;
}
inline int quickpow(int a,int b){
int lre=1;
while(b){
if(b&1)lre=slowpow(lre,a);
b>>=1;
a=slowpow(a,a);
}
return lre;
}
int n,m,res;
int fact[maxn],inv[maxn];
//n个点全部在链上,i条链,方案数:C(n,2i)*i^(n-2i)/2^i
int pw[maxn],pv[maxn];//2^i和2^-i
int C(int a,int b){
if(b==0)return 1;
if(b>a)return 0;
int lre=slowpow(slowpow(fact[a],inv[b]),inv[a-b]);
// cout<<"C("<<a<<","<<b<<")="<<lre<<endl;
return lre;
}
void solve(){
n=read();m=read();
if(m>n){cout<<0<<endl;return;}
if(m==n){
//(n-1)!/2
printf("%lld\n",slowpow(fact[n-1],inv[2]));
return;
}
int k=n-m;
res=pv[k];int lre=0;
// cout<<"k="<<k<<endl;
for(int i=0;i<=n-k;i++){
//((k&1)?-1:1)*C(a,k)*pw[a-k]*C(n-k-1,n-a-k)
int tmp=slowpow(C(k,i),slowpow(pw[k-i],C(n-i-1,k-1)));
if(i&1){
lre=(lre-tmp+mod)%mod;
}else{
lre=(lre+tmp)%mod;
}
}
res=slowpow(res,lre);
res=slowpow(slowpow(res,fact[n]),inv[k]);
printf("%lld\n",res);
}
signed main(){
fact[0]=inv[0]=1;
pw[0]=pv[0]=1;
for(int i=1;i<=100000;i++){
fact[i]=slowpow(fact[i-1],i);
pw[i]=slowpow(pw[i-1],2);
}
inv[100000]=quickpow(fact[100000],mod-2);
pv[100000]=quickpow(pw[100000],mod-2);
for(int i=100000;i>=1;--i){
inv[i-1]=slowpow(inv[i],i);
pv[i-1]=slowpow(pv[i],2);
}
for(int i=1;i<=10;i++){
// cout<<pw[i]<<" "<<fact[i]<<endl;
assert(slowpow(pw[i],pv[i])==1);
assert(slowpow(fact[i],inv[i])==1);
}
int t=read();
while(t--){
solve();
}
return 0;
}
详细
Test #1:
score: 100
Accepted
time: 0ms
memory: 6912kb
input:
3 4 2 4 3 5 3
output:
15 12 90
result:
ok 3 number(s): "15 12 90"
Test #2:
score: 0
Accepted
time: 241ms
memory: 7104kb
input:
17446 3 0 3 1 3 2 3 3 4 0 4 1 4 2 4 3 4 4 5 0 5 1 5 2 5 3 5 4 5 5 6 0 6 1 6 2 6 3 6 4 6 5 6 6 7 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 8 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 9 0 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 11 0 11 1 11 2 11 3 11 4 11 5 11 6 11 7 11...
output:
1 3 3 1 1 6 15 12 3 1 10 45 90 60 12 1 15 105 375 630 360 60 1 21 210 1155 3465 5040 2520 360 1 28 378 2940 13545 35280 45360 20160 2520 1 36 630 6552 42525 170100 393120 453600 181440 20160 1 45 990 13230 114345 643545 2286900 4762800 4989600 1814400 181440 1 55 1485 24750 273735 2047815 10239075 3...
result:
ok 17446 numbers