1801: Mr. S’s Romance
#include <stdio.h>
#include <string.h>
#include <iostream>
#define MAXN 1000005
using namespace std;
typedef long long LL;
bool isprime[MAXN];
int prime[MAXN];
int indexnum[MAXN];
int num;
const int TOP=80000;
const LL MOD=1000000000LL+7;
int get_prime()
{
memset(isprime,true,sizeof(isprime));
isprime[1]=false;
for(int i=2;i*i<MAXN-4;i++)
if(isprime[i])
for(int j=2;i*j<MAXN-4;j++)
isprime[i*j]=false;
num=0;
for(int i=1;i<MAXN-4;i++)
if(isprime[i])
indexnum[i]=num,prime[num++]=i;
return num;
}
int a[TOP];
void deal(int x)
{
for(int i=0;i<num;i++){
if(isprime[x]){
a[indexnum[x]]++;
break;
}
while(x%prime[i]==0){
a[i]++;
x/=prime[i];
}
if(x==1)
break;
}
}
LL mul(LL x,LL n,LL mod)
{
LL tmp=x;
LL ans=1;
while(n){
if(n&1){
ans*=tmp;
ans%=mod;
}
tmp*=tmp;
tmp%=mod;
n>>=1;
}
return ans%mod;
}
int main()
{
get_prime();
int T,K=1;
for(cin>>T;T--;){
int n;
scanf("%d",&n);
memset(a,0,sizeof(a));
for(int i=0;i<n;i++){
int tmp;
scanf("%d",&tmp);
deal(tmp);
}
LL ans=1;
for(int i=0;i<num;i++)
if(a[i])
ans=ans*mul(2,a[i]-1,MOD)%MOD;
ans=(ans-1+MOD)%MOD;
printf("Case #%d:\n%lld\n",K++,ans);
}
return 0;
}
#include<iostream>
#include<stdio.h>
#include<string.h>
#include<math.h>
#define inf 0x3f3f3f3f
using namespace std;
int n,m;
int map[200][200];
int main()
{
int test;
scanf("%d",&test);
while(test--)
{
memset(map,0,sizeof(map));
int a,b;
scanf("%d%d",&n,&m);
for(int i=1;i<=m;i++)
{
scanf("%d%d",&a,&b);
map[b][a]=1;
}
for(int i=1;i<=n;i++)
{
for(int j=1;j<=n;j++)
{
for(int k=1;k<=n;k++)
{
if(map[j][i]==1&&map[i][k]==1)
{
map[j][k]=1;
}
}
}
}
int flag=0;
for(int i=1;i<=n;i++)
{
for(int j=1;j<=n;j++)
{
if(map[j][i]==1&&map[i][j]==1)
{
flag=1;
break;
}
}
if(flag==1)break;
}
if(flag==1)
{
printf("Wrong\n");
continue;
}
int num=0;
int is_sure1=1;
for(int i=1;i<=n;i++)
{
int is_sure=1;
for(int j=1;j<=n;j++)
{
if(i==j)continue;
if(map[i][j]==0&&map[j][i]==0)
{
is_sure=0;
break;
}
}
if(is_sure==1)num++;
}
int rank=1;
for(int i=2;i<=n;i++)
{
if(map[1][i]==1)
{
rank++;
continue;
}
if(map[i][1]==0)
{
is_sure1=0;
break;
}
}
if(is_sure1==0) printf("-1\n");
else printf("%d\n",rank);
printf("%d\n",num);
}
}
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int mo=1e9+7;
const int maxn=1e5+10;
int head[maxn],e[2*maxn],nex[2*maxn];
int a[maxn],b[maxn],vis[maxn],f[maxn];
int ans,tot;
void add_edge(int u,int v){
e[tot]=v;nex[tot]=head[u];head[u]=tot++;
}
void dfs(int u){
int v,i;
f[u]=0;vis[u]=1;
if (head[u]==-1) {
f[u]=b[u];
return;
}
for (i=head[u];i!=-1;i=nex[i]){
v=e[i];
if (!vis[v]) dfs(v);
f[u]=(f[u]+f[v])%mo;
}
ans=(ans+(long long)f[u]*a[u]%mo)%mo;
f[u]=(f[u]+b[u])%mo;
}
int main()
{
int i,n,m,u,v;
while (scanf("%d %d",&n,&m)!=-1){
for (i=1;i<=n;i++) head[i]=-1;
tot=0;
for (i=1;i<=n;i++){
scanf("%d %d",&a[i],&b[i]);
}
for (i=1;i<=m;i++){
scanf("%d %d",&u,&v);
add_edge(u,v);
}
memset(vis,0,sizeof(vis));
ans=0;
for (i=1;i<=n;i++){
if (!vis[i]) dfs(i);
}
printf("%d\n",ans);
}
return 0;
}
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <cmath>
#include <string>
#include <vector>
#include <cstdio>
#include <cctype>
#include <cstring>
#include <sstream>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#pragma comment(linker,"/STACK:102400000,102400000")
using namespace std;
#define MAX 100010
#define MAXN 1000005
#define maxnode 5
#define sigma_size 30
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define lrt rt<<1
#define rrt rt<<1|1
#define middle int m=(r+l)>>1
#define LL long long
#define ull unsigned long long
#define mem(x,v) memset(x,v,sizeof(x))
#define lowbit(x) (x&-x)
#define pii pair<int,int>
#define bits(a) __builtin_popcount(a)
#define mk make_pair
#define limit 10000
const int INF = 0x3f3f3f3f;
const LL INFF = 0x3f3f;
const double pi = acos(-1.0);
const double inf = 1e18;
const double eps = 1e-6;
const LL mod = 1e9+7;
const ull mx = 133333331;
inline void RI(int &x) {
char c;
while((c=getchar())<'0' || c>'9');
x=c-'0';
while((c=getchar())>='0' && c<='9') x=(x<<3)+(x<<1)+c-'0';
}
bool isFreeX[5];
LL A[5][5];
LL atob,atoc,btoa,btoc,ctob,ctoa;
LL gauss(int n, int m) {
for(int i = 0; i < m; ++i) isFreeX[i] = false;
LL ret = 1, neg = 0;
int r = 1, c = 1;
for(; r < n && c < m; ++r, ++c) {
int p = r;
for(; p < n; ++p) if(A[p][c]) break;
if(p == n) {--r; isFreeX[c] = true; continue;}
if(p != r) {
neg ^= 1;
for(int i = c; i <= m; ++i) swap(A[p][i], A[r][i]);
}
for(int i = r + 1; i < n; ++i) {
while(A[i][c]) {
LL delta = A[i][c] / A[r][c];
for(int j = c; j <= m; ++j) {
A[i][j] += mod - delta * A[r][j] % mod;
A[i][j] %= mod;
}
if(!A[i][c]) break;
neg ^= 1;
for(int j = c; j <= m; ++j) swap(A[r][j], A[i][j]);
}
}
}
if(r != n) return 0;
for(int i = 1; i < r; ++i) ret = ret * A[i][i] % mod;
if(neg) ret = (-ret + mod) % mod;
return ret;
}
int deg[5];
LL fact[MAX];
void init(){
fact[0]=1;
for(int i=1;i<=100000;i++) fact[i]=fact[i-1]*i%mod;
}
LL qpow(LL a,LL n){
LL ans=1;
while(n){
if(n&1) ans=ans*a%mod;
a=a*a%mod;
n>>=1;
}
return ans;
}
LL C(int n,int m){
return (fact[n]*qpow(fact[m],mod-2)%mod)*qpow(fact[n-m],mod-2)%mod;
}
int main()
{
int a,b,c;
init();
while(cin>>a>>b>>c){
LL ans=0;
LL aa=a+b,bb=a+c,cc=c+b;
if(aa%2||bb%2||cc%2){
puts("0");continue;
}
for(int x=0;x<=a;x++)
{
atob=x;btoa=a-x;
btoc=bb/2-btoa;atoc=aa/2-x;
ctob=c-btoc;ctoa=b-atoc;
if(atoc<0||atob<0||btoa<0||btoc<0||ctoa<0||ctob<0) continue;
deg[0]=aa/2;
deg[1]=bb/2;
deg[2]=cc/2;
for(int i=0;i<3;i++) A[i][i]=deg[i];
A[0][1]=atob;A[0][2]=atoc;
A[1][0]=btoa;A[1][2]=btoc;
A[2][0]=ctoa;A[2][1]=ctob;
LL ret=(C(a,x)*C(b,atoc)%mod)*C(c,btoc)%mod;
ret=ret*gauss(3,3)%mod;
for(int i=0;i<3;i++) ret=ret*fact[deg[i]-1]%mod;
ret=ret*deg[0]%mod;
ans+=ret;
if(ans>=mod) ans-=mod;
}
cout<<ans<<endl;
}
return 0;
}
#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <algorithm>
#include <queue>
#include <cmath>
#include <vector>
#include <set>
#include <bitset>
#include <stack>
#include <map>
#include <climits>
#include <functional>
using namespace std;
#define LL long long
const int INF=0x3f3f3f3f;
const double eps=1e-8;
int n,m,t;
int s[20],nt[200],e[200],c[200],d[200],cnt;
int visit[20];
double dis[20];
double SPFA(double x)
{
for(int i=0;i<=n;i++) dis[i]=1.0*INF;
memset(visit,0,sizeof visit);
queue<int>q;
visit[1]=1;
q.push(1);
dis[1]=0;
while(!q.empty())
{
int pre=q.front();
q.pop();
visit[pre]=0;
for(int i=s[pre];~i;i=nt[i])
{
if(dis[pre]+c[i]*x+d[i]<dis[e[i]])
{
dis[e[i]]=dis[pre]+c[i]*x+d[i];
if(!visit[e[i]])
{
visit[e[i]]=1;
q.push(e[i]);
}
}
}
}
return dis[n];
}
double get(double L,double R)
{
return (R-L)*(SPFA(L)+4*SPFA((L+R)/2)+SPFA(R))/6;
}
double Ans(double L,double R)
{
double mid=(L+R)/2;
double s0=get(L,R),s1=get(L,mid),s2=get(mid,R);
if(fabs(s0-(s1+s2))<=eps) return s0;
else return Ans(L,mid)+Ans(mid,R);
}
int main()
{
while(~scanf("%d%d%d",&n,&m,&t))
{
memset(s,-1,sizeof s);
cnt=1;
for(int i=1;i<=m;i++)
{
int u,v,cc,dd;
scanf("%d%d%d%d",&u,&v,&cc,&dd);
nt[cnt]=s[u],e[cnt]=v,c[cnt]=cc,d[cnt]=dd,s[u]=cnt++;
}
printf("%.8lf\n",Ans(0,1.0*t)/t);
}
return 0;
}