专项测试(图论2)
改题历程极其艰辛
再一次挫伤了我的自信心......
T1 收藏家
对时间建立节点，最大流就行了
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<<3)+(s<<1)+ch-'0';ch=getchar();}
return s*t;
}
const int inf=0x3f3f3f3f3f3f3f3f;
const int N=10005;
int T,n,m,s=9001,t=9002,a[N];
struct E{int to,nxt,val;}e[N*10];
int head[N],hea[N],rp=1;
void clear(){
memset(head,0,sizeof(head));rp=1;
}
void add_edg(int x,int y,int z){
e[++rp].to=y;e[rp].val=z;
e[rp].nxt=head[x];head[x]=rp;
}
int dis[N];
bool bfs(){
memset(dis,0x3f,sizeof(dis));
memcpy(head,hea,sizeof(hea));
queue<int> q;while(!q.empty())q.pop();
q.push(s);dis[s]=0;
while(!q.empty()){
int x=q.front();q.pop();
for(int i=head[x];i;i=e[i].nxt){
int y=e[i].to;
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){
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(rest,e[i].val));
if(go)e[i].val-=go,e[i^1].val+=go,rest-=go;
else dis[y]=0;
if(!rest)break;
}
return in-rest;
}
int dinic(){
int ret=0;memcpy(hea,head,sizeof(head));
while(bfs())ret+=dfs(s,inf);
return ret;
}
int now[N],cn,p=1;
signed main(){
T=read();
while(T--){
clear();
cn=n=read();m=read();
fo(i,1,n)now[i]=i;
fo(i,1,n){
a[i]=read();
if(a[i]==0)continue;
add_edg(s,i,1);
add_edg(i,s,0);
}
fo(i,1,m){
int x=read(),y=read();
add_edg(now[x],now[y],1);
add_edg(now[y],now[x],1);
if(x!=1){add_edg(now[x],++cn,a[x]);add_edg(cn,now[x],0);now[x]=cn;}
if(y!=1){add_edg(now[y],++cn,a[y]);add_edg(cn,now[y],0);now[y]=cn;}
}
add_edg(1,t,a[1]);add_edg(t,1,0);
printf("%lld\n",dinic());
}
return 0;
}
T2 旅行
发现转移方程是个分数规划，于是二分，用最大闭合子图判断
AC_code
#include<bits/stdc++.h>
using namespace std;
#define double long double
#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<<3)+(s<<1)+ch-'0';ch=getchar();}
return s*t;
}
const double eps=1e-10;
const double inf=1e9;
const int N=55;
const int M=505;
const int K=2005;
int n,m,k;
struct E{int to,nxt,id;}e[M*2],ek[K*2];
int head[N],hk[M],rp,rk,du[N];
void add_e(int x,int y,int id){
e[++rp].to=y;e[rp].id=id;du[y]++;
e[rp].nxt=head[x];head[x]=rp;
}
void add_k(int x,int y){
ek[++rk].to=y;ek[rk].nxt=hk[x];hk[x]=rk;
}
int ji[M],ys[M],cj;
double dp[N],f[M];
struct W{
int s=501,t=502;
struct E{int to,nxt;double val;}e[K*4];
int head[M],hea[M],rp=1;
void add_edg(int x,int y,double z){
e[++rp].to=y;e[rp].val=z;
e[rp].nxt=head[x];head[x]=rp;
}
int dis[M];
bool bfs(){
memset(dis,0x3f,sizeof(dis));
memcpy(head,hea,sizeof(hea));
queue<int> q;while(!q.empty())q.pop();
q.push(s);dis[s]=0;
while(!q.empty()){
int x=q.front();q.pop();
// cout<<"X "<<x<<endl;
for(int i=head[x];i;i=e[i].nxt){
int y=e[i].to;
// if(x==2)cout<<x<<" "<<y<<" "<<e[i].val<<" "<<dis[y]<<endl;
if(fabs(e[i].val)<eps||dis[y]<=dis[x]+1)continue;
dis[y]=dis[x]+1;q.push(y);
if(y==t)return true;
}
}
return false;
}
double dfs(int x,double in){
if(x==t)return in;
double rest=in,go=0;
for(int i=head[x];i;head[x]=i=e[i].nxt){
int y=e[i].to;
if(fabs(e[i].val)<eps||dis[y]!=dis[x]+1)continue;
go=dfs(y,min(rest,e[i].val));
if(go)e[i].val-=go,e[i^1].val+=go,rest-=go;
else dis[y]=0;
if(fabs(rest)<eps)break;
}
return in-rest;
}
double dinic(){
double ret=0;
memset(head,0,sizeof(head));rp=1;
fo(i,1,cj)ys[ji[i]]=i;
// cout<<"one"<<endl;
fo(i,1,cj){
// cout<<i<<" "<<ji[i]<<" "<<f[ji[i]]<<endl;
if(f[ji[i]]>eps){
ret+=f[ji[i]];
add_edg(s,i,f[ji[i]]);
add_edg(i,s,0);
}
else {
add_edg(i,t,-f[ji[i]]);
add_edg(t,i,0);
}
}
fo(x,1,cj){
for(int i=hk[ji[x]];i;i=ek[i].nxt){
int y=ys[ek[i].to];
// cout<<"SB"<<" "<<x<<" "<<ji[x]<<" "<<ji[y]<<" "<<inf<<" "<<"ZZ"<<endl;
add_edg(x,y,inf);
add_edg(y,x,0);
}
}
// cout<<ret<<endl;
// cout<<head[1]<<endl;
memcpy(hea,head,sizeof(head));
while(bfs())ret-=dfs(s,inf);//cout<<"ZZ"<<endl;
// cout<<ret<<endl;
return ret;
}
}w;
int tpn[N],ipn[N],cnt;
void topu(){
queue<int> q;while(!q.empty())q.pop();
fo(i,1,n)if(!du[i])q.push(i);
while(!q.empty()){
int x=q.front();q.pop();
tpn[x]=++cnt;ipn[cnt]=x;
for(int i=head[x];i;i=e[i].nxt){
int y=e[i].to;
if(!--du[y])q.push(y);
}
}
}
signed main(){
n=read();m=read();k=read();
fo(i,1,m){
int x=read(),y=read();
add_e(x,y,i);
}
fo(i,1,k){
int x=read(),y=read();
add_k(x,y);
}
topu();
// cout<<"SB"<<endl;
fu(o,cnt,1){
int x=ipn[o];cj=0;
if(!head[x]){dp[x]=0;continue;}
double l=0,r=0,mid;
for(int i=head[x];i;i=e[i].nxt){
int y=e[i].to;
ji[++cj]=e[i].id;
r=max(r,dp[y]+1);
}
// cout<<l<<" "<<r<<endl;
while(r-l>eps){
mid=(r+l)/2;
for(int i=head[x];i;i=e[i].nxt){
int y=e[i].to;
f[e[i].id]=dp[y]+1-mid;
}
if(w.dinic()>=eps)l=mid;
else r=mid;
}
dp[x]=l;
// cout<<"dp"<<" "<<x<<" "<<dp[x]<<endl;
}
printf("%.10Lf",dp[1]);
}
T3 字符串
\(LCT\)维护\(SAM\)，于是乎，我们需要一颗主席树，维护最长匹配段
注意，只要用到的节点，就\(splay\)一下，防止没有标记下放
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 N=1e5+5;
int rt[N],n,m,lans,R;
struct ZXS{
struct POT{int mx,ls,rs;}tr[N*400];
int seg;
void pushup(int x){tr[x].mx=max(tr[tr[x].ls].mx,tr[tr[x].rs].mx);}
void ins(int pr,int &x,int l,int r,int pos,int v){
x=++seg;tr[x]=tr[pr];
if(l==r)return tr[x].mx=v,void();
int mid=l+r>>1;
if(pos<=mid)ins(tr[pr].ls,tr[x].ls,l,mid,pos,v);
else ins(tr[pr].rs,tr[x].rs,mid+1,r,pos,v);
pushup(x);return ;
}
int query(int x,int l,int r,int ql,int qr){
if(!x)return 0;
if(ql<=l&&r<=qr)return tr[x].mx;
int mid=l+r>>1,ret=0;
if(ql<=mid)ret=max(ret,query(tr[x].ls,l,mid,ql,qr));
if(qr>mid)ret=max(ret,query(tr[x].rs,mid+1,r,ql,qr));
return ret;
}
}zxs;
struct LCT{
struct POT{int len,lst,tag,son[2],fa;}tr[N*2];
int pth[N*2],pt;
void pusht(int x,int v){tr[x].lst=tr[x].tag=v;}
void pushdown(int x){
if(!tr[x].tag)return ;
if(tr[x].son[0])pusht(tr[x].son[0],tr[x].tag);
if(tr[x].son[1])pusht(tr[x].son[1],tr[x].tag);
tr[x].tag=0;
}
bool nroot(int x){return tr[tr[x].fa].son[0]==x||tr[tr[x].fa].son[1]==x;}
int get(int x){return tr[tr[x].fa].son[1]==x;}
void rotate(int x){
int y=tr[x].fa,z=tr[y].fa;
int xpos=get(x),ypos=get(y);
if(nroot(y))tr[z].son[ypos]=x;
tr[x].fa=z;tr[y].fa=x;
tr[y].son[xpos]=tr[x].son[xpos^1];
tr[tr[x].son[xpos^1]].fa=y;
tr[x].son[xpos^1]=y;
}
void splay(int x){
int now=x;pth[++pt]=now;
while(nroot(now))pth[++pt]=now=tr[now].fa;
while(pt)pushdown(pth[pt--]);
while(nroot(x)){
int y=tr[x].fa,z=tr[y].fa;
int xpos=get(x),ypos=get(y);
if(nroot(y)){
if(xpos==ypos)rotate(y);
else rotate(x);
}
rotate(x);
}
}
void access(int x,int id){
for(int y=0,now=x;now;y=now,now=tr[now].fa){
splay(now);tr[now].son[1]=y;
if(now!=1&&tr[now].lst&&zxs.query(rt[id],1,R,tr[now].lst,tr[now].lst)<tr[now].len)
zxs.ins(rt[id],rt[id],1,R,tr[now].lst,tr[now].len);
}
}
void link(int x,int y){
splay(x);splay(y);tr[x].fa=y;
}
void links(int x,int y){
splay(x);splay(y);tr[x].fa=y;
tr[y].son[1]=x;
}
bool cut(int x,int y){
bool ret=false;
splay(x);splay(y);tr[x].fa=0;
if(tr[y].son[1]==x)tr[y].son[1]=0,ret=true;
return ret;
}
}lct;
struct SAM{
struct POT{int len,son[26],fail;}tr[N*2];
int seg,las;
SAM(){seg=las=1;}
void ins(int c,int id){
int p=las,np=++seg;las=np;
lct.tr[np].len=tr[np].len=tr[p].len+1;
while(p&&!tr[p].son[c])tr[p].son[c]=np,p=tr[p].fail;
if(!p){tr[np].fail=1;lct.link(np,1);}
else {
int q=tr[p].son[c];
if(tr[q].len==tr[p].len+1){tr[np].fail=q;lct.link(np,q);}
else {
int nq=++seg;lct.splay(q);
tr[nq]=tr[q];lct.tr[nq]=lct.tr[q];
lct.tr[nq].son[0]=lct.tr[nq].son[1]=lct.tr[nq].fa=0;
if(lct.cut(q,tr[q].fail))lct.links(nq,tr[q].fail);
else lct.link(nq,tr[q].fail);
tr[nq].len=lct.tr[nq].len=tr[p].len+1;
tr[np].fail=tr[q].fail=nq;
lct.link(np,nq);lct.links(q,nq);
while(p&&tr[p].son[c]==q)tr[p].son[c]=nq,p=tr[p].fail;
}
}
rt[id]=rt[id-1];lct.access(las,id);lct.splay(las);lct.pusht(las,id);
}
}sam;
int work(int s,int t){
// if(s>t)return 0;
int l=0,r=t-s,mid;
while(l<r){
mid=l+r+1>>1;
if(zxs.query(rt[t],1,R,s+mid-1,t)>=mid)l=mid;
else r=mid-1;
}
return l;
}
char a[N];
signed main(){
scanf("%s",a+1);m=read();
n=strlen(a+1);R=n+m;
fo(i,1,n)sam.ins(a[i]-'a',i);
while(m--){
int tp=read(),l,r;
if(tp==1){
scanf("%s",a+1);a[1]=(a[1]-'a'+lans)%26+'a';
sam.ins(a[1]-'a',++n);
}
else {
l=(read()-1+lans)%n+1,r=(read()-1+lans)%n+1;
if(l>r)swap(l,r);
printf("%d\n",lans=work(l,r));
}
}
}
QQ:2953174821
