Induction (a): And look up the set

The round in my eyes. 1: Simple and check set

int fa[maxn];int find(int x) {    return fa[x]==x?x:fa[x]=find(fa[x]);}void un(int x,int y) {    fa[find(x)]=find(y);}

Round 2: Merging by rank

int fa[maxn],siz[maxn];int find(int x) {    return fa[x]==x?x:find(fa[x]);}void un(int x,int y) {    if(siz[x=find(x)]>siz[y=find(y)])        fa[x]=y,siz[y]+=siz[x];    else fa[y]=x,siz[x]+=siz[y];}

Example 1: Repairing highways

Surface

Can be counted as a unicom block, or by rank merge + path compression

Unicom, and together, siz add up, if siz=n, the direct output time can be.

10min cut.

Code:

#include<bits/stdc++.h>const int maxn=1000+5;const int maxm=1e5+5;int fa[maxn],siz[maxn];struct Edge {    int x,y,t;}e[maxm];int find(int x) {    return fa[x]==x?x:fa[x]=find(fa[x]);}void un(int x,int y) {    if(x==y) return ;    fa[x]=y;    siz[y]+=siz[x];}bool cmp(const Edge &a,const Edge &b) {    return a.t<b.t;}int main() {    int n,m;scanf("%d%d",&n,&m);    for(int i=1;i<=n;i++) fa[i]=i,siz[i]=1;    for(int i=1;i<=m;i++)        scanf("%d%d%d",&e[i].x,&e[i].y,&e[i].t);    std::sort(e+1,e+m+1,cmp);    for(int i=1;i<=m;i++) {        int xx=find(e[i].x),yy=find(e[i].y);        un(xx,yy);        if(siz[yy]==n) return !printf("%d",e[i].t);    }    printf("-1");    return 0;}

For a long time, I thought it was all part of the collection.

Until:

Round 3: Types and search Sets

Maybe it's called the name, and I don't know.

And the collection can be very good to say that relatives of relatives are relatives of this relationship, but the enemy is a friend of enemies this situation seems powerless.

Using twice times the i+n, I means the same, the relative is the opposite, so there is relative relative is the same relationship.

Example (b): Food chain

Surface

The prey of my prey is my natural enemy. (really violate the laws of nature OK)

So open three times times the size of the and check set, I said the same kind, i+n means prey, i+n+n represents predators.

So it was settled.

#include<bits/stdc++.h>const int maxn=5e4+5;int fa[maxn*3];int find(int x) {    return x==fa[x]?x:fa[x]=find(fa[x]);}int main() {    int n,k;scanf("%d%d",&n,&k);    for(int i=1;i<=n*3;i++) fa[i]=i;    int ans=0;    while(k--) {        int opt,x,y;scanf("%d%d%d",&opt,&x,&y);        if(x>n || y>n) {++ans;continue;}        if(opt==1) {            if(find(x)==find(y+n) || find(y)==find(x+n)) ++ans;            else for(int i=0;i<3;i++) fa[find(x+i*n)]=find(y+i*n);        }        else {            if(find(x)==find(y) || find(x)==find(y+n)) ++ans;            else for(int i=0;i<3;i++) fa[find(x+(i+1)%3*n)]=find(y+i*n);        }    }    printf("%d",ans);    return 0;}

Example (iii): Star Wars

Surface

To build a diagram, the first all destroyed, in the back from the backward time, the practice with the repair of highway computing connected block and similar to the wonderful.

#include <cstdio> #include <cstring> #include <iostream> #include <algorithm>const int maxn=1e6 +5;struct Edge {int nxt,v,frm;}    E[maxn];int h[maxn],tot;void add_edge (int u,int v) {e[++tot].v=v;    E[tot].nxt=h[u];    H[u]=tot; E[tot].frm=u;} int fa[maxn];int Find (int x) {return fa[x]==x?x:fa[x]=find (fa[x]);}    int Z[maxn];bool vis[maxn];int Ans[maxn];int main () {int n,m;scanf ("%d%d", &n,&m);    for (int i=0;i<n;i++) fa[i]=i,h[i]=-1;        for (int i=0;i<m;i++) {int x,y;scanf ("%d%d", &x,&y);        Add_edge (x, y);    Add_edge (Y,X);    } int k;scanf ("%d", &k);    int cnt=n-k;        for (int i=1;i<=k;i++) {scanf ("%d", z+i);    Vis[z[i]]=true; } for (int i=0;i<m+m;i++) {if (!vis[e[i].frm) && (!VIS[E[I].V]) && (Find (E[I].FRM)!=find (e[i    ].V)) Fa[find (e[i].frm)]=find (E[I].V),--cnt;    } ans[k+1]=cnt;        for (int t=k;t>0;t--) {vis[z[t]]=false;        ++cnt; FoR (int i=h[z[t]];~i;i=e[i].nxt) {if (!vis[e[i].v]) && (Find (E[I].V)!=find (Z[t])) Fa[fin        D (E[I].V)]=find (z[t]),--CNT;    } ans[t]=cnt;    } for (int i=1;i<=k+1;i++) printf ("%d\n", Ans[i]); return 0;}

Mastered these several, feel basic can be said to be more comprehensive grasp and check set.
(actually just after the test field)

Can be persisted and checked.

I have written in my blog.

Re-post the code again

#include <bits/stdc++.h> #define FN "build" const int Maxn=1e5+5;inline int read () {int X;char ch;bool flag=false;w    Hile (!isdigit (Ch=getchar ())) (ch== '-') && (flag=true);    for (x=ch-' 0 '; IsDigit (Ch=getchar ()); x= (x<<3) + (x<<1) +ch-' 0 '); return (FLAG?-X:X);}        namespace HJT {int n;        struct Node {node *ls,*rs;    int SIZ,FA;        }POOL[MAXN*32], *ROOT[MAXN], *zero, *tail=pool;        Node *newnode () {node *nd=++tail;        nd->ls=nd->rs=zero;        nd->siz=nd->fa=0;    return nd;        } node *fmodify (node *p,int l,int r,int pos,int RT) {node *nd=newnode ();            if (l==r) {nd->fa=rt;            nd->siz=p->siz;        return nd;        } int mid=l+r>>1;            if (pos<=mid) {nd->rs=p->rs;        Nd->ls=fmodify (P-&GT;LS,L,MID,POS,RT);            } else {nd->ls=p->ls; Nd->rs=fmodify (p->rs,mid+1,r,pos,rT);    } return nd;        } node *smodify (node *p,int l,int r,int pos,int RT) {node *nd=newnode ();            if (l==r) {nd->fa=p->fa;            nd->siz=p->siz+rt;        return nd;        } int mid=l+r>>1;            if (pos<=mid) {nd->rs=p->rs;        Nd->ls=smodify (P-&GT;LS,L,MID,POS,RT);            } else {nd->ls=p->ls;        Nd->rs=smodify (P-&GT;RS,MID+1,R,POS,RT);    } return nd;        } int fquery (Node *nd,int l,int r,int pos) {if (l==r) return nd->fa;        int mid=l+r>>1;        if (Pos<=mid) return fquery (Nd->ls,l,mid,pos);    else return fquery (Nd->rs,mid+1,r,pos);        } int squery (Node *nd,int l,int r,int pos) {if (l==r) return nd->siz;        int mid=l+r>>1;        if (Pos<=mid) return squery (Nd->ls,l,mid,pos);    else return squery (Nd->rs,mid+1,r,pos); } int Find (int i,node *Nd,int x) {int ff=fquery (ND,1,N,X);        if (ff==x) return x;    return find (I,ND,FF);        } node *build (int l,int r) {node *nd=newnode ();            if (l==r) {nd->siz=1;            nd->fa=l;        return nd;        } int mid=l+r>>1;        Nd->ls=build (L,mid);        Nd->rs=build (MID+1,R);    return nd;        } void Work () {int m=read (); N=read ();        int lastans=0,tot=0;        Zero=++tail;        zero->ls=zero->rs=zero;        zero->fa=zero->siz=0;        Root[0]=build (1,n);            for (int i=1;i<=m;i++) {int opt=read ();            int U=lastans+read ();            int V=lastans+read ();                if (opt==1) {u=find (tot,root[tot],u);                V=find (TOT,ROOT[TOT],V);                    if (u==v) {++tot;                    ROOT[TOT]=ROOT[TOT-1];                Continue } int Siz1=squery (ROOT[TOT],1,N,V);                int Siz2=squery (ROOT[TOT],1,N,U);                    if (SIZ1&GT;SIZ2) {std::swap (SIZ1,SIZ2);                Std::swap (U,V);                } ++tot;                Root[tot]=fmodify (Root[tot-1],1,n,v,u);            Root[tot]=smodify (ROOT[TOT],1,N,U,SIZ1);                } else {int ff=find (U,ROOT[U],V);                int Siz1=squery (ROOT[U],1,N,FF);                Root[tot+1]=root[tot];                ++tot;                LASTANS=SIZ1;            printf ("%d\n", SIZ1);    }}}}int Main () {Freopen (FN ". In", "R", stdin);    Freopen (FN ". Out", "w", stdout);    Hjt::work (); return 0;}

Can be persisted and check the set really do not know is not counted and check set, really the difference is too big.

Induction (a): And look up the set