「POI2012」约会 Rendezvous

#2691. 「POI2012」约会 Rendezvous

这题我简直不想说什么了，什么素质，卡常数……

“每个顶点有且仅有一条出边”，所以是一道基环树的题，首先tarjan缩点，在缩完点后的图上求a，b的LCA，如果LCA在环内，求出a，b分别对应环中的哪一个点，显然这两个点中的一个为最优解。

我一开始是在求LCA时顺便求出的a，b对应的点，这样使常数变大，虽然在LOJ和bzoj上都A了，但是在某OJ上疯狂T94，调了一下午+一晚上……

这个可以提前一边dfs预处理出来：

void dfs2(int x,int ci,int ff)
{
    incir[x]=ci;
    for(int i=f(x);i;i=n(i))
    if(v(i)!=ff && belong[v(i)]!=belong[x])
        dfs2(v(i),ci,x);
}

for(int i=1;i<=tot;i++)
    if(scc[i].size()>1)
        for(int j=0;j<scc[i].size();j++)
            dfs2(scc[i][j],scc[i][j],d[scc[i][j]]);

感谢ooo帮忙卡常以及mikufun大佬提醒。

#include<iostream>
#include<cstring>
#include<cstdio>
#include<vector>
#include<queue>
#include<cmath>
#define rint register int
#define MAXN 500010
#define ma(x) memset(x,0,sizeof(x))
#define max(a,b) ((a)>(b)?(a):(b))
#define min(a,b) ((a)<(b)?(a):(b))
const int L=1<<20|1;
char buffer[L],*S,*T;
#define getchar() ((S==T&&(T=(S=buffer)+fread(buffer,1,L,stdin),S==T))?EOF:*S++)
using namespace std;
struct edge
{
    int u,v,nxt;
    #define u(x) ed[x].u
    #define v(x) ed[x].v
    #define n(x) ed[x].nxt
    #define v2(x) ed2[x].v
    #define n2(x) ed2[x].nxt
}ed[MAXN],ed2[MAXN];
int first[MAXN],num_e;
#define f(x) first[x]
int first2[MAXN],num_e2;
#define f2(x) first2[x]

int n,k;
int d[MAXN];
inline void add(rint u,rint v);
inline void add2(rint u,rint v);
inline void swap(rint *a,rint* b)
{
    *a = *a ^ *b;
    *b = *a ^ *b;
    *a = *a ^ *b;
}
inline int read()
{
    int s=0;char a=getchar();
    while(a<'0'||a>'9')a=getchar();
    while(a>='0'&&a<='9'){s=s*10+a-'0';a=getchar();}
    return s;
}
int dfn[MAXN],low[MAXN],cnt;
int stack[MAXN],top;
bool vi[MAXN];
int tot,belong[MAXN];
vector<int> scc[MAXN];
int sor[MAXN],ooo;
int intree[MAXN],tr;
void tarjan(int x)
{
    dfn[x]=++cnt;low[x]=cnt;
    vi[x]=1;
    stack[++top]=x;
    for(rint i=f(x);i;i=n(i))
        if(!dfn[v(i)])tarjan(v(i)),low[x]=min(low[x],low[v(i)]);
        else if(vi[v(i)])low[x]=min(low[x],low[v(i)]);
    if(dfn[x]==low[x])
    {
        tot++;vi[x]=0;ooo=0;
        while(stack[top]!=x)
        {
            belong[stack[top]]=tot;
            scc[tot].push_back(stack[top]);
            sor[stack[top]]=++ooo;
            vi[stack[top--]]=0;
        }
        sor[stack[top]]=++ooo;
        scc[tot].push_back(stack[top]);
        belong[stack[top--]]=tot;
    }
}

int dep[MAXN],fa[MAXN][21];
int bin[21];
void dfs(int x,int ff,int de,int tr)
{
    fa[x][0]=ff;dep[x]=de;intree[x]=tr;
    for(rint i=f2(x);i;i=n2(i))
        if(v2(i)!=ff && !dep[v2(i)])
            dfs(v2(i),x,de+1,tr);
}
int LCA(int a,int b,int x,int y,int &xi,int &yi,int &xx,int &yy)
{
    xi=yi=0;xx=a;yy=b;
    bool pd=0;
    if(dep[x]>dep[y]){swap(x,y);swap(xx,yy);pd=1;}
    if(dep[x]!=dep[y])
    {
        while(dep[x]!=dep[y]-1)
            for(rint i=0;;i++)
            if(dep[fa[y][i]]-1<dep[x])
            {y=fa[y][i-1];yi+=bin[i-1];break;}
        yy=scc[y][0];yy=d[yy];
        y=fa[y][0],yi++;
    }
    if(x==y)
    {
        if(pd){swap(xi,yi);swap(xx,yy);}
        return y;
    }
    while(fa[x][0]!=fa[y][0])
        for(rint i=0;;i++)
        if(fa[x][i]==fa[y][i])    
        {x=fa[x][i-1],y=fa[y][i-1];xi+=bin[i-1],yi+=bin[i-1];break;}
    if(pd){swap(xi,yi);swap(x,y);}++xi,++yi;
    xx=d[scc[x][0]],yy=d[scc[y][0]];
    return fa[x][0];
}
int du[MAXN];
signed main()
{
//    freopen("1.in","r",stdin);
//    freopen("in.txt","r",stdin);

    bin[0]=1;for(rint i=1;i<20;i++)bin[i]=bin[i-1]<<1;
    n=read(),k=read();
    for(rint i=1;i<=n;i++){d[i]=read();add(d[i],i);}
    for(rint i=1;i<=n;i++)
        if(!dfn[i])tarjan(i);
    for(rint i=1;i<=num_e;i++)
        if(belong[u(i)]!=belong[v(i)])
            add2(belong[u(i)],belong[v(i)]),du[belong[v(i)]]++;
    for(rint i=1;i<=tot;i++)
        if(!du[i])dfs(i,0,1,++tr);
    for(rint i=1;i<20;i++)
        for(rint j=1;j<=tot;j++)
            fa[j][i]=fa[fa[j][i-1]][i-1];
    int a,b,xi,yi,xx,yy;
    int lca,t1,t2,x1,x2,y1,y2;
    for(rint i=1;i<=k;i++)
    {
        a=read(),b=read();
        if(intree[belong[a]]!=intree[belong[b]]){puts("-1 -1");continue;}
        lca=LCA(a,b,belong[a],belong[b],xi,yi,xx,yy);
        if(!lca){puts("-1 -1");continue;}
        if(scc[lca].size()==1){printf("%d %d
",xi,yi);continue;}
        t1=(sor[xx]-sor[yy]+scc[belong[xx]].size()),
        t2=(sor[yy]-sor[xx]+scc[belong[xx]].size());
        if(t1>=scc[belong[xx]].size())t1-=scc[belong[xx]].size();
        if(t2>=scc[belong[xx]].size())t2-=scc[belong[xx]].size();
        swap(t1,t2);
        x1=xi,y1=yi+t2;
        x2=xi+t1,y2=yi;
        int ma1=max(x1,y1),ma2=max(x2,y2),mi1=min(x1,y1),mi2=min(x2,y2);
        if(ma1!=ma2){ma1<ma2?printf("%d %d
",x1,y1):printf("%d %d
",x2,y2);}
        else if(mi1!=mi2){mi1<mi2?printf("%d %d
",x1,y1):printf("%d %d
",x2,y2);}
        else{x1>=y1?printf("%d %d
",x1,y1):printf("%d %d
",x2,y2);}
    }
}
inline void add(rint u,rint v)
{
    u(++num_e)=u;
    v(num_e)=v;
    n(num_e)=f(u);
    f(u)=num_e;
}
inline void add2(rint u,rint v)
{
    v2(++num_e2)=v;
    n2(num_e2)=f2(u);
    f2(u)=num_e2;
}

#include<iostream>
#include<cstring>
#include<cstdio>
#include<vector>
#include<queue>
#include<cmath>
#define rint register int
#define MAXN 500010
#define ma(x) memset(x,0,sizeof(x))
#define max(a,b) ((a)>(b)?(a):(b))
#define min(a,b) ((a)<(b)?(a):(b))
const int L=1<<20|1;
char buffer[L],*S,*T;
#define getchar() ((S==T&&(T=(S=buffer)+fread(buffer,1,L,stdin),S==T))?EOF:*S++)
using namespace std;
struct edge
{
    int u,v,nxt;
    #define u(x) ed[x].u
    #define v(x) ed[x].v
    #define n(x) ed[x].nxt
    #define v2(x) ed2[x].v
    #define n2(x) ed2[x].nxt
}ed[MAXN],ed2[MAXN];
int first[MAXN],num_e;
#define f(x) first[x]
int first2[MAXN],num_e2;
#define f2(x) first2[x]

int n,k;
int d[MAXN];
inline void add(rint u,rint v);
inline void add2(rint u,rint v);
inline void swap(rint *a,rint* b)
{
    *a = *a ^ *b;
    *b = *a ^ *b;
    *a = *a ^ *b;
}
inline int read()
{
    int s=0;char a=getchar();
    while(a<'0'||a>'9')a=getchar();
    while(a>='0'&&a<='9'){s=s*10+a-'0';a=getchar();}
    return s;
}
int dfn[MAXN],low[MAXN],cnt;
int stack[MAXN],top;
bool vi[MAXN];
int tot,belong[MAXN];
vector<int> scc[MAXN];
int sor[MAXN],ooo;
int intree[MAXN],tr;
int incir[MAXN],ci;
void tarjan(int x)
{
    dfn[x]=++cnt;low[x]=cnt;
    vi[x]=1;
    stack[++top]=x;
    for(rint i=f(x);i;i=n(i))
        if(!dfn[v(i)])tarjan(v(i)),low[x]=min(low[x],low[v(i)]);
        else if(vi[v(i)])low[x]=min(low[x],low[v(i)]);
    if(dfn[x]==low[x])
    {
        tot++;vi[x]=0;ooo=0;
        while(stack[top]!=x)
        {
            belong[stack[top]]=tot;
            scc[tot].push_back(stack[top]);
            sor[stack[top]]=++ooo;
            vi[stack[top--]]=0;
        }
        sor[stack[top]]=++ooo;
        scc[tot].push_back(stack[top]);
        belong[stack[top--]]=tot;
    }
}

int dep[MAXN],fa[MAXN][21];
int bin[21];
void dfs(int x,int ff,int de,int tr)
{
    fa[x][0]=ff;dep[x]=de;intree[x]=tr;
    for(rint i=f2(x);i;i=n2(i))
        if(v2(i)!=ff && !dep[v2(i)])
            dfs(v2(i),x,de+1,tr);
}
void dfs2(int x,int ci,int ff)
{
    incir[x]=ci;
    for(int i=f(x);i;i=n(i))
    if(v(i)!=ff && belong[v(i)]!=belong[x])
        dfs2(v(i),ci,x);
}
int LCA(int x,int y)
{
    if(dep[x]>dep[y])swap(x,y);
        while(dep[x]!=dep[y])
            for(rint i=0;;i++)
            if(dep[fa[y][i]]<dep[x])
            {y=fa[y][i-1];break;}
    if(x==y){return y;}
    while(fa[x][0]!=fa[y][0])
        for(rint i=0;;i++)
        if(fa[x][i]==fa[y][i])    
        {x=fa[x][i-1],y=fa[y][i-1];break;}
    return fa[x][0];
}
int du[MAXN];
signed main()
{
//    freopen("1.in","r",stdin);
//    freopen("in.txt","r",stdin);

    bin[0]=1;for(rint i=1;i<20;i++)bin[i]=bin[i-1]<<1;
    n=read(),k=read();
    for(rint i=1;i<=n;i++){d[i]=read();add(d[i],i);}
    for(rint i=1;i<=n;i++)
        if(!dfn[i])tarjan(i);
    for(rint i=1;i<=num_e;i++)
        if(belong[u(i)]!=belong[v(i)])
            add2(belong[u(i)],belong[v(i)]),du[belong[v(i)]]++;
    for(rint i=1;i<=tot;i++)
        if(!du[i])dfs(i,0,1,++tr);
    for(rint i=1;i<20;i++)
        for(rint j=1;j<=tot;j++)
            fa[j][i]=fa[fa[j][i-1]][i-1];
    for(int i=1;i<=tot;i++)
    if(scc[i].size()>1)
        for(int j=0;j<scc[i].size();j++)
            dfs2(scc[i][j],scc[i][j],d[scc[i][j]]);
    int a,b,xi,yi,xx,yy;
    int lca,t1,t2,x1,x2,y1,y2;
    for(rint i=1;i<=k;i++)
    {
        a=read(),b=read();
        if(intree[belong[a]]!=intree[belong[b]]){puts("-1 -1");continue;}
        if(incir[a]==incir[b])
        {
            lca=LCA(belong[a],belong[b]);
            printf("%d %d
",dep[belong[a]]-dep[lca],dep[belong[b]]-dep[lca]);
            continue;
        }
        else
            xx=incir[a],yy=incir[b],xi=dep[belong[a]]-dep[belong[incir[a]]],yi=dep[belong[b]]-dep[belong[incir[b]]];
        t1=(sor[xx]-sor[yy]+scc[belong[xx]].size()),
        t2=(sor[yy]-sor[xx]+scc[belong[xx]].size());
        if(t1>=scc[belong[xx]].size())t1-=scc[belong[xx]].size();
        if(t2>=scc[belong[xx]].size())t2-=scc[belong[xx]].size();
        swap(t1,t2);
        x1=xi,y1=yi+t2;
        x2=xi+t1,y2=yi;
        int ma1=max(x1,y1),ma2=max(x2,y2),mi1=min(x1,y1),mi2=min(x2,y2);
        if(ma1!=ma2){ma1<ma2?printf("%d %d
",x1,y1):printf("%d %d
",x2,y2);}
        else if(mi1!=mi2){mi1<mi2?printf("%d %d
",x1,y1):printf("%d %d
",x2,y2);}
        else{x1>=y1?printf("%d %d
",x1,y1):printf("%d %d
",x2,y2);}
    }
}
inline void add(rint u,rint v)
{
    u(++num_e)=u;
    v(num_e)=v;
    n(num_e)=f(u);
    f(u)=num_e;
}
inline void add2(rint u,rint v)
{
    v2(++num_e2)=v;
    n2(num_e2)=f2(u);
    f2(u)=num_e2;
}