[REVIEW] 图论基础算法

//Kruskal
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define ll long long
#define M(a) memset(a,0,sizeof a)
#define fo(i,j,k) for(i=j;i<=k;i++)
using namespace std;
const int mxn=200005;
struct edge {int l,r,w;} f[mxn];
ll ans;
int n,m,cnt;
int father[mxn];
inline bool comp(edge x,edge y) {return x.w<y.w;}
inline int find(int x)
{
if(x!=father[x]) father[x]=find(father[x]);
return father[x];
}
inline void kruskal()
{
int i,j;
fo(i,1,m)
{
int t1=find(f[i].l),t2=find(f[i].r);
if(t1!=t2) father[t1]=t2,cnt++,ans+=f[i].w;
}
}
int main()
{
int i,j;
scanf("%d%d",&n,&m);
fo(i,1,n) father[i]=i;
fo(i,1,m)
scanf("%d%d%d",&f[i].l,&f[i].r,&f[i].w);
sort(f+1,f+m+1,comp);
kruskal();
if(cnt==n-1) printf("%lld\n",ans);
else printf("orz\n");
return 0;
}

//偏移量并查集
//NOI 2002 银河英雄传说
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define ll long long
#define M(a) memset(a,0,sizeof a)
#define fo(i,j,k) for(i=j;i<=k;i++)
using namespace std;
const int mxn=30005;
int father[mxn],dis[mxn],siz[mxn];
int T;
char s[10];
inline int find(int x)
{
if(x!=father[x])
{
int fa=find(father[x]);
if(father[x]!=fa) dis[x]=dis[x]+dis[father[x]]-1;
father[x]=fa;
}
return father[x];
}
inline void Union(int x,int y)
{
int t1=find(x),t2=find(y);
father[t1]=t2;
dis[t1]=siz[t2]+1;
siz[t2]+=siz[t1];
siz[t1]=0;
}
int main()
{
int i,j,x,y;
scanf("%d",&T);
fo(i,1,30000) father[i]=i,dis[i]=siz[i]=1;
while(T--)
{
scanf("%s",s);
scanf("%d%d",&x,&y);
if(s[0]=='M')
Union(x,y);
else
{
if(find(x)!=find(y)) printf("-1\n");
else printf("%d\n",abs(dis[x]-dis[y])-1);
}
}
return 0;
}

//spfa
#include<queue>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define ll long long
#define M(a) memset(a,0,sizeof a)
#define fo(i,j,k) for(i=j;i<=k;i++)
using namespace std;
const int mxn=100005;
queue <int> q;
int n,m,s,cnt;
int head[mxn],dis[mxn];
struct edge {int to,d,next;} f[500005];
bool vis[mxn];
inline void add(int u,int v,int w)
{
f[++cnt].to=v,f[cnt].d=w,f[cnt].next=head[u],head[u]=cnt;
}
inline void spfa()
{
int i,j;
fo(i,1,n) dis[i]=2147483647ll;
dis[s]=0;
q.push(s);
while(!q.empty())
{
int u=q.front();
q.pop();
vis[u]=0;
for(i=head[u];i;i=f[i].next)
{
int v=f[i].to,d=f[i].d;
if(dis[v]>dis[u]+d)
{
dis[v]=dis[u]+d;
if(!vis[v]) vis[v]=1,q.push(v);
}
}
}
}
int main()
{
int i,j,k,u,v,w;
scanf("%d%d%d",&n,&m,&s);
while(m--)
{
scanf("%d%d%d",&u,&v,&w);
add(u,v,w);
}
spfa();
fo(i,1,n) printf("%d ",dis[i]);
return 0;
}

//top sort
#include<queue>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define ll long long
#define M(a) memset(a,0,sizeof a)
#define fo(i,j,k) for(i=j;i<=k;i++)
using namespace std;
const int mxn=100005;
queue <int> q;
int n,m,s,cnt;
int head[mxn],dep[mxn],du[mxn];
struct edge {int to,next;} f[200005];
inline void add(int u,int v)
{
f[++cnt].to=v,f[cnt].next=head[u],head[u]=cnt;
}
inline void topsort()
{
int i,j;
fo(i,1,n) if(!du[i]) dep[i]=1,q.push(i);
while(!q.empty())
{
int u=q.front();
q.pop();
for(i=head[u];i;i=f[i].next)
{
int v=f[i].to;
du[v]--;
dep[v]=max(dep[v],dep[u]+1);
if(du[v]==0) q.push(v);
}
}
}
int main()
{
int i,j,k,u,v,w;
scanf("%d%d",&n,&m);
while(m--)
{
scanf("%d%d",&u,&v);
add(u,v),du[v]++;
}
topsort();
fo(i,1,n) printf("%d\n",dep[i]);
return 0;
}

//强连通
#include<stack>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define M(a) memset(a,0,sizeof a)
#define fo(i,j,k) for(i=j;i<=k;i++)
using namespace std;
const int mxn=200005;
stack <int> s;
int n,tim,ans=1e9;
int to[mxn],low[mxn],dfn[mxn];
bool in[mxn];
inline void tarjan(int u)
{
dfn[u]=low[u]=++tim;
in[u]=1;
s.push(u);
int v=to[u];
if(!dfn[v]) tarjan(v),low[u]=min(low[u],low[v]);
else if(in[v]) low[u]=min(low[u],dfn[v]);
if(dfn[u]==low[u])
{
int siz=0;
do
{
v=s.top();
s.pop();
in[v]=0;
siz++;
}while(u!=v);
if(siz>1) ans=min(ans,siz);
}
}
int main()
{
int i,j;
scanf("%d",&n);
fo(i,1,n) scanf("%d",&to[i]);
fo(i,1,n) if(!dfn[i]) tarjan(i);
printf("%d\n",ans);
return 0;
}