省选模拟6
所以说我爆蛋了......
T1 高中数列题
化式子后可以一直递归下去
AC_code
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define fo(i,x,y) for(int i=(x);i<=(y);i++)
#define fu(i,x,y) for(int i=(x);i>=(y);i--)
int read(){
int s=0,t=1;char ch=getchar();
while(!isdigit(ch)){if(ch=='-')t=-1;ch=getchar();}
while(isdigit(ch)){s=s*10+ch-'0';ch=getchar();}
return s*t;
}
const int mod=1004535809;
int ksm(int x,int y){
int ret=1;x=(x%mod+mod)%mod;
while(y){
if(y&1)ret=ret*x%mod;
x=x*x%mod;y>>=1;
}return ret;
}
unordered_map<int,int> mp;
int inv(int x){
if(mp.find(x)!=mp.end())return mp[x];
else return mp[x]=ksm(x,mod-2);
}
int lglr(int *y,int c,int t){
if(t<0)return 0;
if(t<=c)return y[t];
t%=mod;
int bas=(c&1)?-1:1,tmp=1,ret=0;
fo(i,1,c)tmp=tmp*(t-i)%mod;
fo(i,1,c)tmp=tmp*inv(i)%mod;
fo(i,0,c){
ret=(ret+bas*y[i]*tmp+mod)%mod;
tmp=tmp*(t-i)%mod*inv(t-i-1)%mod;
tmp=tmp*(c-i)%mod*inv(i+1)%mod;
bas=-bas;
}
return (ret%mod+mod)%mod;
}
int nn,m,a,b,c,p[25];
int get(int x){
int tmp=1,ret=0;
fo(i,0,m)ret=(ret+tmp*p[i])%mod,tmp=tmp*x%mod;
return ret;
}
int f[105][2005],sf[105][2005];
int P(int x){return (x+b)/c;}
int Q(int x){if((nn+b)/c<x)return nn+1;return x*c-b;}
int sol(int d,int n,int c){
if(!n)return 0;
int ret=a*lglr(sf[d],c+1,n)%mod,nc=c+1+m;
fo(i,0,nc+1){
if(n<Q(i))break;
f[d+1][i]=get(i)*(lglr(sf[d],c+1,n)-lglr(sf[d],c+1,Q(i)-1)+mod)%mod;
}
// sf[d+1][0]=f[d+1][0];
fo(i,1,nc+1)sf[d+1][i]=(sf[d+1][i-1]+f[d+1][i])%mod;
ret=(ret+sol(d+1,P(n),nc))%mod;
// cout<<ret<<endl;
return ret;
}
signed main(){
freopen("seq.in","r",stdin);
freopen("seq.out","w",stdout);
nn=read();a=read();b=read();c=read();m=read();
fo(i,0,m)p[i]=read()%mod;
fo(i,0,m+1)f[1][i]=get(i);
// sf[1][0]=f[1][0];
fo(i,1,m+1)sf[1][i]=(sf[1][i-1]+f[1][i])%mod;
printf("%lld",(a+sol(1,nn,m))%mod);
return 0;
}
T2 机动车限行
类似士兵占领，网络流跑可以省去多少
AC_code
#include<bits/stdc++.h>
using namespace std;
#define fo(i,x,y) for(int i=(x);i<=(y);i++)
#define fu(i,x,y) for(int i=(x);i>=(y);i--)
int read(){
int s=0,t=1;char ch=getchar();
while(!isdigit(ch)){if(ch=='-')t=-1;ch=getchar();}
while(isdigit(ch)){s=s*10+ch-'0';ch=getchar();}
return s*t;
}
const int inf=0x3f3f3f3f;
const int N=1e5+5;
struct E{int to,nxt,val;}e[N*8];
int hea[N*2],head[N*2],s=2e5+1,t=2e5+2,rp;
void add_edg(int x,int y,int z){
e[++rp].to=y;e[rp].nxt=head[x];
head[x]=rp;e[rp].val=z;
}
int dis[N*2];
bool bfs(){
memcpy(head,hea,sizeof(hea));
memset(dis,0x3f,sizeof(dis));
queue<int> q;while(!q.empty())q.pop();
dis[s]=0;q.push(s);
while(!q.empty()){
int x=q.front();q.pop();
// cout<<x<<endl;
for(int i=head[x];i;i=e[i].nxt){
int y=e[i].to;//cout<<y<<" "<<e[i].val<<endl;
if(!e[i].val||dis[y]<=dis[x]+1)continue;
dis[y]=dis[x]+1;q.push(y);
if(y==t)return true;
}
}
return false;
}
int dfs(int x,int in){
// cout<<x<<" "<<in<<endl;
if(x==t)return in;
int rest=in,go=0;
for(int i=head[x];i;head[x]=i=e[i].nxt){
int y=e[i].to;
if(!e[i].val||dis[y]!=dis[x]+1)continue;
go=dfs(y,min(e[i].val,rest));
if(go)rest-=go,e[i].val-=go,e[i^1].val+=go;
else dis[y]=0;
if(!rest)break;
}
return in-rest;
}
int dinic(){
memcpy(hea,head,sizeof(head));
int ret=0;
while(bfs())ret+=dfs(s,inf);
return ret;
}
int fa1[N],vi1[N];
int find1(int x){return fa1[x]==x?x:fa1[x]=find1(fa1[x]);}
int fa2[N],vi2[N],vis[N*2];
int find2(int x){return fa2[x]==x?x:fa2[x]=find2(fa2[x]);}
int n,m,bl[N],ans;
struct D{int x,y;}d[N*2];
int id[N];
signed main(){
freopen("restriction.in","r",stdin);
freopen("restriction.out","w",stdout);
n=read();m=read();
fo(i,1,n)bl[i]=read();
fo(i,1,m)d[i].x=read(),d[i].y=read();
fo(i,1,n)fa1[i]=i,fa2[i]=i,vi1[i]=0,vi2[i]=0;
fo(i,1,2*n)vis[i]=0;
fo(i,1,m){
if(bl[d[i].x]!=2&&bl[d[i].y]!=2){
fa1[find1(d[i].x)]=find1(d[i].y);
}
if(bl[d[i].x]!=3&&bl[d[i].y]!=3){
fa2[find2(d[i].x)]=find2(d[i].y);
}
}
memset(head,0,sizeof(head));rp=1;
fo(i,1,n){
if(bl[i]!=1)continue;
vi1[find1(i)]=true;
vi2[find2(i)]=true;
// cout<<find1(i)<<" "<<find2(i)<<endl;
add_edg(find1(i),find2(i)+n,inf);
add_edg(find2(i)+n,find1(i),0);
id[i]=rp;
}ans=0;
// cout<<rp<<endl;
fo(i,1,n){
if(vi1[i]){ans++;
// cout<<i<<endl;
add_edg(s,i,1);
add_edg(i,s,0);
}
if(vi2[i]){ans++;
// cout<<i+n<<endl;
add_edg(i+n,t,1);
add_edg(t,i+n,0);
}
}
// cout<<ans<<endl;
// cout<<rp<<endl;
ans-=dinic();
printf("%d ",ans);
fo(i,1,n){
if(bl[i]!=1)continue;
if(e[id[i]].val){
printf("%d ",i);
vis[find1(i)]=vis[find2(i)+n]=true;
}
}
fo(i,1,n){
if(bl[i]!=1)continue;
if(!vis[find1(i)]||!vis[find2(i)+n]){
printf("%d ",i);
vis[find1(i)]=vis[find2(i)+n]=true;
}
}
printf("\n");
fo(i,1,n)fa1[i]=i,fa2[i]=i,vi1[i]=0,vi2[i]=0;
fo(i,1,2*n)vis[i]=0;
fo(i,1,m){
if(bl[d[i].x]!=1&&bl[d[i].y]!=1){
fa1[find1(d[i].x)]=find1(d[i].y);
}
if(bl[d[i].x]!=3&&bl[d[i].y]!=3){
fa2[find2(d[i].x)]=find2(d[i].y);
}
}
memset(head,0,sizeof(head));rp=1;
fo(i,1,n){
if(bl[i]!=2)continue;
vi1[find1(i)]=true;
vi2[find2(i)]=true;
// cout<<find1(i)<<" "<<find2(i)<<endl;
add_edg(find1(i),find2(i)+n,inf);
add_edg(find2(i)+n,find1(i),0);
id[i]=rp;
}ans=0;
// cout<<rp<<endl;
fo(i,1,n){
if(vi1[i]){ans++;
// cout<<i<<endl;
add_edg(s,i,1);
add_edg(i,s,0);
}
if(vi2[i]){ans++;
// cout<<i+n<<endl;
add_edg(i+n,t,1);
add_edg(t,i+n,0);
}
}
// cout<<ans<<endl;
// cout<<rp<<endl;
ans-=dinic();
printf("%d ",ans);
fo(i,1,n){
if(bl[i]!=2)continue;
if(e[id[i]].val){
printf("%d ",i);
vis[find1(i)]=vis[find2(i)+n]=true;
}
}
fo(i,1,n){
if(bl[i]!=2)continue;
if(!vis[find1(i)]||!vis[find2(i)+n]){
printf("%d ",i);
vis[find1(i)]=vis[find2(i)+n]=true;
}
}
printf("\n");
fo(i,1,n)fa1[i]=i,fa2[i]=i,vi1[i]=0,vi2[i]=0;
fo(i,1,2*n)vis[i]=0;
fo(i,1,m){
if(bl[d[i].x]!=2&&bl[d[i].y]!=2){
fa1[find1(d[i].x)]=find1(d[i].y);
}
if(bl[d[i].x]!=1&&bl[d[i].y]!=1){
fa2[find2(d[i].x)]=find2(d[i].y);
}
}
memset(head,0,sizeof(head));rp=1;
fo(i,1,n){
if(bl[i]!=3)continue;
vi1[find1(i)]=true;
vi2[find2(i)]=true;
// cout<<find1(i)<<" "<<find2(i)<<endl;
add_edg(find1(i),find2(i)+n,inf);
add_edg(find2(i)+n,find1(i),0);
id[i]=rp;
}ans=0;
// cout<<rp<<endl;
fo(i,1,n){
if(vi1[i]){ans++;
// cout<<i<<endl;
add_edg(s,i,1);
add_edg(i,s,0);
}
if(vi2[i]){ans++;
// cout<<i+n<<endl;
add_edg(i+n,t,1);
add_edg(t,i+n,0);
}
}
// cout<<ans<<endl;
// cout<<rp<<endl;
ans-=dinic();
printf("%d ",ans);
fo(i,1,n){
if(bl[i]!=3)continue;
if(e[id[i]].val){
printf("%d ",i);
vis[find1(i)]=vis[find2(i)+n]=true;
}
}
fo(i,1,n){
if(bl[i]!=3)continue;
if(!vis[find1(i)]||!vis[find2(i)+n]){
printf("%d ",i);
vis[find1(i)]=vis[find2(i)+n]=true;
}
}
return 0;
}
T3 城市绿化
直接按深度分层
然后询问和某一个点的距离，分治
AC_code
#include<bits/stdc++.h>
#include "green.h"
using namespace std;
#define fo(i,x,y) for(int i=(x);i<=(y);i++)
#define fu(i,x,y) for(int i=(x);i>=(y);i--)
int visit(int x,int y);
const int N=1e5+5;
int dep[N],fa[N],mxd;
vector<int> vec[N];
int dis[N];
bool com(int x,int y){return dis[x]<dis[y];}
void sol(int d,int l1,int r1,int l2,int r2){
// printf("%d %d %d %d %d\n",d,l1,r1,l2,r2);
if(l1>r1||l2>r2)return ;
if(l1==r1){
// printf("%d %d\n",l2,r2);
fo(i,l2,r2){
int x=vec[d+1][i];
// printf("s%d %d\n",i,x);
fa[x]=vec[d][l1];
}
return ;
}
dis[vec[d][l1]]=0;
fo(i,l1+1,r1)dis[vec[d][i]]=visit(vec[d][l1],vec[d][i]);//printf("%d\n",i);
fo(i,l2,r2)dis[vec[d+1][i]]=visit(vec[d][l1],vec[d+1][i]);
sort(vec[d].begin()+l1,vec[d].begin()+r1+1,com);
sort(vec[d+1].begin()+l2,vec[d+1].begin()+r2+1,com);
// printf("%d\n",vec[d][1]);
int s1=l1,s2=l2;
while(dis[vec[d+1][s2]]==1)fa[vec[d+1][s2]]=vec[d][l1],s2++;
int t2=s2;s1++;
// printf("%d %d %d\n",s1,s2,t2);
fo(i,l1+1,r1){
// printf("%d %d %d\n",i,dis[vec[d][i]],dis[vec[d][i+1]]);
if(i==r1||dis[vec[d][i]]!=dis[vec[d][i+1]]){
while(t2<r2){
if(dis[vec[d+1][t2]]!=dis[vec[d+1][t2+1]])break;
t2++;
}
// printf("%d %d %d %d\n",i,s1,s2,t2);
if(dis[vec[d][s1]]+1==dis[vec[d+1][s2]]){
// printf("%d %d %d %d %d\n",d,s1,i,s2,t2);
sol(d,s1,i,s2,t2);
s2=t2+1;t2=s2;
}s1=i+1;
if(s2>r2||s1>r1)break;
}
}
}
void findtree(int n,int m,int *p){
fo(i,2,n){
dep[i]=visit(1,i);
mxd=max(mxd,dep[i]);
vec[dep[i]].push_back(i);
}
for(int i:vec[1])p[i]=1;
fo(i,1,mxd-1){
sol(i,0,(int)vec[i].size()-1,0,(int)vec[i+1].size()-1);
for(int j:vec[i+1])p[j]=fa[j];//printf("%d %d\n",j,fa[j]);
}
}
QQ:2953174821
