2017 计蒜之道 复赛 题解

A. 阿里云秘钥池

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<functional>
#include<iostream>
#include<cmath>
#include<cctype>
#include<ctime>
#include<iomanip>
#include<vector>
#include<string>
#include<queue>
#include<stack>
#include<map>
#include<sstream>
#include<complex>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int>
#define pi pair<int,int>
#define vpi vector<pi >
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a
<<endl;
#define PRi2D(a,n,m) For(i,n) { \
For(j,m-1) cout<<a[i][j]<<' ';\
cout<<a[i][m]<<endl; \
}
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
int read()
{
int x=0,f=1; char ch=getchar();
while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
return x*f;
}
#define MAXN (123456)
int p[MAXN],tot;
bool b[MAXN]={0};
ll mul[MAXN];
void make_prime(int n)
{
tot=0; mul[1]=1;
Fork(i,2,n)
{
if (!b[i]) p[++tot]=i,mul[i]=-1;
For(j,tot)
{
if (i*p[j]>n) break;
b[i*p[j]]=1;
mul[i*p[j]]=-mul[i];
if (i%p[j]==0) {
mul[i*p[j]]=0;
break;
}
}
}
}
#undef MAXN
#define MAXN (80)
#define MAXL (100010)
ll f[2][MAXL][2];
ll g[MAXL];
ll len,c[MAXL];
int gcd(int a,int b){if (!b)return a;return gcd(b,a%b);}

ll calc(ll n,int p) {
len=0;
if (!n) return 0;
while(n) c[++len]=n%p,n/=p;
For(i,len/2) swap(c[i],c[len-i+1]);

Rep(j,p) Rep(l,2) f[1][j][l]=f[0][j][l]=0;

f[1][c[1]][0]=1;
For(j,c[1]-1) f[1][j][1]=1;

int nx=0,no=1;

For(i,len-1) {
For(j,p-1) g[j]=0;
For(j,p-1)
{
for(int l=j;l<p;l+=j)
g[j]+=f[no][l][1];
}

Rep(j,p) Rep(l,2) f[nx][j][l]=0;

f[nx][c[i+1]][0]+=(c[i+1]!=0)*f[no][c[i]][0]*(gcd(c[i],c[i+1])==1);

For(j,c[i+1]-1) {
f[nx][j][1]+=f[no][c[i]][0]*(gcd(c[i],j)==1);
}

For(d,p-1) // 枚举 转移后
{
for(int k=d;k<p;k+=d)
f[nx][k][1]+=g[d]*mul[d];
}

For(j,p-1) f[nx][j][1]++;

swap(no,nx);
}
ll ans=0;
For(j,p-1) Rep(l,2) ans+=f[no][j][l];
return ans;
}
int main()
{
//  freopen("a.in","r",stdin);
//  freopen(".out","w",stdout);
int T=read();
make_prime(123451);
while(T--) {
ll l,r;
scanf("%lld%lld\n",&l,&r);
int p=read();
printf("%lld\n",calc(r,p)-calc(l-1,p));
}

return 0;
}

B. Windows 画图

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<functional>
#include<iostream>
#include<cmath>
#include<cctype>
#include<ctime>
#include<iomanip>
#include<vector>
#include<string>
#include<queue>
#include<stack>
#include<map>
#include<sstream>
#include<complex>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int>
#define pi pair<int,int>
#define vpi vector<pi >
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a
<<endl;
#define PRi2D(a,n,m) For(i,n) { \
For(j,m-1) cout<<a[i][j]<<' ';\
cout<<a[i][m]<<endl; \
}
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
int read()
{
int x=0,f=1; char ch=getchar();
while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
return x*f;
}
int f[1000][1000]={};
int gcd(int x,int y) {if (!y) return x;return gcd(y,x%y);}
int main()
{
//  freopen("B.in","r",stdin);
//  freopen(".out","w",stdout);
int n=read(),m=read();
For(i,n) {
int X1=read(),Y1=read(),X2=read(),Y2=read();
int p1=X1,p2=Y1,p3=X2,p4=Y2;
int t=gcd(abs(X1-X2),abs(Y1-Y2));
X2=(X2-X1)/t;
Y2=(Y2-Y1)/t;

int a=X1,b=Y1;
while(a<=max(p1,p3)&b<=max(p2,p4)&&a>=min(p1,p3)&&b<=max(p2,p4)) {
f[a][b]=i;
a-=X2;b-=Y2;
}
a+=X2,b+=Y2;
while(a<=max(p1,p3)&b<=max(p2,p4)&&a>=min(p1,p3)&&b<=max(p2,p4)) {
f[a][b]=i;
a+=X2;b+=Y2;
}
}
int q=read();
while(q--) {
int x=read(),y=read();
printf("%d\n",f[x][y]);
}

return 0;
}

D. 百度地图导航

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<functional>
#include<iostream>
#include<cmath>
#include<cctype>
#include<ctime>
#include<iomanip>
#include<vector>
#include<string>
#include<queue>
#include<stack>
#include<map>
#include<sstream>
#include<complex>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int>
#define pi pair<int,int>
#define vpi vector<pi >
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a
<<endl;
#define PRi2D(a,n,m) For(i,n) { \
For(j,m-1) cout<<a[i][j]<<' ';\
cout<<a[i][m]<<endl; \
}
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
int read()
{
int x=0,f=1; char ch=getchar();
while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
return x*f;
}
#define MAXN (60010)
#define MAXM (4000000)
class SPFA
{
public:
void mem()
{
MEM(pre) MEM(edge) MEM(pre) MEM(weight) size=1;
}
int q[MAXN*100];
ll edge[MAXM],next[MAXM],pre[MAXN],weight[MAXM],size;
void addedge(int u,int v,ll w)
{
edge[++size]=v;
weight[size]=w;
next[size]=pre[u];
pre[u]=size;
}
void addedge2(int u,int v,ll w){addedge(u,v,w);addedge(v,u,w);}
ll d[MAXN];
bool b[MAXN];
ll spfa(int s,int t)
{
MEM(b) MEMI(d)
b[s]=1; d[s]=0;
q[1]=s;
int head=1,tail=1;
while(head<=tail)
{
int now=q[head++];
b[now]=0;
Forp(now)
{
int v=edge[p];
if (d[now]+weight[p]<d[v]) {
d[v]=d[now]+weight[p];
if (!b[v]) { b[v]=1,q[++tail]=v;
}
}
}
}
if (d[t]>20000*1e6) return -1;
return d[t];
}
}S;
vi st[MAXN];
int main()
{
//  freopen("d.in","r",stdin);
//  freopen(".out","w",stdout);
int n=read(),m=read();
S.mem();
For(i,m) {
int k=read();
while(k--) {
int x=read();
S.addedge(x,n+i,0);
S.addedge(n+m+i,x,0);
}
}
int m1=read();
For(i,m1) {
int u=read(),v=read(),c=read();
S.addedge2(u,v,c);
}
int m2=read();
For(i,m2) {
int u=read(),v=read(),c=read();
S.addedge(n+u,n+m+v,c);
S.addedge(n+v,n+m+u,c);

}

int s=read(),t=read();
printf("%lld\n",S.spfa(s,t));

return 0;
}

F. 腾讯消消乐

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<functional>
#include<iostream>
#include<cmath>
#include<cctype>
#include<ctime>
#include<iomanip>
#include<vector>
#include<string>
#include<queue>
#include<stack>
#include<map>
#include<sstream>
#include<complex>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int>
#define pi pair<int,int>
#define vpi vector<pi >
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a
<<endl;
#define PRi2D(a,n,m) For(i,n) { \
For(j,m-1) cout<<a[i][j]<<' ';\
cout<<a[i][m]<<endl; \
}
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
int read()
{
int x=0,f=1; char ch=getchar();
while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
return x*f;
}
#define MAXN (19)
ll f[MAXN][1<<18]={0};
int gcd(int a,int b){if(!b)return a;return gcd(b,a%b);}
int g[1<<18]={},a[MAXN];
int main()
{
//  freopen("F.in","r",stdin);
//  freopen(".out","w",stdout);
int n=read(),k=read();

int tot=1<<n;
Rep(i,n) a[i]=read();
For(i,tot) {
Rep(j,n) if ((i>>j)&1) {
g[i]=gcd(g[(i)^(1<<j)],a[j]);
}
}
ll ans=0;
f[0][0]=1;
For(i,n) {
Rep(s,tot) {
Rep(l,n) if ((s >>l)&1) {
int ss=s;
Fork(r,l,n-1) if ((s>>r)&1) {
ss&=~(1<<r);
if (g[s^ss]>=k) {
f[i][s]+=f[i-1][ss];
} else break;
}
}
}
ans+=(ll)f[i][tot-1]*i%F;
ans%=F;
}
printf("%lld\n",ans);

return 0;
}