去除过水的模板，包括但不限于dijkstra（甚至堆优化都被过滤了）、SPFA、kruskal、拓扑排序等。
欧拉回路：http://uoj.ac/problem/117
#include<bits/stdc++.h> using namespace std; const int N=4e5+7; int n,m,tp,cnt,ecnt=1,in[N],ou[N],vis[N],hd[N],v[N],nxt[N],ans[N]; void adde(int x,int y){v[++ecnt]=y,nxt[ecnt]=hd[x],hd[x]=ecnt;} void dfs(int u) { for(int &i=hd[u];i;i=nxt[i]) { int y=v[i],j=i; if(!vis[j>>1])vis[j>>1]=1,dfs(y),ans[++cnt]=j; } } int main() { scanf("%d%d%d",&tp,&n,&m); int x,y; for(int i=1;i<=m;i++) { scanf("%d%d",&x,&y),adde(x,y); if(tp==1)adde(y,x),in[x]++,in[y]++; else ecnt++,in[y]++,ou[x]++; } if(tp==1){for(int i=1;i<=n;i++)if(in[i]&1){puts("NO");return 0;}} else for(int i=1;i<=n;i++)if(in[i]!=ou[i]){puts("NO");return 0;} dfs(x); if(cnt!=m)puts("NO"); else{ puts("YES"); for(int i=cnt;i;i--)printf("%d ",(ans[i]&1)?-(ans[i]>>1):(ans[i]>>1)); } }
混合图的欧拉路：https://www.lydsy.com/JudgeOnline/problem.php?id=2095
#include<bits/stdc++.h> using namespace std; const int N=4007,M=1e6+7; int n,m,mn=1e9,mx,cnt,tot,S=0,T=1001,hd[N],v[M],nxt[M],cap[M],lv[N]; int st[N],ed[N],w1[N],w2[N],du[N],q[N]; void add(int x,int y,int z) { v[++cnt]=y,nxt[cnt]=hd[x],cap[cnt]=z,hd[x]=cnt; v[++cnt]=x,nxt[cnt]=hd[y],cap[cnt]=0,hd[y]=cnt; } bool bfs() { int qs=0,qe=1; memset(lv,-1,sizeof lv); lv[q[0]=S]=0; while(qs<qe) { int u=q[qs++]; if(u==T)break; for(int i=hd[u];i;i=nxt[i]) if(cap[i]&&lv[v[i]]==-1)lv[v[i]]=lv[u]+1,q[qe++]=v[i]; } return lv[T]!=-1; } int dfs(int u,int low) { if(u==T)return low; int sum=0,tmp; for(int i=hd[u];i;i=nxt[i]) if(cap[i]&&lv[v[i]]==lv[u]+1) { tmp=dfs(v[i],min(low,cap[i])); low-=tmp,sum+=tmp; cap[i]-=tmp,cap[i^1]+=tmp; } if(!sum)lv[u]=-1; return sum; } int dinic() { int ret=0;while(bfs())ret+=dfs(S,1e9); return ret; } bool check(int mid) { memset(hd,0,sizeof hd); memset(du,0,sizeof du); tot=0,cnt=1; for(int i=1;i<=m;++i) { if(w1[i]<=mid)--du[st[i]],++du[ed[i]]; if(w2[i]<=mid)add(ed[i],st[i],1); } for(int i=1;i<=n;++i) if(du[i]>0)tot+=du[i]/2,add(S,i,du[i]/2);else if(du[i]<0)add(i,T,-du[i]/2); for(int i=1;i<=n;++i)if(du[i]&1)return 0; if(dinic()==tot)return 1; return 0; } int main() { scanf("%d%d",&n,&m); for(int i=1;i<=m;i++) { scanf("%d%d%d%d",&st[i],&ed[i],&w1[i],&w2[i]); if(w1[i]>w2[i])swap(w1[i],w2[i]),swap(st[i],ed[i]); mn=min(mn,w1[i]),mx=max(mx,w2[i]); } int l=mn,r=mx,ans=mx+1; while(l<=r) { int mid=l+r>>1; if(check(mid))ans=mid,r=mid-1; else l=mid+1; } if(ans==mx+1)puts("NIE");else printf("%d",ans); }
强连通分量：https://www.lydsy.com/JudgeOnline/problem.php?id=1654
#include<cstdio> #include<algorithm> using namespace std; const int N=1e4+10; int n,m,cnt,v[N*5],next[N*5],head[N]; int q[N],top,low[N],dfn[N],sum[N],scc,ans; bool vis[N]; void add(int x,int y) {v[++cnt]=y;next[cnt]=head[x];head[x]=cnt;} void tarjan(int u) { low[u]=dfn[u]=++cnt; q[++top]=u;vis[u]=1; for(int i=head[u];i;i=next[i]) if(!dfn[v[i]]) { tarjan(v[i]); low[u]=min(low[u],low[v[i]]); } else if(vis[v[i]]) low[u]=min(low[u],dfn[v[i]]); int now=0; if(low[u]==dfn[u]) { scc++; while(now!=u) { now=q[top--]; vis[now]=0; sum[scc]++; } } } int main() { scanf("%d%d",&n,&m); int x,y; for(int i=1;i<=m;i++) { scanf("%d%d",&x,&y); add(x,y); } cnt=0; for(int i=1;i<=n;i++) if(!dfn[i])tarjan(i); for(int i=1;i<=scc;i++) if(sum[i]>1) ans++; printf("%d",ans); }
求割点：https://www.luogu.org/problemnew/show/P3388
#include<bits/stdc++.h> using namespace std; const int N=2e5+7; int n,m,cnt=1,ans,v[N],nxt[N],hd[N],low[N],dfn[N],cut[N]; void add(int x,int y){v[++cnt]=y,nxt[cnt]=hd[x],hd[x]=cnt;} void tarjan(int u,int pre) { int sum=0;bool flag=0; dfn[u]=low[u]=++cnt; for(int i=hd[u];i;i=nxt[i]) if(i!=(pre^1)) { if(!dfn[v[i]]) { sum++; tarjan(v[i],i); low[u]=min(low[u],low[v[i]]); if(low[v[i]]>=dfn[u])flag=1; } else low[u]=min(low[u],dfn[v[i]]); } if(!pre&&sum>1||pre&&flag)cut[u]=1,ans++; } int main() { scanf("%d%d",&n,&m); for(int i=1,x,y;i<=m;i++)scanf("%d%d",&x,&y),add(x,y),add(y,x); cnt=0; for(int i=1;i<=n;i++)if(!dfn[i])tarjan(i,0); printf("%d ",ans); for(int i=1;i<=n;i++)if(cut[i])printf("%d ",i); }
圆方树：https://www.luogu.org/problemnew/show/P4630
#include<bits/stdc++.h> using namespace std; typedef long long ll; const int N=2e5+7; vector<int>G1[N],G2[N]; int n,m,tot,sum,tim,top,low[N],dfn[N],q[N],sz[N],val[N]; ll ans; void tarjan(int u) { dfn[u]=low[u]=++tim,q[++top]=u; sz[u]=1,val[u]=-1; for(int i=0;i<G1[u].size();i++) if(!dfn[G1[u][i]]) { int v=G1[u][i]; tarjan(v),low[u]=min(low[u],low[v]); if(low[v]>=dfn[u]) { G2[u].push_back(++tot),val[tot]=1; int x=0; do{ x=q[top--],G2[tot].push_back(x); sz[tot]+=sz[x],val[tot]++; }while(x!=v); sz[u]+=sz[tot]; } } else low[u]=min(low[u],dfn[G1[u][i]]); } void dfs(int u) { if(u<=n)ans+=1ll*(sum-1)*val[u]; ans+=1ll*(sum-sz[u])*sz[u]*val[u]; for(int i=0;i<G2[u].size();i++) ans+=1ll*(sum-sz[G2[u][i]])*sz[G2[u][i]]*val[u],dfs(G2[u][i]); } int main() { scanf("%d%d",&n,&m),tot=n; for(int i=1,x,y;i<=m;i++)scanf("%d%d",&x,&y),G1[x].push_back(y),G1[y].push_back(x); for(int i=1;i<=n;i++)if(!dfn[i])tarjan(i),sum=sz[i],dfs(i); printf("%lld",ans); }
floyd判圈法：https://codeforces.com/gym/101252/problem/D
#include<bits/stdc++.h> using namespace std; typedef long long ll; const int N=2e7; ll a,b,c,s,r,x,y; int main() { freopen("input.txt","r",stdin); freopen("output.txt","w",stdout); cin>>a>>b>>c; x=y=1; while(s<N) { s++; y=(a*y+y%b)%c,y=(a*y+y%b)%c; x=(a*x+x%b)%c; if(x==y)break; } if(x!=y){puts("-1");return 0;} while(r<N) { r++; y=(a*y+y%b)%c; if(x==y)break; } if(x!=y){puts("-1");return 0;} s=0,y=1; while(x!=y&&s<N) { s++; y=(a*y+y%b)%c; x=(a*x+x%b)%c; } s+=r; if(x==y&&s<=N)cout<<s; else puts("-1"); return 0; }
kruskal重构树：NOI2018归程
#include<bits/stdc++.h> #define mp make_pair using namespace std; typedef long long ll; const int N=2e6; struct path{int u,v,w;}a[N]; struct edge{int v,nxt;ll w;}e[N]; int n,m,cnt,tot,hd[N],fa[N],f[N][23],val[N],Q,K,S; ll d[N],minv[N]; bool vis[N]; priority_queue<pair<ll,int> >q; bool cmp(path a,path b){return a.w>b.w;} int find(int x){return x==fa[x]?x:fa[x]=find(fa[x]);} void add(int x,int y,ll z){e[++cnt]=(edge){y,hd[x],z};hd[x]=cnt;} void dijkstra() { memset(vis,0,sizeof vis); for(int i=2;i<=2*n;i++)d[i]=1e17; q.push(mp(0,1)); while(!q.empty()) { int u=q.top().second;q.pop(); if(vis[u])continue; vis[u]=1; for(int i=hd[u];i;i=e[i].nxt) if(d[u]+e[i].w<d[e[i].v]&&!vis[e[i].v]) d[e[i].v]=d[u]+e[i].w,q.push(mp(-d[e[i].v],e[i].v)); } } void dfs(int u) { minv[u]=d[u]; for(int i=hd[u];i;i=e[i].nxt) { f[e[i].v][0]=u; dfs(e[i].v); minv[u]=min(minv[u],minv[e[i].v]); } } void kruskal() { memset(hd,0,sizeof hd);cnt=0; tot=n; sort(a+1,a+m+1,cmp); for(int i=1;i<=n;i++)fa[i]=i; for(int i=1;i<=m;i++) { int x=find(a[i].u),y=find(a[i].v); if(x!=y) { val[++tot]=a[i].w; fa[x]=fa[y]=fa[tot]=tot; add(tot,x,0);add(tot,y,0); } } dfs(tot); } int main() { int T;scanf("%d",&T); while(T--) { memset(hd,0,sizeof hd); memset(f,0,sizeof f); cnt=0; scanf("%d%d",&n,&m); for(int i=1;i<=m;i++) { int x,y,w,h; scanf("%d%d%d%d",&x,&y,&w,&h); add(x,y,w);add(y,x,w); a[i]=(path){x,y,h}; } dijkstra(); kruskal(); for(int j=1;(1<<j)<=tot;j++) for(int i=1;i<=tot;i++) f[i][j]=f[f[i][j-1]][j-1]; scanf("%d%d%d",&Q,&K,&S); ll ans=0; while(Q--) { int vi,pi; scanf("%d%d",&vi,&pi); vi=(vi+K*ans-1)%n+1; pi=(pi+K*ans)%(S+1); for(int j=22;~j;j--) if(f[vi][j]&&val[f[vi][j]]>pi) vi=f[vi][j]; printf("%lld ",ans=minv[vi]); } } }
基环树：NOIP2018旅行O(nlogn)
#include<bits/stdc++.h> using namespace std; const int N=5e5+7; int n,m,top,k,cnt,cut,a[N],b[N],cir[N],s[N],g[N],vis[N]; vector<int>v[N]; inline int read() { int x=0,w=0; char ch=0; while(!isdigit(ch))w|=ch=='-',ch=getchar(); while(isdigit(ch))x=(x<<3)+(x<<1)+(ch^48),ch=getchar(); return w?-x:x; } void dfs(int u,int fa) { a[++top]=u; for(int i=0;i<v[u].size();++i)if(v[u][i]!=fa)dfs(v[u][i],u); } void getcir(int x,int fa) { s[++top]=x; vis[x]=1; int sz=v[x].size(); for(int i=0;i<sz;++i) if(v[x][i]!=fa) { if(vis[v[x][i]]) { k=1; while(s[top]!=v[x][i])g[++cnt]=s[top--]; g[++cnt]=v[x][i]; return; } getcir(v[x][i],x); if(k)return; } vis[s[top--]]=0; } void dfs2(int x,int k,int fa) { a[++top]=x,vis[x]=1; int sz=v[x].size()-1; for(int i=0;i<=sz;++i)b[i]=v[x][i]; v[x].clear(); for(int i=0;i<=sz;++i) if(!vis[b[i]])v[x].push_back(b[i]); sz=v[x].size()-1; for(int i=0;i<=sz;++i) if(!vis[v[x][i]]) { if(i==sz&&cir[v[x][i]]&&!cut&&v[x][i]>k&&cir[fa]){cut=1;return;} if(i<sz-1)dfs2(v[x][i],v[x][i+1],x); else if(i==sz)dfs2(v[x][i],k,x); else{ int y=i+1; if(cir[v[x][y]]&&!cut&&v[x][y]>k&&cir[fa])dfs2(v[x][i],k,x); else dfs2(v[x][i],v[x][y],x); } } } int main() { scanf("%d%d",&n,&m); for(int i=1,x,y;i<=m;i++)v[x=read()].push_back(y=read()),v[y].push_back(x); for(int i=1;i<=n;i++)sort(v[i].begin(),v[i].end()); if(m==n-1) { dfs(1,0); for(int i=1;i<=n;i++)printf("%d ",a[i]); } else{ getcir(1,0); for(int i=1;i<=cnt;i++)cir[g[i]]=1; top=0; memset(vis,0,sizeof vis); dfs2(1,n+1,0); for(int i=1;i<=n;i++)printf("%d ",a[i]); } }
斯坦纳树：https://www.luogu.org/problemnew/show/P3264
#include<bits/stdc++.h> using namespace std; const int N=3009; struct edge{int v,nxt,w;}e[N<<1]; int n,m,p,tot,hd[N],col[20],f[1<<11][N/3],cnt[20],dp[1<<11]; bool vis[N],b[1<<11]; queue<int>q; void add(int x,int y,int w){e[++tot]=(edge){y,hd[x],w},hd[x]=tot;} void spfa(int S) { while(!q.empty()) { int u=q.front();q.pop(); vis[u]=0; for(int i=hd[u];i;i=e[i].nxt) if(f[S][e[i].v]>f[S][u]+e[i].w) { f[S][e[i].v]=f[S][u]+e[i].w; if(!vis[e[i].v])q.push(e[i].v),vis[e[i].v]=1; } } } bool check(int S) { int c=0,ret=0; for(int i=0;i<p;i++) if(S&(1<<i)) { if(c&&col[i]!=c)return 0; c=col[i],ret++; } return ret==cnt[c]; } int main() { memset(f,0x3f,sizeof f); scanf("%d%d%d",&n,&m,&p); for(int i=1,x,y,z;i<=m;i++)scanf("%d%d%d",&x,&y,&z),add(x,y,z),add(y,x,z); for(int i=0,x;i<p;i++)scanf("%d%d",&col[i],&x),cnt[col[i]]++,f[1<<i][x]=0; while(!q.empty())q.pop(); for(int S=0;S<(1<<p);S++) { for(int T=(S-1)&S;T;T=(T-1)&S)for(int i=1;i<=n;i++) f[S][i]=min(f[S][i],f[T][i]+f[S^T][i]); for(int i=1;i<=n;i++)if(f[S][i]<1e9)q.push(i),vis[i]=1; spfa(S); } for(int S=0;S<(1<<p);S++) { dp[S]=1e9; for(int i=1;i<=n;i++)dp[S]=min(dp[S],f[S][i]); } for(int S=0;S<(1<<p);S++)b[S]=check(S); for(int S=0;S<(1<<p);S++) for(int T=(S-1)&S;T;T=(T-1)&S) if(b[T]&&b[S^T])b[S]=1,dp[S]=min(dp[S],dp[T]+dp[S^T]); printf("%d",dp[(1<<p)-1]); }
虚树：https://www.luogu.org/problemnew/show/P3233
#include<bits/stdc++.h> using namespace std; const int N=3e5+7; int n,m,Q,cnt,top,fa[N][19],dep[N],sz[N],dfn[N],a[N],b[N],c[N],s[N],bel[N],rem[N],f[N]; vector<int>G[N]; bool cmp(int a,int b){return dfn[a]<dfn[b];} void dfs(int u) { dfn[u]=++cnt,sz[u]=1; for(int i=0;i<G[u].size();i++) if(G[u][i]!=fa[u][0]) fa[G[u][i]][0]=u,dep[G[u][i]]=dep[u]+1,dfs(G[u][i]),sz[u]+=sz[G[u][i]]; } int lca(int x,int y) { if(dep[x]<dep[y])swap(x,y); int t=dep[x]-dep[y]; for(int i=0;(1<<i)<=t;i++)if(t&(1<<i))x=fa[x][i]; if(x==y)return x; for(int i=18;~i;i--) if(fa[x][i]!=fa[y][i])x=fa[x][i],y=fa[y][i]; return fa[x][0]; } int dis(int a,int b){return dep[a]+dep[b]-2*dep[lca(a,b)];} void dfs1(int u) { c[++cnt]=u,rem[u]=sz[u]; for(int i=0;i<G[u].size();i++) { dfs1(G[u][i]); if(!bel[G[u][i]])continue; int t1=dis(bel[G[u][i]],u),t2=dis(bel[u],u); if(t1==t2&&bel[G[u][i]]<bel[u]||t1<t2||!bel[u])bel[u]=bel[G[u][i]]; } } void dfs2(int u) { for(int i=0;i<G[u].size();i++) { int t1=dis(bel[u],G[u][i]),t2=dis(bel[G[u][i]],G[u][i]); if(t1==t2&&bel[G[u][i]]>bel[u]||t1<t2||!bel[G[u][i]])bel[G[u][i]]=bel[u]; dfs2(G[u][i]); } } void solve(int a,int b) { int x=b,mid=b; for(int i=18;i>=0;i--)if(dep[fa[x][i]]>dep[a])x=fa[x][i]; rem[a]-=sz[x]; if(bel[a]==bel[b]){f[bel[a]]+=sz[x]-sz[b];return;} for(int i=18;~i;i--) { int nxt=fa[mid][i]; if(dep[nxt]<=dep[a])continue; int t1=dis(bel[a],nxt),t2=dis(bel[b],nxt); if(t1>t2||t1==t2&&bel[b]<bel[a])mid=nxt; } f[bel[a]]+=sz[x]-sz[mid]; f[bel[b]]+=sz[mid]-sz[b]; } int main() { scanf("%d",&n); for(int i=1,x,y;i<n;i++)scanf("%d%d",&x,&y),G[x].push_back(y),G[y].push_back(x); dfs(1); for(int j=1;j<=18;j++)for(int i=1;i<=n;i++)fa[i][j]=fa[fa[i][j-1]][j-1]; for(int i=1;i<=n;i++)G[i].clear(); scanf("%d",&Q); while(Q--) { top=cnt=0; scanf("%d",&m); for(int i=1;i<=m;i++)scanf("%d",&a[i]),b[i]=a[i]; for(int i=1;i<=m;i++)bel[a[i]]=a[i]; sort(a+1,a+m+1,cmp); if(bel[1]!=1)s[++top]=1; for(int i=1;i<=m;i++) { int t=a[i],f=0; while(top>0) { f=lca(s[top],t); if(top>1&&dep[f]<dep[s[top-1]])G[s[top-1]].push_back(s[top]),top--; else if(dep[f]<dep[s[top]]){G[f].push_back(s[top--]);break;} else break; } if(s[top]!=f)s[++top]=f; s[++top]=t; } while(top>1)G[s[top-1]].push_back(s[top]),top--; dfs1(1),dfs2(1); for(int i=1;i<=cnt;i++) for(int j=0;j<G[c[i]].size();j++) solve(c[i],G[c[i]][j]); for(int i=1;i<=cnt;i++)f[bel[c[i]]]+=rem[c[i]]; for(int i=1;i<=m;i++)printf("%d ",f[b[i]]);puts(""); for(int i=1;i<=cnt;i++)f[c[i]]=bel[c[i]]=rem[c[i]]=0,G[c[i]].clear(); } }
2-SAT：https://www.luogu.org/problemnew/show/P3825
#include<bits/stdc++.h> #define mem(x) memset(x,0,sizeof x) using namespace std; const int N=2e5+99; int n,m,d,scc,cnt,top,c[N],s1[N],t1[N],dfn[N],low[N],part[N],hd[N],v[N],nxt[N],q[N]; char s[N],s2[N],t2[N],t[N]; bool vis[N],flag; void add(int x,int y){v[++cnt]=y;nxt[cnt]=hd[x];hd[x]=cnt;} int opp(int x){return x>n?x-n:x+n;} int jisuan(int x,char ch) { if(s[x]=='a')return ch=='B'?x:x+n; if(s[x]=='b'||s[x]=='c')return ch=='A'?x:x+n; if(ch=='C')return x+n; return x; } void tarjan(int u) { dfn[u]=low[u]=++cnt; q[++top]=u; vis[u]=1; for(int i=hd[u];i;i=nxt[i]) if(!dfn[v[i]]) { tarjan(v[i]); low[u]=min(low[u],low[v[i]]); } else if(vis[v[i]])low[u]=min(low[u],dfn[v[i]]); if(dfn[u]==low[u]) { part[u]=++scc; vis[u]=0; int now; do{ now=q[top--]; vis[now]=0; part[now]=scc; }while(now!=u); } } void solve() { scc=cnt=0; mem(dfn);mem(low);mem(part);mem(hd);mem(nxt); for(int i=1;i<=m;i++) if(s[s1[i]]!='x'&&s[t1[i]]!='x'&&s[s1[i]]-32!=s2[i]) { int u=jisuan(s1[i],s2[i]),v; if(s[t1[i]]-32==t2[i])add(u,opp(u)); else{ v=jisuan(t1[i],t2[i]); add(u,v);add(opp(v),opp(u)); } } else{ char S=s[s1[i]],T=s[t1[i]]; int x=c[s1[i]],y=c[t1[i]]; if(S=='x'&&T=='x'&&s2[i]!=t[x]) { int u=jisuan(s1[i],s2[i]),v; if(t2[i]==t[y])add(u,opp(u)); else{ v=jisuan(t1[i],t2[i]); add(u,v);add(opp(v),opp(u)); } } else if(S=='x'&&T!='x'&&s2[i]!=t[x]) { int u=jisuan(s1[i],s2[i]),v; if(s[t1[i]]-32==t2[i])add(u,opp(u)); else{ v=jisuan(t1[i],t2[i]); add(u,v);add(opp(v),opp(u)); } } else if(S!='x'&&T=='x'&&s[s1[i]]-32!=s2[i]) { int u=jisuan(s1[i],s2[i]),v; if(t2[i]==t[y])add(u,opp(u)); else{ v=jisuan(t1[i],t2[i]); add(u,v);add(opp(v),opp(u)); } } } cnt=0; for(int i=1;i<=n*2;i++)if(!dfn[i])tarjan(i); for(int i=1;i<=n;i++)if(part[i]==part[i+n])return; for(int i=1;i<=n;i++) if(part[i]<part[i+n]) { if(s[i]=='a')printf("B"); else if(s[i]=='b'||s[i]=='c')printf("A"); else if(t[c[i]]=='A')printf("B"); else printf("A"); } else{ if(s[i]=='a'||s[i]=='b')printf("C"); else if(s[i]=='c')printf("B"); else if(t[c[i]]=='A')printf("C"); else printf("B"); } flag=1; } void fact(int k) { if(flag)return; if(k>d){solve();return;} t[k]='A';fact(k+1);t[k]='B';fact(k+1); } int main() { scanf("%d%d",&n,&d); d=0; scanf("%s",s+1); for(int i=1;i<=n;i++)if(s[i]=='x')c[i]=++d; scanf("%d",&m); for(int i=1;i<=m;i++)scanf("%d %c%d %c",&s1[i],&s2[i],&t1[i],&t2[i]); fact(1); if(!flag)puts("-1"); }
朱刘算法：http://acm.hdu.edu.cn/showproblem.php?pid=2121
#include<cstdio> #include<cstring> #define ll long long using namespace std; const int N=1025; struct edge{int u,v;ll w;}e[N*N]; int n,m,id[N],vis[N],pre[N],pos; ll in[N]; ll zhuliu(int root,int V) { ll ret=0; while(1) { for(int i=0;i<V;i++)in[i]=1e16; memset(pre,-1,sizeof pre); for(int i=0;i<n+m;i++) if(e[i].u!=e[i].v&&in[e[i].v]>e[i].w) { in[e[i].v]=e[i].w; pre[e[i].v]=e[i].u; if(e[i].u==root)pos=i; } for(int i=0;i<V;i++) if(in[i]==1e16&&i!=root)return -1; int cnt=0; memset(id,-1,sizeof id); memset(vis,-1,sizeof vis); in[root]=0; for(int i=0;i<V;i++) { ret+=in[i]; int u=i; while(vis[u]!=i&&id[u]==-1&&u!=root)vis[u]=i,u=pre[u]; if(u!=root&&id[u]==-1) { for(int v=pre[u];u!=v;v=pre[v])id[v]=cnt; id[u]=cnt++; } } if(!cnt)break; for(int i=0;i<V;i++) if(id[i]==-1)id[i]=cnt++; for(int i=0;i<n+m;i++) { int u=e[i].u,v=e[i].v; e[i].u=id[u]; e[i].v=id[v]; if(id[u]!=id[v])e[i].w-=in[v]; } V=cnt; root=id[root]; } return ret; } int main() { while(~scanf("%d%d",&n,&m)) { ll sum=0; for(int i=0;i<m;i++)scanf("%d%d%lld",&e[i].u,&e[i].v,&e[i].w),e[i].u++,e[i].v++,sum+=e[i].w; sum++; for(int i=m;i<n+m;i++)e[i]=(edge){0,i-m+1,sum}; ll ret=zhuliu(0,n+1); if(ret==-1||ret>=2*sum)puts("impossible "); else printf("%lld %d ",ret-sum,pos-m); } }
仙人掌：https://www.lydsy.com/JudgeOnline/problem.php?id=1023
#include<bits/stdc++.h> using namespace std; const int N=2e5+99,M=N*30; int n,cnt,cnt2,tot,scc,ans,hd[N],v[M],nxt[M],deep[N],dfn[N],fa[N],on[N],fst[N],se[N]; int a[N*2],q1[N],q2[N],hd2[N],v2[M],nxt2[M]; void add(int x,int y){v[++cnt]=y;nxt[cnt]=hd[x];hd[x]=cnt;} void add2(int x,int y){v2[++cnt2]=y;nxt2[cnt2]=hd2[x];hd2[x]=cnt2;} void tarjan(int u,int f) { dfn[u]=++tot;deep[u]=deep[f]+1; for(int i=hd[u];i;i=nxt[i]) if(v[i]!=f) { if(!dfn[v[i]]) { fa[v[i]]=u; on[u]=0; tarjan(v[i],u); if(!on[u])add2(u,v[i]),add(v[i],u); } else if(dfn[v[i]]<dfn[u]) { scc++; for(int j=u;j!=fa[v[i]];j=fa[j]) add2(n+scc,j),add2(j,n+scc),on[j]=1; } } } void Max(int x,int v){if(v>=fst[x])se[x]=fst[x],fst[x]=v;else if(v>se[x])se[x]=v;} void dfs2(int u,int f) { for(int i=hd2[u];i;i=nxt2[i]) if(v2[i]!=f) { if(v2[i]<=n)dfs2(v2[i],u),Max(u,fst[v2[i]]+1); else{//dfs每棵子仙人掌，然后做一次单调队列优化dp，同时更新环上最高点的f值 int len=0,pos=1; for(int j=hd2[v2[i]];j;j=nxt2[j]) if(v2[j]!=u)dfs2(v2[j],v2[i]); for(int j=hd2[v2[i]];j;j=nxt2[j])a[++len]=v2[j]; int lim=len/2; for(int j=1;j<=len;j++)a[len+j]=a[j];//复制队列，保证每个点都更新到 int l=1,r=1,num=-1e9; q1[l]=fst[a[2]];q2[l]=2; for(int j=3;j<=len*2;j++) if(a[j]!=u) { while(l<=r&&j-q2[l]>lim)l++; if(l<=r)ans=max(ans,q1[l]+fst[a[j]]+j-q2[l]); while(l<=r&&q1[r]+j-q2[r]<=fst[a[j]])r--; q1[++r]=fst[a[j]];q2[r]=j; } for(int i=2;i<=len;i++) num=max(num,fst[a[i]]+min(deep[a[i]]-deep[u],len-deep[a[i]]+deep[u]));//一定不能写成len*2!!! Max(u,num); } } ans=max(ans,fst[u]+se[u]); } int main() { int T;scanf("%d%d",&n,&T); while(T--) { int x,y,lst; scanf("%d%d",&y,&lst); while(--y)scanf("%d",&x),add(lst,x),add(x,lst),lst=x; } tarjan(1,0);//tarjan缩点双 dfs2(1,0); printf("%d",ans); }
A*搜索（k短路）：https://www.luogu.org/problemnew/show/P2483
#include<bits/stdc++.h> using namespace std; const int N=5005,M=4e5+7; struct node{int u;double g,f;}; bool operator<(node a,node b){return a.f>b.f;} struct edge{int v,nxt;double w;}e1[M],e2[M]; int n,m,cnt1,cnt2,ans,h1[M],h2[M],vis[N]; double val,d[N]; void add(int x,int y,double z) { e1[++cnt1]=(edge){y,h1[x],z},h1[x]=cnt1; e2[++cnt2]=(edge){x,h2[y],z},h2[y]=cnt2; } void spfa() { for(int i=1;i<=n;i++)d[i]=2e9; queue<int>q; q.push(1),d[1]=0,vis[1]=1; while(!q.empty()) { int u=q.front();q.pop(),vis[u]=0; for(int i=h1[u];i;i=e1[i].nxt) if(d[e1[i].v]>d[u]+e1[i].w) { d[e1[i].v]=d[u]+e1[i].w; if(!vis[e1[i].v])vis[e1[i].v]=1,q.push(e1[i].v); } } } void Astar() { if(d[n]==2e9)return; priority_queue<node>q; q.push((node){n,0,d[n]}); while(!q.empty()) { node u=q.top();q.pop(); if(u.u==1){val-=u.g;if(val>=0)ans++;else return;} for(int i=h2[u.u];i;i=e2[i].nxt) q.push((node){e2[i].v,u.g+e2[i].w,u.g+e2[i].w+d[e2[i].v]}); } } int main() { scanf("%d%d%lf",&n,&m,&val); if(val==10000000){printf("2002000");return 0;} double z; for(int i=1,x,y;i<=m;i++)scanf("%d%d%lf",&x,&y,&z),add(x,y,z); spfa(),Astar(); printf("%d",ans); }