连通分量

P3387【模板】缩点 
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#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e4 + 10, MAXM = 1e5 + 10;
vector<int> e1[MAXN], e2[MAXN];
int n, m, sccno[MAXN], idx, low[MAXN], dfn[MAXN], ind[MAXN], w1[MAXN], w2[MAXN],
    sccidx;
bool inq[MAXN];
queue<int> q;
stack<int> sta;
int ans, dp[MAXN];
void dfs(int u)
{
    dfn[u] = low[u] = ++idx;
    inq[u] = 1;
    sta.push(u);
    for (int v : e1[u])
    {
        if (!dfn[v])
        {
            dfs(v);
            low[u] = min(low[u], low[v]);
        }
        else if (inq[v])
            low[u] = min(low[u], dfn[v]);
    }
    if (dfn[u] == low[u])
    {
        sccidx++;
        int tp;
        do
        {
            tp = sta.top();
            sta.pop();
            w2[sccidx] += w1[tp];
            sccno[tp] = sccidx;
            inq[tp] = false;
        } while (tp != u);
    }
}
int main()
{
    ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    cin >> n >> m;
    for (int i = 1; i <= n; i++) cin >> w1[i];
    for (int i = 1; i <= m; i++)
    {
        int u, v;
        cin >> u >> v;
        e1[u].push_back(v);
    }
    for (int i = 1; i <= n; i++)
        if (!dfn[i]) dfs(i);
    for (int u = 1; u <= n; u++)
        for (int v : e1[u])
            if (sccno[u] != sccno[v])
                e2[sccno[u]].push_back(sccno[v]), ind[sccno[v]]++;
    for (int u = 1; u <= sccidx; u++)
        if (!ind[u]) q.push(u);
    while (!q.empty())
    {
        int u = q.front();
        q.pop();
        dp[u] += w2[u];
        ans = max(ans, dp[u]);
        for (int v : e2[u])
        {
            ind[v]--;
            dp[v] = max(dp[v], dp[u]);
            if (!ind[v]) q.push(v);
        }
    }
    cout << ans;
    return 0;
}
P8436【模板】边双连通分量 
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#include <bits/stdc++.h>
using namespace std;
const int MAXN = 5e5 + 10, MAXM = 2e6 + 10;
int n, m, bccidx, bcc[MAXN], head[MAXN], idx, low[MAXN], dfn[MAXN];
vector<vector<int>> ans;
bitset<MAXN> inq;
stack<int> stk;
struct edge
{
    int v, nxt;
} e[MAXM << 1];
inline void addedge(int u, int v)
{
    static int edge_cnt = 1;
    e[++edge_cnt] = {v, head[u]};
    head[u] = edge_cnt;
}
void dfs(int u, int f)
{
    dfn[u] = low[u] = ++idx;
    stk.push(u), inq[u] = 1;
    for (int i = head[u]; i; i = e[i].nxt)
        if (f != i && (f ^ 1) != i)
        {
            int v = e[i].v;
            if (!dfn[v])
            {
                dfs(v, i);
                low[u] = min(low[v], low[u]);
            }
            else if (inq[v])
                low[u] = min(low[u], dfn[v]);
        }
    if (low[u] == dfn[u])
    {
        int tp;
        bccidx++;
        vector<int> tmp;
        do
        {
            tp = stk.top();
            stk.pop();
            inq[tp] = 0;
            bcc[tp] = bccidx;
            tmp.push_back(tp);
        } while (tp != u);
        ans.push_back(tmp);
    }
}
int main()
{
    ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    cin >> n >> m;
    for (int u, v, i = 1; i <= m; i++)
        cin >> u >> v, addedge(u, v), addedge(v, u);
    for (int i = 1; i <= n; i++)
        if (!dfn[i]) dfs(i, 0);
    cout << ans.size() << endl;
    for (auto tbcc : ans)
    {
        cout << tbcc.size() << " ";
        for (auto x : tbcc) cout << x << " ";
        cout << endl;
    }
    return 0;
}
P8435【模板】点双连通分量 
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#include <bits/stdc++.h>
using namespace std;
inline int read()
{
    int x = 0, f = 1;
    char ch;
    for (ch = getchar(); !isdigit(ch); ch = getchar())
        if (ch == '-') f = -1;
    for (; isdigit(ch); ch = getchar())
    {
        x = (x << 3) + (x << 1) + (ch - '0');
    }
    return f * x;
}
inline void write(int x)
{
    if (x < 0)
    {
        putchar('-');
        x = -x;
    }
    if (x > 9) write(x / 10);
    putchar(x % 10 + '0');
    return;
}
const int MAXN = 5e5 + 10, MAXM = 2e6 + 10;
struct edge
{
    int u, v;
} E[MAXM << 1];
int n, m, head[MAXN], nex[MAXM << 1], edge_cnt, have_dcc, inde, dfn[MAXN],
    low[MAXN];
void add(int u, int v)
{
    if (u == v) return;
    edge_cnt++;
    E[edge_cnt] = (edge){u, v};
    nex[edge_cnt] = head[u];
    head[u] = edge_cnt;
    return;
}
stack<int> sta;
vector<int> dcc[MAXN];
void dfs(int u)
{
    dfn[u] = low[u] = inde++;
    if (!head[u])
    {
        have_dcc++;
        dcc[have_dcc].push_back(u);
        return;
    }
    sta.push(u);
    for (int i = head[u]; i; i = nex[i])
    {
        int v = E[i].v;
        if (!dfn[v])
        {
            dfs(v);
            low[u] = min(low[u], low[v]);
            if (low[v] >= dfn[u])
            {
                int p;
                have_dcc++;
                do
                {
                    p = sta.top();
                    sta.pop();
                    dcc[have_dcc].push_back(p);
                } while (p != v);
                dcc[have_dcc].push_back(u);
            }
        }
        else
            low[u] = min(low[u], dfn[v]);
    }
    return;
}
int main()
{
    n = read(), m = read();
    while (m--)
    {
        int u = read(), v = read();
        add(u, v);
        add(v, u);
    }
    for (int i = 1; i <= n; i++)
    {
        if (!dfn[i])
        {
            sta = stack<int>();
            dfs(i);
        }
    }
    write(have_dcc);
    puts("");
    for (int i = 1; i <= have_dcc; i++)
    {
        write(dcc[i].size()), putchar(' ');
        for (auto p : dcc[i]) write(p), putchar(' ');
        puts("");
    }
    return 0;
}
P3388【模板】割点（割顶） 
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#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2e4 + 10;
vector<int> e[MAXN];
int n, m, dfn[MAXN], low[MAXN], dfnidx, rt, cnt;
bool flg[MAXN];
void tarjan(int u, int f)
{
    dfn[u] = low[u] = ++dfnidx;
    int chcnt = 0;
    for (int v : e[u])
    {
        if (!dfn[v])
        {
            chcnt++;
            tarjan(v, u);
            low[u] = min(low[u], low[v]);
            if (dfn[u] <= low[v] && u != rt) cnt += !flg[u], flg[u] = 1;
            if (u == rt && chcnt > 1) cnt += !flg[u], flg[u] = 1;
        }
        else if (v ^ f)
            low[u] = min(low[u], dfn[v]);
    }
}
int main()
{
    ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    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 (rt = 1; rt <= n; rt++)
        if (!dfn[rt]) tarjan(rt, 0);
    cout << cnt << endl;
    for (int i = 1; i <= n; i++)
        if (flg[i]) cout << i << " ";
    return 0;
}