fzyzojP3412 -- [校内训练20171212]奇数-LMLPHP

fzyzojP3412 -- [校内训练20171212]奇数-LMLPHP

套路地,

考虑dfs树上搞事情

容易发现,对于(x,y)如果dfs树上距离为奇数,或者dfs树上路径中有一条边在某个简单奇环上,那么可以经过奇数条边到达

判断边在某个奇环上:

点双,点双中黑白染色,如果有一个奇环,那么点双中的所有边都在一个奇环中

询问

倍增预处理,LCA搞一下即可

#include<bits/stdc++.h>
#define il inline
#define reg register int
#define numb (ch^'0')
using namespace std;
typedef long long ll;
il void rd(int &x){
char ch;bool fl=false;
while(!isdigit(ch=getchar()))(ch=='-')&&(fl=true);
for(x=numb;isdigit(ch=getchar());x=x*+numb);
(fl==true)&&(x=-x);
}
namespace Miracle{
const int N=+;
int n,m;
struct node{
int nxt,to;
int id;
}e[*N];
int a[N][];
int hd[N],cnt=;
int ok[N],dep[N];
int fa[N][],has[N][];
int blo[N],bls;
void add(int x,int y,int d){
e[++cnt].nxt=hd[x];
e[cnt].to=y;
e[cnt].id=d;
hd[x]=cnt;
}
int dfn[N],low[N];
int df;
int be[N];
int dcc;
vector<int>mem[N];
int exi[N];//dcc exi a jihuan int sta[N],top;
int ge[N];
int rt;
void tarjan(int x){
// cout<<" tarjan "<<x<<endl;
dfn[x]=low[x]=++df;
sta[++top]=x;
blo[x]=bls;
bool fl=false;
for(reg i=hd[x];i;i=e[i].nxt){
int y=e[i].to;
if(!dfn[y]){
tarjan(y);
low[x]=min(low[x],low[y]);
if(low[y]>=dfn[x]){
if(fl||x!=rt) ge[x]=;
fl=true;
++dcc;
mem[dcc].push_back(x);
int z;
do{
z=sta[top--];
mem[dcc].push_back(z);
}while(z!=y);
}
}else low[x]=min(low[x],dfn[y]);
}
}
int co[N];//white(2) or black(1) or blank(0)
int bian[*N],num;
bool fl;
void dfs1(int x,int c,int col){
co[x]=col;
for(reg i=hd[x];i;i=e[i].nxt){
int y=e[i].to;
if(be[y]!=be[x]) continue;
bian[++num]=e[i].id;
if(!co[y]){
dfs1(y,c,col^);
}else{
if(co[y]==co[x]){
fl=false;
}
}
}
}
bool vis[N];
void dfs2(int x,int d){
dep[x]=d;
vis[x]=;
// cout<<" dfs2 "<<x<<" "<<d<<endl;
for(reg i=hd[x];i;i=e[i].nxt){
int y=e[i].to;
if(vis[y]) continue;
fa[y][]=x;
has[y][]=ok[e[i].id];
dfs2(y,d+);
}
}
bool wrk(int x,int y){
int lp=;
int tmp=dep[x]+dep[y];
if(dep[x]<dep[y]) swap(x,y);
for(reg j=;j>=;--j){
if(dep[fa[x][j]]>=dep[y]){
lp|=has[x][j];
x=fa[x][j];
}
}
if(x==y) {
if((tmp-*dep[x])%==) return true;
if(lp) return true;
return false;
}
for(reg j=;j>=;--j){
if(fa[x][j]!=fa[y][j]){
lp|=has[x][j];
lp|=has[y][j];
x=fa[x][j];y=fa[y][j];
}
}
lp|=has[x][]|has[y][];
x=fa[x][]; if((tmp-*dep[x])%==) return true;
if(lp) return true;
return false;
}
int main(){
rd(n);rd(m);
int x,y;
for(reg i=;i<=m;++i){
rd(x);rd(y);
a[i][]=x;a[i][]=y;
add(x,y,i);add(y,x,i);
}
for(reg i=;i<=n;++i){
if(!dfn[i]){
top=;
++bls;
rt=i;
tarjan(i);
}
}
//cout<<" dcc "<<dcc<<endl;
for(reg i=;i<=dcc;++i){
// cout<<" nunumumuun "<<i<<endl;
for(reg j=;j<(int)mem[i].size();++j){
// cout<<mem[i][j]<<endl;
be[mem[i][j]]=i;
co[mem[i][j]]=;
}
num=;
fl=true;
dfs1(mem[i][],i,);
if(!fl){
for(reg j=;j<=num;++j){
// cout<<" bian[i] "<<bian[j]<<endl;
ok[bian[j]]=;
}
}
}
memset(dfn,,sizeof dfn);
for(reg i=;i<=n;++i){
if(!vis[i]){
dfs2(i,);
}
}
for(reg j=;j<=;++j){
for(reg i=;i<=n;++i){
fa[i][j]=fa[fa[i][j-]][j-];
has[i][j]=has[i][j-]|has[fa[i][j-]][j-];
}
}
int q;
rd(q);
while(q--){
rd(x);rd(y);
if(blo[x]!=blo[y]){
puts("No");
}
else puts(wrk(x,y)?"Yes":"No");
}
return ;
} }
signed main(){
// freopen("data3412.in","r",stdin);
// freopen("data3412.out","w",stdout);
Miracle::main();
return ;
} /*
Author: *Miracle*
Date: 2019/2/2 13:27:37
*/
05-11 17:50