graph/test/block_cut_tree.test.cpp

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Last update: 2025-06-28 10:05:47+09:00
Problem: https://judge.yosupo.jp/problem/biconnected_components

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/biconnected_components"
#define FAST_IO
#include "../../graph/block_cut_tree.hpp"
#include "../../template/template.hpp"

void solve() {
    I32(n, m);
    Graph<> g(n);
    REP(i, m) {
        I32(u, v);
        g.add_edge(u, v);
    }
    g.build();
    Graph<> bct = block_cut_tree(g);
    cout << bct.v() - n << '\n';
    REP(i, n, bct.v()) {
        cout << LEN(bct[i]);
        for (auto e : bct[i]) {
            cout << ' ' << e.to;
        }
        cout << '\n';
    }
}

int main() {
    i32 t = 1;
    // cin >> t;
    while (t--) {
        solve();
    }
}

#line 1 "graph/test/block_cut_tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/biconnected_components"
#define FAST_IO
#line 2 "graph/graph.hpp"
#include <iostream>
#include <cassert>
#include <vector>
template <typename T>
struct Edge {
    using W = T;
    int from, to, id;
    W weight;
    Edge<T> rev() const {
        return Edge<T>{to, from, id, weight};
    }
};
template <typename T>
void debug(const Edge<T> &e) {
    std::cerr << e.from << " -> " << e.to << " id = " << e.id << std::cerr << " weight = ";
    debug(e.weight);
}
template <typename T = int, bool DIR = false>
class Graph {
public:
    using E = Edge<T>;
    using W = T;
    static constexpr bool DIRECTED = DIR;
    struct Adjacency {
        using Iter = typename std::vector<E>::iterator;
        Iter be, en;
        Iter begin() const { return be; }
        Iter end() const { return en; }
        int size() const { return (int)std::distance(be, en); }
        E &operator[](int idx) const { return be[idx]; }
    };
    struct ConstAdjacency {
        using Iter = typename std::vector<E>::const_iterator;
        Iter be, en;
        Iter begin() const { return be; }
        Iter end() const { return en; }
        int size() const { return (int)std::distance(be, en); }
        const E &operator[](int idx) const { return be[idx]; }
    };

private:
    int n, m;
    std::vector<E> edges, csr;
    std::vector<int> sep;
    bool built;

public:
    Graph(int n) : n(n), m(0), built(false) {}
    int v() const { return n; }
    int e() const { return m; }
    int add_vertex() {
        return n++;
    }
    void add_edge(int from, int to, W weight = 1) {
        assert(0 <= from && from < n && 0 <= to && to < n);
        edges.emplace_back(E{from, to, m++, weight});
    }
    void build() {
        sep.assign(n + 1, 0);
        csr.resize(DIRECTED ? m : 2 * m);
        for (const E &e : edges) {
            ++sep[e.from + 1];
            if (!DIRECTED) {
                ++sep[e.to + 1];
            }
        }
        for (int i = 0; i < n; ++i) {
            sep[i + 1] += sep[i];
        }
        std::vector<int> c = sep;
        for (const E &e : edges) {
            csr[c[e.from]++] = e;
            if (!DIRECTED) {
                csr[c[e.to]++] = e.rev();
            }
        }
        built = true;
    }
    Adjacency operator[](int v) {
        assert(built && 0 <= v && v < n);
        return Adjacency{csr.begin() + sep[v], csr.begin() + sep[v + 1]};
    }
    ConstAdjacency operator[](int v) const {
        assert(built && 0 <= v && v < n);
        return ConstAdjacency{csr.begin() + sep[v], csr.begin() + sep[v + 1]};
    }
};
#line 3 "graph/block_cut_tree.hpp"
template <typename T>
Graph<> block_cut_tree(const Graph<T> &g) {
    std::vector<int> ord(g.v()), low(g.v()), used(g.v(), 0);
    std::vector<int> vstc;
    vstc.reserve(g.v());
    Graph<> tree(g.v());
    int t = 0;
    auto dfs = [&](auto dfs, int v, int p) -> void {
        used[v] = 1;
        ord[v] = t++;
        low[v] = t;
        vstc.push_back(v);
        bool pf = false;
        int chl = 0;
        for (const auto &e : g[v]) {
            if (e.to == p && !pf) {
                pf = true;
                continue;
            }
            if (used[e.to]) {
                low[v] = std::min(low[v], ord[e.to]);
            } else {
                int vsz = (int)vstc.size();
                ++chl;
                dfs(dfs, e.to, v);
                low[v] = std::min(low[v], low[e.to]);
                if ((p == -1 && chl >= 2) || (p != -1 && low[e.to] >= ord[v])) {
                    int bcc = tree.add_vertex();
                    while ((int)vstc.size() > vsz) {
                        tree.add_edge(bcc, vstc.back());
                        vstc.pop_back();
                    }
                    tree.add_edge(bcc, v);
                }
            }
        }
    };
    for (int i = 0; i < g.v(); ++i) {
        if (!used[i]) {
            dfs(dfs, i, -1);
            int bcc = tree.add_vertex();
            for (int v : vstc) {
                tree.add_edge(bcc, v);
            }
            vstc.clear();
        }
    }
    tree.build();
    return tree;
}
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
    return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
    return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
    V<i32> ret(arr.size());
    iota(ALL(ret), 0);
    sort(ALL(ret), [&](i32 i, i32 j) -> bool {
        if (arr[i] == arr[j]) {
            return i < j;
        } else {
            return arr[i] < arr[j];
        }
    });
    return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(f64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
    for (T &ele : x) {
        scan(ele);
    }
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
    scan(head);
    read(tail...);
}
#define CHAR(...)     \
    char __VA_ARGS__; \
    read(__VA_ARGS__);
#define U32(...)     \
    u32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define U64(...)     \
    u64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I32(...)     \
    i32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I64(...)     \
    i64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define F64(...)     \
    f64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define STR(...)        \
    string __VA_ARGS__; \
    read(__VA_ARGS__);
#define VEC(type, name, size) \
    V<type> name(size);       \
    read(name);
#define VVEC(type, name, size1, size2)    \
    VV<type> name(size1, V<type>(size2)); \
    read(name);
#line 5 "graph/test/block_cut_tree.test.cpp"

void solve() {
    I32(n, m);
    Graph<> g(n);
    REP(i, m) {
        I32(u, v);
        g.add_edge(u, v);
    }
    g.build();
    Graph<> bct = block_cut_tree(g);
    cout << bct.v() - n << '\n';
    REP(i, n, bct.v()) {
        cout << LEN(bct[i]);
        for (auto e : bct[i]) {
            cout << ' ' << e.to;
        }
        cout << '\n';
    }
}

int main() {
    i32 t = 1;
    // cin >> t;
    while (t--) {
        solve();
    }
}