数论模板
翘了一上午课来机房皮。
//Twenty
#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<queue>
#include<vector>
const int maxn=10000000+5;
int x,tot,prime[maxn],shs[maxn];
using namespace std;
int n,m;
void work(){
for(int i=2;i<=n;i++){
if(!shs[i]) prime[++tot]=i;
for(int j=1;j<=tot&&prime[j]*i<=n;j++){
shs[prime[j]*i]=1;
if(i%prime[j]==0) break;
}
}
}
int main()
{
scanf("%d%d",&n,&m);
work();
for(int i=1;i<=m;i++){
scanf("%d",&x);
if(shs[x]||x==1) printf("No\n");
else printf("Yes\n");
}
return 0;
}
//Twenty
#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<queue>
#include<vector>
using namespace std;
typedef long long ll;
ll n,p;
ll ksm(ll a,ll b){
ll base=a,res=1;
while(b){
if(b&1) (res*=base)%=p;
(base*=base)%=p;
b>>=1;
}
return res;
}
int main()
{
scanf("%d%d",&n,&p);
for(int i=1;i<=n;i++){
printf("%lld\n",ksm((ll)i,(ll)p-2));
}
return 0;
}
//Twenty
#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<queue>
#include<vector>
using namespace std;
int n,p;
void exgcd(int a,int b,int &d,int &x,int &y){
if(b==0) {d=a,x=1,y=0;return ;}
exgcd(b,a%b,d,y,x); y-=x*(a/b);
}
int inv(int a,int n){
int d,x,y;
exgcd(a,n,d,x,y);
return d==1?(x+n)%n:-1;
}
int main()
{
scanf("%d%d",&n,&p);
for(int i=1;i<=n;i++){
printf("%d\n",inv(i,p));
}
return 0;
}
//Twenty
#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<queue>
#include<vector>
const int maxn=1e7;
using namespace std;
long long inv[maxn];
long long n,p;
int main()
{
scanf("%lld%lld",&n,&p);
inv[1]=1;
printf("%lld\n",inv[1]);
for(int i=2;i<=n;i++)
{inv[i]=(p-p/i)*inv[p%i]%p;
printf("%lld\n",inv[i]);}
return 0;
}
//Twenty
#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<queue>
#include<vector>
const int maxn=10000+5;
int x,tot,prime[maxn],shs[maxn];
using namespace std;
int n,m;
int query(int x){
int mi=sqrt(x),res=x;
for(int i=2;i<=mi;i++) if(x%i==0){
res=res-res/i;
while(x%i==0) x/=i;
}
if(x!=1) res=res-res/x;
return res;
}
int main()
{
scanf("%d",&n);
for(int i=1;i<=n;i++){
scanf("%d",&x);
printf("%d\n",query(x));
}
return 0;
}
//Twenty
#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<queue>
#include<vector>
const int maxn=32768+5;
int x,tot,prime[maxn],shs[maxn],ol[maxn];
using namespace std;
int n,m;
int work(){
for(int i=2;i<=maxn;i++){
if(!shs[i]) {prime[++tot]=i;ol[i]=i-1;}
for(int j=1;j<=tot&&prime[j]*i<=maxn;j++){
shs[prime[j]*i]=1;
if(i%prime[j]==0){
ol[prime[j]*i]=ol[i]*prime[j];
break;
}
else ol[prime[j]*i]=ol[i]*(prime[j]-1);
}
}
}
int main()
{
scanf("%d",&n);
work();
for(int i=1;i<=n;i++){
scanf("%d",&x);
printf("%d\n",ol[x]);
}
return 0;
}
//Twenty
#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<queue>
#include<vector>
using namespace std;
long long ans,n,a[65],b[65];
int main()
{
scanf("%lld",&n);
for(int i=1;i<=n;i++) scanf("%lld",&a[i]);
for(int i=1;i<=n;i++)
for(int j=60;j>=0;j--) {
if((1LL<<j)&a[i]) {
if(b[j]) a[i]^=b[j];
else {b[j]=a[i]; break;}
}
}
for(int i=60;i>=0;i--)
if((ans^b[i])>ans) ans^=b[i];
cout<<ans;
return 0;
}
//Twenty
#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<queue>
#include<vector>
using namespace std;
const int maxn=1e5+299;
typedef long long LL;
LL T,n,m,p,c[maxn];
LL ksm(LL a,LL b){
a%=p;
LL res=1,base=a;
while(b){
if(b&1) (res*=base)%=p;
(base*=base)%=p;
b>>=1;
}
return res;
}
LL C(LL n,LL m){
if(n<m) return 0;
return (c[n]*ksm(c[m],p-2)%p*ksm(c[n-m],p-2))%p;
}
LL lucas(LL n,LL m){
if(!m) return 1;
return (C(n%p,m%p)*lucas(n/p,m/p))%p;
}
int main()
{
scanf("%lld",&T);
while(T--){
scanf("%lld%lld%lld",&n,&m,&p);
c[0]=1;
for(int i=1;i<=p;i++)
c[i]=(c[i-1])*i%p;
printf("%lld\n",lucas(n+m,m));
}
return 0;
}
//Twenty
#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<queue>
#include<vector>
using namespace std;
const int maxn=50000+299;
int T,a,b,c,d,k,tot,bo[maxn],prime[maxn],mu[maxn],sum[maxn];
void make_mu(){
mu[1]=1; sum[1]=1;
for(int i=2;i<=maxn;i++){
if(!bo[i]) {prime[++tot]=i; mu[i]=-1;}
for(int j=1;j<=tot&&prime[j]*i<=maxn;j++){
if(i%prime[j]==0){
bo[prime[j]*i]=1;
mu[prime[j]*i]=0;
break;
}
else {
bo[prime[j]*i]=1;
mu[prime[j]*i]=mu[i]*(-1);
}
}
sum[i]=sum[i-1]+mu[i];
}
}
int f(int n,int m){
n/=k; m/=k;
int t=min(n,m),last,ans=0;
for(int i=1;i<=t;i=last+1){
last=min(n/(n/i),m/(m/i));
ans+=(sum[last]-sum[i-1])*(n/i)*(m/i);
}
return ans;
}
int cul(int a,int b,int c,int d){
int res=0;
res+=f(b,d);
res-=f(a-1,d);
res-=f(b,c-1);
res+=f(a-1,c-1);
return res;
}
int main()
{
scanf("%d",&T);
make_mu();
while(T--){
scanf("%d%d%d%d%d",&a,&b,&c,&d,&k);
printf("%d\n",cul(a,b,c,d));
}
return 0;
}
//Twenty
#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<queue>
#include<vector>
const int maxn=1e6+299;
const int mod=1e9+7;
int prime[maxn*2],bo[maxn*2],tot,nxt[maxn*2],pr[20];
typedef long long LL;
LL nn,xx,n,ans;
using namespace std;
void pre(){
for(int i=2;i<=maxn;i++){
if(!bo[i]) { prime[++tot]=i; nxt[i]=tot; }
for(int j=1;j<=tot&&prime[j]*i<=maxn;j++){
bo[prime[j]*i]=1;
nxt[prime[j]*i]=j;
if(i%prime[j]==0) break;
}
}
}
LL rongchi(LL yy){
LL res=0;
for(int i=1;i<(1<<pr[0]);i++){
int flag=0,tmp=1;
for(int j=0;j<pr[0];j++)
if((1<<j)&i) flag++,tmp*=pr[j+1];
if(flag&1) (res+=(LL)yy/tmp)%=mod;
else ((res-=(LL)yy/tmp)+=mod)%=mod;
}
return ((LL)res+mod)%mod;
}
int main()
{
//freopen("C.in","r",stdin);
//freopen("C.out","w",stdout);
scanf("%lld",&n);
pre();
nn=sqrt(n);
for(int i=1;i<=nn;i++){
pr[0]=0;
xx=i;
while(xx!=1){
pr[++pr[0]]=prime[nxt[xx]];
while(xx%pr[pr[0]]==0)
xx/=pr[pr[0]];
}
xx=i;
ans+=((n/i-i-((rongchi(n/i)-rongchi(i))+mod)%mod)+mod)%mod;
}
((ans*=2)+=1%mod)%=mod;
printf("%lld",ans);
return 0;
}
//Twenty
#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<queue>
#include<vector>
const int maxn=110;
using namespace std;
double a[maxn][maxn];
int flag,n;
inline void read(double &x){
char ch=getchar(); double f=1;
while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
if(ch=='-') f=-1,ch=getchar();
for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0';
}
void work(){
for(int i=1;i<=n;i++){
int now=i;
for(int j=i+1;j<=n;j++)
if(fabs(a[j][i]>a[now][i])) now=j;
if(now!=i)
for(int j=i;j<=n+1;j++)
swap(a[i][j],a[now][j]);
if(a[i][i]==0) {flag=1;return;}
for(int j=i+1;j<=n+1;j++)
a[i][j]=a[i][j]/a[i][i];
a[i][i]=1;
for(int j=i+1;j<=n;j++){
for(int k=i+1;k<=n+1;k++)
a[j][k]-=a[i][k]*a[j][i];
a[j][i]=0;
}
}
for(int i=n;i>=1;i--)
for(int j=i+1;j<=n;j++)
a[i][n+1]-=a[i][j]*a[j][n+1];
}
int main()
{
scanf("%d",&n);
for(int i=1;i<=n;i++)
for(int j=1;j<=n+1;j++)
read(a[i][j]);
work();
if(flag) printf("No Solution\n");
else {
for(int i=1;i<=n;i++)
printf("%.2lf\n",a[i][n+1]);
}
return 0;
}
//Achen
#include<algorithm>
#include<iostream>
#include<complex>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#define pi acos(-1)
const int N=3e6+7;
using namespace std;
typedef complex<double> E;
int xx,n,m,r[N],l;
E a[N],b[N];
template<typename T> void read(T &x) {
T f=1; x=0; char ch=getchar();
while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
if(ch=='-') f=-1,ch=getchar();
for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
}
void FFT(E a[],int f) {
for(int i=0;i<n;i++) if(i<r[i]) swap(a[i],a[r[i]]);
for(int i=1;i<n;i<<=1) {
E wn(cos(pi/i),f*sin(pi/i));
for(int p=i<<1,j=0;j<n;j+=p) {
E w(1,0);
for(int k=0;k<i;k++,w*=wn) {
E x=a[j+k],y=w*a[j+k+i];
a[j+k]=x+y; a[j+k+i]=x-y;
}
}
}
}
int main() {
read(n); read(m);
for(int i=0;i<=n;i++) { read(xx); a[i]=xx;}
for(int i=0;i<=m;i++) { read(xx); b[i]=xx;}
m+=n;
for(n=1;n<=m;n<<=1) l++;
for(int i=0;i<n;i++) r[i]=(r[i>>1]>>1)|((i&1)<<(l-1));
FFT(a,1); FFT(b,1);
for(int i=0;i<n;i++) a[i]=a[i]*b[i];
FFT(a,-1);
for(int i=0;i<=m;i++) printf("%d ",(int)(a[i].real()/n+0.5));
return 0;
}
1 //Achen
2 #include<algorithm>
3 #include<iostream>
4 #include<cstring>
5 #include<cstdlib>
6 #include<cstdio>
7 #include<vector>
8 #include<queue>
9 #include<cmath>
10 #include<ctime>
11 const int N=3e6+7,p=998244353,g=3,gi=332748118;
12 typedef long long LL;
13 using namespace std;
14 int n,m,l,r[N],a[N],b[N],inv;
15
16 template<typename T> void read(T &x) {
17 T f=1; x=0; char ch=getchar();
18 while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
19 if(ch=='-') f=-1,ch=getchar();
20 for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
21 }
22
23 LL ksm(LL a,LL b) {
24 LL res=1,base=a;
25 while(b) {
26 if(b&1) (res*=base)%=p;
27 (base*=base)%=p;
28 b>>=1;
29 }
30 return res;
31 }
32
33 void FNT(int a[],int f) {
34 for(int i=0;i<n;i++) if(i<r[i]) swap(a[i],a[r[i]]);
35 for(int i=1;i<n;i<<=1) {
36 int wn=ksm((f==1?g:gi),(p-1)/(i<<1));
37 for(int q=(i<<1),j=0;j<n;j+=q) {
38 int w=1;
39 for(int k=0;k<i;k++,w=(LL)w*wn%p) {
40 int x=a[j+k],y=(LL)w*a[j+k+i]%p;
41 a[j+k]=(LL)(x+y)%p; a[j+k+i]=(LL)(x-y+p)%p;
42 }
43 }
44 }
45 if(f==-1) for(int i=0;i<n;i++) a[i]=(LL)a[i]*inv%p;
46 }
47
48 int main() {
49 read(n); read(m);
50 for(int i=0;i<=n;i++) read(a[i]);
51 for(int i=0;i<=m;i++) read(b[i]);
52 m+=n;
53 for(n=1;n<=m;n<<=1) l++;
54 inv=ksm(n,p-2);
55 for(int i=0;i<n;i++) r[i]=(r[i>>1]>>1)|((i&1)<<(l-1));
56 FNT(a,1); FNT(b,1);
57 for(int i=0;i<n;i++) a[i]=(LL)a[i]*b[i]%p;
58 FNT(a,-1);
59 for(int i=0;i<=m;i++) printf("%d ",a[i]);
60 return 0;
61 }
