Tarjan算法总结

强联通分量

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#include<bits/stdc++.h>using namespace std;int n,m;
vector<int> e[10005];int dfn[10005],low[10005],timtp;
int stk[10005],stktp;
bool instk[10005];
int scccnt,inscc[10005];
vector<int> scc[10005];
bool vis[10005];void tarjan(int x){dfn[x] = low[x] = ++timtp;stk[++stktp] = x;instk[x] = 1;for(auto y:e[x]){if(!dfn[y]){tarjan(y);low[x] = min(low[x],low[y]);}else if(instk[y]) low[x] = min(low[x],dfn[y]);}if(low[x] >= dfn[x]){scccnt++;int y;do{y = stk[stktp--];instk[y] = 0;inscc[y] = scccnt;scc[scccnt].push_back(y);}while(y != x);}}signed main(){cin >> n >> m;for(int i = 1;i <= m;++ i){int u,v;cin >> u >> v;e[u].push_back(v);}for(int i = 1;i <= n;++ i)if(!dfn[i]) tarjan(i);cout << scccnt << endl;for(int i = 1;i <= n;++ i){if(vis[inscc[i]]) continue;vis[inscc[i]] = 1;int w = inscc[i];sort(scc[w].begin(),scc[w].end());for(auto x:scc[w]) cout << x << " ";cout << endl;}return 0;}

缩点

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#include<bits/stdc++.h>#define int long longusing namespace std;int n,m;
int a[10005];
struct bian{int u,v;
}b[100005];
vector<int> e[10005];
vector<int> e2[10005];
int a2[10005];int dfn[10005],low[10005],timtp;
int stk[10005],stktp;
int instk[10005];
int beinscc[10005];
int cntscc;
int sizscc[10005];void dfs(int x){dfn[x] = low[x] = ++timtp;stk[++stktp] = x;instk[x] = 1;for(auto y:e[x]){if(!dfn[y]){dfs(y);low[x] = min(low[x],low[y]);}else if(instk[y]) low[x] = min(low[x],dfn[y]);}if(low[x] == dfn[x]){cntscc++;int y;do{y = stk[stktp--];instk[y] = 0;sizscc[cntscc] += a[y];beinscc[y] = cntscc;}while(y != x);}}int ind[10005];
int ds[10005];signed main(){cin >> n >> m;for(int i = 1;i <= n;++ i)cin >> a[i];for(int i = 1;i <= m;++ i){int u,v;cin >> u >> v;b[i] = {u,v};e[u].push_back(v);}for(int i = 1;i <= n;++ i)if(!dfn[i]) dfs(i);for(int i = 1;i <= m;++ i){if(beinscc[b[i].u] != beinscc[b[i].v]){int u = beinscc[b[i].u];int v = beinscc[b[i].v];e2[u].push_back(v);ind[v]++;}}for(int i = 1;i <= cntscc;++ i)a2[i] = sizscc[i];queue<int> q;for(int i = 1;i <= cntscc;++ i)if(ind[i] == 0) ds[i] = a2[i],q.push(i);while(!q.empty()){int x = q.front();q.pop();for(auto y:e2[x]){ds[y] = max(ds[y],a2[y]+ds[x]);ind[y]--;if(!ind[y]) q.push(y);}}int ans = 0;for(int i = 1;i <= cntscc;++ i)ans = max(ans,ds[i]);cout << ans;return 0;}

割点

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#include<bits/stdc++.h>using namespace std;int n,m;
vector<int> e[20005];int dfn[20005],low[20005],timtp;
int gdcnt,isgd[20005];void tarjan(int x,int com){dfn[x] = low[x] = ++timtp;int child = 0;for(auto y:e[x]){if(!dfn[y]){tarjan(y,com);low[x] = min(low[x],low[y]);child++;if(low[y] >= dfn[x]&&x != com)gdcnt += (!isgd[x]),isgd[x] = 1;}else low[x] = min(low[x],dfn[y]);}if(x == com&&child >= 2) gdcnt += (!isgd[x]),isgd[x] = 1;}signed main(){cin >> n >> m;for(int i = 1;i <= m;++ i){int u,v;cin >> u >> v;e[u].push_back(v);e[v].push_back(u);}for(int i = 1;i <= n;++ i)if(!dfn[i]) tarjan(i,i);cout << gdcnt << endl;for(int i = 1;i <= n;++ i)if(isgd[i]) cout << i << " ";return 0;}

点双联通分量

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#include<bits/stdc++.h>using namespace std;int n,m;
vector<int> e[500005];int dfn[500005],low[500005],timtp;
int stk[500005],stktp;
int scccnt;
vector<int> scc[500005];void tarjan(int x,int root){dfn[x] = low[x] = ++timtp;stk[++stktp] = x;int child = 0;for(auto y:e[x]){if(!dfn[y]){tarjan(y,root);low[x] = min(low[x],low[y]);if(low[y] >= dfn[x]){scccnt++;int w;do{w = stk[stktp--];scc[scccnt].push_back(w);}while(w != y);scc[scccnt].push_back(x);}child++;}else low[x] = min(low[x],dfn[y]);}if(x == root&&child == 0)scc[++scccnt].push_back(x);}signed main(){cin >> n >> m;for(int i = 1;i <= m;++ i){int u,v;cin >> u >> v;e[u].push_back(v);e[v].push_back(u);}for(int i = 1;i <= n;++ i)if(!dfn[i]) stktp = 0,tarjan(i,i);cout << scccnt << endl;for(int i = 1;i <= scccnt;++ i){cout << scc[i].size() << " ";for(auto x:scc[i]) cout << x << " ";cout << endl;}return 0;}

边双联通分量

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#include<bits/stdc++.h>using namespace std;int n,m,w_wo_o;
vector<pair<int,int> > e[500005];int dfn[500005],low[500005],timtp;
int scccnt;
vector<int> scc[500005];
int stk[500005],stktp;void tarjan(int x,int com){dfn[x] = low[x] = ++timtp;stk[++stktp] = x;for(auto [y,whe]:e[x]){if(!dfn[y]){tarjan(y,whe);low[x] = min(low[x],low[y]);}else if(whe != (com^1)) low[x] = min(low[x],dfn[y]);}if(low[x] == dfn[x]){scccnt++;int w;do{w = stk[stktp--];scc[scccnt].push_back(w);}while(w != x);}}signed main(){cin >> n >> m;for(int i = 1;i <= m;++ i){int u,v;cin >> u >> v;e[u].push_back({v,w_wo_o++});e[v].push_back({u,w_wo_o++});}for(int i = 1;i <= n;++ i)if(!dfn[i]) stktp = 0,tarjan(i,-1);cout << scccnt << endl;for(int i = 1;i <= scccnt;++ i){cout << scc[i].size() << " ";for(auto x:scc[i]) cout << x << " ";cout << endl;}return 0;}