CP-Algorithms Library
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Biconnected Components (verify/graph/bcc.test.cpp)
- View this file on GitHub
- Last update: 2025-12-08 19:25:32+01:00
- Problem: https://judge.yosupo.jp/problem/biconnected_components
Depends on
- cp-algo/graph/base.hpp
- cp-algo/graph/concepts.hpp
- cp-algo/graph/dfs.hpp
- cp-algo/graph/dfs_time.hpp
- cp-algo/graph/edge_types.hpp
- cp-algo/graph/tarjan.hpp
- cp-algo/structures/csr.hpp
- cp-algo/structures/stack_union.hpp
- cp-algo/util/big_alloc.hpp
Code
// @brief Biconnected Components
#define PROBLEM "https://judge.yosupo.jp/problem/biconnected_components"
#pragma GCC optimize("Ofast,unroll-loops")
#include <iostream>
#include "blazingio/blazingio.min.hpp"
#include "cp-algo/graph/tarjan.hpp"
#include <bits/stdc++.h>
using namespace std;
using namespace cp_algo::graph;
void solve() {
int n, m;
cin >> n >> m;
graph g(n);
g.read_edges(m);
auto comps = biconnected_components(g);
cout << size(comps) << '\n';
for(auto const& comp: comps.rows()) {
cout << size(comp) << ' ';
for(auto v: comp) {
cout << v << ' ';
}
cout << '\n';
}
}
signed main() {
//freopen("input.txt", "r", stdin);
ios::sync_with_stdio(0);
cin.tie(0);
int t = 1;
//cin >> t;
while(t--) {
solve();
}
}
#line 1 "verify/graph/bcc.test.cpp"
// @brief Biconnected Components
#define PROBLEM "https://judge.yosupo.jp/problem/biconnected_components"
#pragma GCC optimize("Ofast,unroll-loops")
#include <iostream>
#line 1 "blazingio/blazingio.min.hpp"
// NOLINTBEGIN
// clang-format off
// DO NOT REMOVE THIS MESSAGE. The mess that follows is a minified build of
// https://github.com/purplesyringa/blazingio. Refer to the repository for
// a human-readable version and documentation.
// Options: cbfoiedrhWLMXaIaAn
#define M$(x,...)_mm256_##x##_epi8(__VA_ARGS__)
#define $u(...)__VA_ARGS__
#if __APPLE__
#define $m(A,B)A
#else
#define $m(A,B)B
#endif
#if _WIN32
#define $w(A,B)A
#else
#define $w(A,B)B
#endif
#if __i386__|_M_IX86
#define $H(A,B)A
#else
#define $H(A,B)B
#endif
#if __aarch64__
#define $a(A,B)A
#else
#define $a(A,B)B
#endif
#define $P(x)void F(x K){
#define $T template<$c T
#define $c class
#define $C constexpr
#define $R return
#define $O operator
#define u$ uint64_t
#define $r $R*this;
#include<array>
#include<bitset>
#include<complex>
#include<cstring>
#include $a(<arm_neon.h>,<immintrin.h>)
#include<stdint.h>
#include $w(<windows.h>,<sys/mman.h>)
#include<sys/stat.h>
#include $w(<io.h>,<unistd.h>)
#include $w(<ios>,<sys/resource.h>)
#if _MSC_VER
#define __builtin_add_overflow(a,b,c)_addcarry_u64(0,a,b,c)
#define $s
#else
$H(,u$ _umul128(u$ a,u$ b,u$*D){auto x=(__uint128_t)a*b;*D=u$(x>>64);$R(u$)x;})
#define $s $a(,__attribute__((target("avx2"))))
#endif
#define $z $a(16,32)
#define $t $a(uint8x16_t,__m256i)
#define $I $w(__forceinline,__attribute__((always_inline)))
#define $F M(),
#define E$(x)if(!(x))abort();
$w(LONG WINAPI $x(_EXCEPTION_POINTERS*);,)namespace $f{using namespace std;struct B{enum $c A:char{}c;B&$O=(char x){c=A{x};$r}$O char(){$R(char)c;}};$C u$ C=~0ULL/255;struct D{string&K;};static B E[65568];template<int F>struct G{B*H,*S;void K(off_t C){$w(char*D=(char*)VirtualAlloc(0,(C+8191)&-4096,8192,1);E$(D)E$(VirtualFree(D,0,32768))DWORD A=C&-65536;E$(!A||MapViewOfFileEx(CreateFileMapping(GetStdHandle(-10),0,2,0,A,0),4,0,0,0,D)==D)E$(VirtualAlloc(D+A,65536,12288,4)==D+A)E$(~_lseek(0,A,0))DWORD E=0;ReadFile(GetStdHandle(-10),D+A,65536,&E,0);,int A=getpagesize();char*D=(char*)mmap(0,C+A,3,2,0,0);E$(D!=(void*)-1)E$(mmap(D+((C+A-1)&-A),A,3,$m(4114,50),-1,0)!=(void*)-1))H=(B*)D+C;*H=10;H[1]=48;H[2]=0;S=(B*)D;}void L(){H=S=E;}$I void M(){if(F&&S==H){$w(DWORD A=0;ReadFile(GetStdHandle(-10),S=E,65536,&A,0);,$a($u(register long A asm("x0")=0,D asm("x1")=(long)E,G asm("x2")=65536,C asm($m("x16","x8"))=$m(3,63);asm volatile("svc 0" $m("x80",):"+r"(A),"+r"(D):"r"(C),"r"(G));S=launder(E);),off_t A=$H(3,$m(33554435,0));B*D=E;asm volatile($H("int $128","syscall"):"+a"(A),$H("+c"(D):"b","+S"(D):"D")(0),"d"(65536)$H(,$u(:"rcx","r11")));S=D;))H=S+A;*H=10;if(!A)E[1]=48,E[2]=0;}}$T>$I void N(T&x){while($F(*S&240)==48)x=T(x*10+(*S++-48));}$T>$I decltype((void)~T{1})O(T&x){M();int A=is_signed_v<T>&&*S==45;S+=A;N(x=0);x=A?1+~x:x;}$T>$I decltype((void)T{1.})O(T&x){M();int A=*S==45;S+=A;$F S+=*S==43;u$ n=0;int i=0;for(;i<18&&($F*S&240)==48;i++)n=n*10+*S++-48;int B=20;int C=*S==46;S+=C;for(;i<18&&($F*S&240)==48;i++)n=n*10+*S++-48,B-=C;x=(T)n;while(($F*S&240)==48)x=x*10+*S++-48,B-=C;if(*S==46)S++,C=1;while(($F*S&240)==48)x=x*10+*S++-48,B-=C;int D;if((*S|32)==101)S++,$F S+=*S==43,O(D),B+=D;static $C auto E=[](){array<T,41>E{};T x=1;for(int i=21;i--;)E[40-i]=x,E[i]=1/x,x*=10;$R E;}();while(B>40)x*=(T)1e10,B-=10;while(B<0)x*=(T)1e-10,B+=10;x*=E[B];x=A?-x:x;}$I void O(bool&x){$F x=*S++==49;}$I void O(char&x){$F x=*S++;}$I void O(uint8_t&x){$F x=*S++;}$I void O(int8_t&x){$F x=*S++;}$T>$s void P(string&K,T C){M();B*G=S;C();K.assign((char*)G,S-G);while(F&&S==H&&($F H!=E)){C();K.append(E,S);}}$s void O(string&K){P(K,[&]()$s{B*p=S;$w(ULONG R;,)$t x;$a(uint64x2_t A;while(memcpy(&x,p,16),A=uint64x2_t(x<33),!(A[0]|A[1]))p+=16;S=p+(A[0]?0:8)+$w((_BitScanForward64(&R,A[0]?A[0]:A[1]),R),__builtin_ctzll(A[0]?A[0]:A[1]))/8;,int J;$t C=M$(set1,32);while(memcpy(&x,p,32),!(J=M$(movemask,M$(cmpeq,C,_mm256_max_epu8(C,x)))))p+=32;S=p+$w((_BitScanForward(&R,J),R),__builtin_ctz(J));)});}$s void O(D&A){P(A.K,[&](){S=(B*)memchr(S,10,H-S+1);});if(A.K.size()&&A.K.back()==13)A.K.pop_back();if(A.K.empty()||S<H)S+=*S==10;}$T>$I void O(complex<T>&K){T A,B{};if($F*S==40){S++;O(A);if($F*S++==44)Q(B),S++;}else O(A);K={A,B};}template<size_t N>$s void O(bitset<N>&K){if(N>4095&&!*this)$R;ptrdiff_t i=N;while(i)if($F i%$z||H-S<$z)K[--i]=*S++==49;else{B*p=S;for(int64_t j=0;j<min(i,H-S)/$z;j++){i-=$z;$t x;memcpy(&x,p,$z);$a(auto B=(uint8x16_t)vdupq_n_u64(~2ULL/254)&(48-x);auto C=vzip_u8(vget_high_u8(B),vget_low_u8(B));auto y=vaddvq_u16((uint16x8_t)vcombine_u8(C.val[0],C.val[1]));,u$ a=~0ULL/65025;auto y=$w(_byteswap_ulong,__builtin_bswap32)(M$(movemask,M$(shuffle,_mm256_slli_epi32(x,7),_mm256_set_epi64x(a+C*24,a+C*16,a+C*8,a))));)p+=$z;memcpy((char*)&K+i/8,&y,$z/8);}S=p;}}$T>$I void Q(T&K){if(!is_same_v<T,D>)while($F(uint8_t)*S<33)S++;O(K);}$O bool(){$R!!*this;}bool $O!(){$R S>H;}};struct U{G<0>A;G<1>B;U(){struct stat D;E$(~fstat(0,&D))(D.st_mode>>12)==8?A.K(D.st_size):B.L();}U*tie(nullptr_t){$R this;}void sync_with_stdio(bool){}$T>$I U&$O>>(T&K){A.S?A.Q(K):B.Q(K);$r}$O bool(){$R!!*this;}bool $O!(){$R A.S?!A:!B;}};short A[100];char L[64]{1};struct
V{char*D;B*S;int J;V(){$w(E$(D=(char*)VirtualAlloc(0,536870912,8192,4))E$(VirtualAlloc(D,4096,4096,260))AddVectoredExceptionHandler(1,$x);,size_t C=536870912;$m(,rlimit E;getrlimit(RLIMIT_AS,&E);if(~E.rlim_cur)C=25165824;)D=(char*)mmap(0,C,3,$m(4162,16418),-1,0);E$(D!=(void*)-1))S=(B*)D;for(int i=0;i<100;i++)A[i]=short((48+i/10)|((48+i%10)<<8));for(int i=1;i<64;i++)L[i]=L[i-1]+(0x8922489224892249>>i&1);}~V(){flush($w(!J,));}void flush($w(int F=0,)){$w(J=1;auto E=GetStdHandle(-11);auto C=F?ReOpenFile(E,1073741824,7,2684354560):(void*)-1;DWORD A;E$(C==(void*)-1?WriteFile(E,D,DWORD((char*)S-D),&A,0):(WriteFile(C,D,DWORD(((char*)S-D+4095)&-4096),&A,0)&&~_chsize(1,int((char*)S-D)))),auto G=D;ssize_t A;while((A=write(1,G,(char*)S-G))>0)G+=A;E$(~A))S=(B*)D;}$P(char)*S++=K;}$P(uint8_t)*S++=K;}$P(int8_t)*S++=K;}$P(bool)*S++=48+K;}$T>decltype((void)~T{1})F(T K){using D=make_unsigned_t<T>;D C=K;if(K<0)F('-'),C=1+~C;static $C auto N=[](){array<D,5*sizeof(T)/2>N{};D n=1;for(size_t i=1;i<N.size();i++)n*=10,N[i]=n;$R N;}();$w(ULONG M;,)int G=L[$w(($H(_BitScanReverse(&M,ULONG((int64_t)C>>32))?M+=32:_BitScanReverse(&M,(ULONG)C|1),_BitScanReverse64(&M,C|1)),M),63^__builtin_clzll(C|1))];G-=C<N[G-1];short H[20];if $C(sizeof(T)==2){auto n=33555U*C-C/2;u$ H=A[n>>25];n=(n&33554431)*25;H|=A[n>>23]<<16;H|=u$(48+((n&8388607)*5>>22))<<32;H>>=40-G*8;memcpy(S,&H,8);}else if $C(sizeof(T)==4){auto n=1441151881ULL*C;$H(n>>=25;n++;for(int i=0;i<5;i++){H[i]=A[n>>32];n=(n&~0U)*100;},int K=57;auto J=~0ULL>>7;for(int i=0;i<5;i++){H[i]=A[n>>K];n=(n&J)*25;K-=2;J/=4;})memcpy(S,(B*)H+10-G,16);}else{$H($u(if(C<(1ULL<<32)){$R F((uint32_t)C);}auto J=(u$)1e10;auto x=C/J,y=C%J;int K=100000,b[]{int(x/K),int(x%K),int(y/K),int(y%K)};B H[40];for(int i=0;i<4;i++){int n=int((429497ULL*b[i]>>7)+1);B*p=H+i*5;*p=48+char(n>>25);n=(n&~0U>>7)*25;memcpy(p+1,A+(n>>23),2);memcpy(p+3,A+((n&~0U>>9)*25>>21),2);}),$u(u$ D,E=_umul128(18,C,&D),F;_umul128(0x725dd1d243aba0e8,C,&F);D+=__builtin_add_overflow(E,F+1,&E);for(int i=0;i<10;i++)H[i]=A[D],E=_umul128(100,E,&D);))memcpy(S,(B*)H+20-G,20);}S+=G;}$T>decltype((void)T{1.})F(T K){if(K<0)F('-'),K=-K;auto G=[&](){auto x=u$(K*1e12);$H($u(x-=x>999999999999;uint32_t n[]{uint32_t(x/1000000*429497>>7)+1,uint32_t(x%1000000*429497>>7)+1};int K=25,J=~0U>>7;for(int i=0;i<3;i++){for(int j=0;j<2;j++)memcpy(S+i*2+j*6,A+(n[j]>>K),2),n[j]=(n[j]&J)*25;K-=2;J/=4;}S+=12;),$u(u$ D,E=_umul128(472236648287,x,&D)>>8;E|=D<<56;D>>=8;E++;for(int i=0;i<6;i++)memcpy(S,A+D,2),S+=2,E=_umul128(100,E,&D);))};if(K==0)$R F('0');if(K>=1e16){K*=(T)1e-16;int B=16;while(K>=1)K*=(T).1,B++;F("0.");G();F('e');F(B);}else if(K>=1){auto B=(u$)K;F(B);if((K-=(T)B)>0)F('.'),G();}else F("0."),G();}$P(const char*)$w(size_t A=strlen(K);memcpy((char*)S,K,A);S+=A;,S=(B*)stpcpy((char*)S,K);)}$P(const uint8_t*)F((char*)K);}$P(const int8_t*)F((char*)K);}$P(string_view)memcpy(S,K.data(),K.size());S+=K.size();}$T>$P(complex<T>)*this<<'('<<K.real()<<','<<K.imag()<<')';}template<size_t N>$s $P(const bitset<N>&)auto i=N;while(i%$z)*S++=48+K[--i];B*p=S;while(i){i-=$z;$a(short,int)x;memcpy(&x,(char*)&K+i/8,$z/8);$a(auto A=(uint8x8_t)vdup_n_u16(x);vst1q_u8((uint8_t*)p,48-vtstq_u8(vcombine_u8(vuzp2_u8(A,A),vuzp1_u8(A,A)),(uint8x16_t)vdupq_n_u64(~2ULL/254)));,auto b=_mm256_set1_epi64x(~2ULL/254);_mm256_storeu_si256(($t*)p,M$(sub,M$(set1,48),M$(cmpeq,_mm256_and_si256(M$(shuffle,_mm256_set1_epi32(x),_mm256_set_epi64x(0,C,C*2,C*3)),b),b)));)p+=$z;}S=p;}$T>V&$O<<(const T&K){F(K);$r}V&$O<<(V&(*A)(V&)){$R A(*this);}};struct W{$T>W&$O<<(const T&K){$r}W&$O<<(W&(*A)(W&)){$R A(*this);}};}namespace std{$f::U i$;$f::V o$;$f::W e$;$f::U&getline($f::U&B,string&K){$f::D A{K};$R B>>A;}$f::V&flush($f::V&B){if(!i$.A.S)B.flush();$R B;}$f::V&endl($f::V&B){$R B<<'\n'<<flush;}$f::W&endl($f::W&B){$R B;}$f::W&flush($f::W&B){$R B;}}$w(LONG WINAPI $x(_EXCEPTION_POINTERS*A){auto C=A->ExceptionRecord;auto B=C->ExceptionInformation[1];if(C->ExceptionCode==2147483649&&B-(ULONG_PTR)std::o$.D<0x40000000){E$(VirtualAlloc((char*)B,16777216,4096,4)&&VirtualAlloc((char*)(B+16777216),4096,4096,260))$R-1;}$R 0;},)
#define freopen(...)if(freopen(__VA_ARGS__)==stdin)std::i$=$f::U{}
#define cin i$
#define cout o$
#ifdef ONLINE_JUDGE
#define cerr e$
#define clog e$
#endif
// End of blazingio
// NOLINTEND
// clang-format on
#line 1 "cp-algo/graph/tarjan.hpp"
#line 1 "cp-algo/graph/dfs_time.hpp"
#line 1 "cp-algo/graph/dfs.hpp"
#line 1 "cp-algo/graph/base.hpp"
#line 1 "cp-algo/graph/edge_types.hpp"
#line 4 "cp-algo/graph/edge_types.hpp"
#include <cstdint>
namespace cp_algo::graph {
using node_index = int;
struct edge_base {
int xor_nodes;
edge_base() {}
edge_base(node_index from, node_index to): xor_nodes(from ^ to) {}
// Given one endpoint, return the other
node_index traverse(node_index from) const {
return xor_nodes ^ from;
}
static auto read(node_index v0 = 0) {
node_index u, v;
std::cin >> u >> v;
u -= v0;
v -= v0;
return std::pair{u, edge_base(u, v)};
}
};
struct weighted_edge: edge_base {
int64_t w;
weighted_edge() {}
weighted_edge(node_index from, node_index to, int64_t w): edge_base(from, to), w(w) {}
static auto read(node_index v0 = 0) {
auto [u, e] = edge_base::read(v0);
int64_t w;
std::cin >> w;
return std::pair{u, weighted_edge(u, e.traverse(u), w)};
}
};
template<typename edge>
concept edge_type = std::is_base_of_v<edge_base, edge>;
template<typename edge>
concept weighted_edge_type = std::is_base_of_v<weighted_edge, edge>;
}
#line 1 "cp-algo/graph/concepts.hpp"
#line 4 "cp-algo/graph/concepts.hpp"
#include <type_traits>
namespace cp_algo::graph {
// Shared graph mode enum for all graph headers
enum graph_mode { directed, undirected };
// Traits: true for types that expose `edge_t` and static `mode`
template<typename T, typename = void>
struct graph_traits : std::false_type {};
template<typename T>
struct graph_traits<T, std::void_t<typename T::edge_t, decltype(T::mode)>> : std::true_type {
using edge_t = typename T::edge_t;
static constexpr auto mode = T::mode;
static constexpr bool is_directed = mode == directed;
static constexpr bool is_undirected = mode == undirected;
static constexpr bool is_weighted = weighted_edge_type<edge_t>;
};
// Concepts
template<typename G>
concept graph_type = graph_traits<G>::value;
template<typename G>
concept digraph_type = graph_type<G> && graph_traits<G>::is_directed;
template<typename G>
concept undirected_graph_type = graph_type<G> && graph_traits<G>::is_undirected;
template<typename G>
concept weighted_graph_type = graph_type<G> && graph_traits<G>::is_weighted;
template<typename G>
concept weighted_digraph_type = digraph_type<G> && graph_traits<G>::is_weighted;
template<typename G>
concept weighted_undirected_graph_type = undirected_graph_type<G> && graph_traits<G>::is_weighted;
}
#line 1 "cp-algo/structures/stack_union.hpp"
#line 1 "cp-algo/util/big_alloc.hpp"
#include <map>
#include <deque>
#include <vector>
#include <string>
#include <cstddef>
#line 10 "cp-algo/util/big_alloc.hpp"
// Single macro to detect POSIX platforms (Linux, Unix, macOS)
#if defined(__linux__) || defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))
# define CP_ALGO_USE_MMAP 1
# include <sys/mman.h>
#else
# define CP_ALGO_USE_MMAP 0
#endif
namespace cp_algo {
template <typename T, std::size_t Align = 32>
class big_alloc {
static_assert( Align >= alignof(void*), "Align must be at least pointer-size");
static_assert(std::popcount(Align) == 1, "Align must be a power of two");
public:
using value_type = T;
template <class U> struct rebind { using other = big_alloc<U, Align>; };
constexpr bool operator==(const big_alloc&) const = default;
constexpr bool operator!=(const big_alloc&) const = default;
big_alloc() noexcept = default;
template <typename U, std::size_t A>
big_alloc(const big_alloc<U, A>&) noexcept {}
[[nodiscard]] T* allocate(std::size_t n) {
std::size_t padded = round_up(n * sizeof(T));
std::size_t align = std::max<std::size_t>(alignof(T), Align);
#if CP_ALGO_USE_MMAP
if (padded >= MEGABYTE) {
void* raw = mmap(nullptr, padded,
PROT_READ | PROT_WRITE,
MAP_PRIVATE | MAP_ANONYMOUS, -1, 0);
madvise(raw, padded, MADV_HUGEPAGE);
madvise(raw, padded, MADV_POPULATE_WRITE);
return static_cast<T*>(raw);
}
#endif
return static_cast<T*>(::operator new(padded, std::align_val_t(align)));
}
void deallocate(T* p, std::size_t n) noexcept {
if (!p) return;
std::size_t padded = round_up(n * sizeof(T));
std::size_t align = std::max<std::size_t>(alignof(T), Align);
#if CP_ALGO_USE_MMAP
if (padded >= MEGABYTE) { munmap(p, padded); return; }
#endif
::operator delete(p, padded, std::align_val_t(align));
}
private:
static constexpr std::size_t MEGABYTE = 1 << 20;
static constexpr std::size_t round_up(std::size_t x) noexcept {
return (x + Align - 1) / Align * Align;
}
};
template<typename T>
using big_vector = std::vector<T, big_alloc<T>>;
template<typename T>
using big_basic_string = std::basic_string<T, std::char_traits<T>, big_alloc<T>>;
template<typename T>
using big_deque = std::deque<T, big_alloc<T>>;
template<typename Key, typename Value, typename Compare = std::less<Key>>
using big_map = std::map<Key, Value, Compare, big_alloc<std::pair<const Key, Value>>>;
using big_string = big_basic_string<char>;
}
#line 5 "cp-algo/structures/stack_union.hpp"
#include <iterator>
#include <ranges>
namespace cp_algo::structures {
template<class datatype>
struct stack_union {
stack_union(int n = 0): head(n), next(1), data(1) {}
void push(int v, datatype const& vdata) {
next.push_back(head[v]);
head[v] = (int)std::size(next) - 1;
data.push_back(vdata);
}
template<typename... Args>
void emplace(int v, Args&&... vdata) {
next.push_back(head[v]);
head[v] = (int)std::size(next) - 1;
data.emplace_back(std::forward<Args>(vdata)...);
}
void reserve(int m) {
data.reserve(m);
next.reserve(m);
}
size_t size() const {return std::size(head);}
size_t nodes() const {return std::size(data);}
template<typename Su>
struct _iterator {
using value_type = std::conditional_t<std::is_const_v<Su>, const datatype, datatype>;
using difference_type = std::ptrdiff_t;
Su* su = nullptr;
int sv = 0;
value_type& operator*() const { return su->data[sv]; }
_iterator& operator++() {
sv = su->next[sv];
return *this;
}
_iterator operator++(int) { auto tmp = *this; ++*this; return tmp; }
friend bool operator==(_iterator const& it, std::default_sentinel_t) {
return it.sv == 0;
}
};
using iterator = _iterator<stack_union<datatype>>;
using const_iterator = _iterator<const stack_union<datatype>>;
auto operator[](this auto&& self, int v) {
using Iter = _iterator<std::remove_reference_t<decltype(self)>>;
return std::ranges::subrange(Iter{&self, self.head[v]}, std::default_sentinel);
}
big_vector<int> head, next;
big_vector<datatype> data;
};
}
#line 7 "cp-algo/graph/base.hpp"
namespace cp_algo::graph {
using edge_index = int;
template<edge_type _edge_t = edge_base, graph_mode _mode = undirected>
struct graph {
using edge_t = _edge_t;
static constexpr auto mode = _mode;
using incidence_list = structures::stack_union<edge_index>;
graph(int n, int v0 = 0): v0(v0), adj(n) {}
graph transpose() const {
static_assert(mode == directed, "transpose is only defined for directed graphs");
graph<edge_t, mode> gt(n(), v0);
for(auto v: nodes()) {
for(auto e: outgoing(v)) {
gt.add_edge(edge(e).traverse(v), edge(e));
}
}
return gt;
}
edge_index add_edge(node_index u, edge_t e) {
edge_index idx = (edge_index)size(E);
E.push_back(e);
adj.push(u, idx);
if constexpr (mode == undirected) {
adj.push(e.traverse(u), idx);
}
return idx;
}
edge_index add_edge(node_index u, auto... Args) {
return add_edge(u, edge_t(u, Args...));
}
void read_edges(node_index m) {
adj.reserve(mode == undirected ? 2 * m : m);
for(edge_index i = 0; i < m; i++) {
auto [u, e] = edge_t::read(v0);
add_edge(u, e);
}
}
auto outgoing(node_index v) const {return adj[v];}
auto edges() const {return E | std::views::all;}
auto nodes() const {return std::views::iota(node_index(0), n());}
auto edge_indices() const {return std::views::iota(edge_index(0), m());}
auto&& incidence_lists(this auto&& self) {return self.adj;}
auto&& edge(this auto&& self, edge_index e) {return self.E[e];}
node_index n() const {return (node_index)incidence_lists().size();}
edge_index m() const {return (edge_index)edges().size();}
private:
node_index v0;
big_vector<edge_t> E;
incidence_list adj;
};
// aliases for most standard cases
template<edge_type edge_t = edge_base>
using digraph = graph<edge_t, directed>;
template<weighted_edge_type edge_t = weighted_edge, graph_mode mode = undirected>
using weighted_graph = graph<edge_t, mode>;
template<weighted_edge_type edge_t = weighted_edge>
using weighted_digraph = digraph<edge_t>;
}
#line 4 "cp-algo/graph/dfs.hpp"
#include <variant>
#include <stack>
namespace cp_algo::graph {
enum node_state { unvisited, visiting, visited, blocked };
template<graph_type graph>
struct dfs_context {
big_vector<node_state> state;
graph const* g;
bool done = false; // Set to true to stop DFS early
dfs_context(graph const& g): state(g.n()), g(&g) {}
// Called when first entering a node
void on_enter(node_index) {}
// Called when discovering a tree edge (v->u is a tree edge, u is unvisited)
void on_tree_edge(node_index, edge_index) {}
// Called after returning from a child via tree edge
void on_return_from_child(node_index, edge_index) {}
// Called when encountering a back edge (v->u, u is visiting)
void on_back_edge(node_index, edge_index) {}
// Called when encountering a forward/cross edge (v->u, u is visited)
void on_forward_cross_edge(node_index, edge_index) {}
// Called when exiting a node (all edges processed)
void on_exit(node_index) {}
};
template<template<typename> class Context, graph_type graph>
Context<graph> dfs(graph const& g) {
Context<graph> context(g);
auto const& adj = g.incidence_lists();
struct frame {
node_index v;
[[no_unique_address]] std::conditional_t<
undirected_graph_type<graph>,
edge_index, std::monostate> ep;
int sv; // edge index in stack_union
enum { INIT, PROCESS_EDGES, HANDLE_CHILD } state;
};
std::stack<frame> dfs_stack;
for (auto root: g.nodes()) {
if (context.done) break;
if (context.state[root] != unvisited) continue;
if constexpr (undirected_graph_type<graph>) {
dfs_stack.push({root, -1, 0, frame::INIT});
} else {
dfs_stack.push({root, {}, 0, frame::INIT});
}
while (!empty(dfs_stack)) {
auto& f = dfs_stack.top();
if (f.state == frame::INIT) {
context.state[f.v] = visiting;
context.on_enter(f.v);
f.sv = adj.head[f.v];
f.state = frame::PROCESS_EDGES;
continue;
}
if (f.state == frame::HANDLE_CHILD) {
auto e = adj.data[f.sv];
f.sv = adj.next[f.sv];
context.on_return_from_child(f.v, e);
f.state = frame::PROCESS_EDGES;
continue;
}
// PROCESS_EDGES
bool found_child = false;
while (f.sv != 0 && !context.done) {
auto e = adj.data[f.sv];
if constexpr (undirected_graph_type<graph>) {
if (f.ep == e) {
f.sv = adj.next[f.sv];
continue;
}
}
node_index u = g.edge(e).traverse(f.v);
if (context.state[u] == unvisited) {
context.on_tree_edge(f.v, e);
f.state = frame::HANDLE_CHILD;
if constexpr (undirected_graph_type<graph>) {
dfs_stack.push({u, e, 0, frame::INIT});
} else {
dfs_stack.push({u, {}, 0, frame::INIT});
}
found_child = true;
break;
} else if (context.state[u] == visiting) {
context.on_back_edge(f.v, e);
} else if (context.state[u] == visited) {
context.on_forward_cross_edge(f.v, e);
}
f.sv = adj.next[f.sv];
}
if (found_child) continue;
// All edges processed
context.state[f.v] = visited;
context.on_exit(f.v);
dfs_stack.pop();
}
}
return context;
}
}
#line 5 "cp-algo/graph/dfs_time.hpp"
namespace cp_algo::graph {
// Context that maintains discovery time (tin)
template<graph_type graph>
struct dfs_time_context: dfs_context<graph> {
using base = dfs_context<graph>;
big_vector<int> tin;
int timer;
dfs_time_context(graph const& g): base(g), tin(g.n()), timer(0) {}
void on_enter(node_index v) {
tin[v] = timer++;
}
};
// Context that maintains both discovery time (tin) and finish time (tout)
template<graph_type graph>
struct dfs_time_range_context: dfs_time_context<graph> {
using base = dfs_time_context<graph>;
big_vector<int> tout;
dfs_time_range_context(graph const& g): base(g), tout(g.n()) {}
void on_exit(node_index v) {
tout[v] = base::timer;
}
};
// Context that maintains tin and low (for Tarjan-like algorithms)
template<graph_type graph>
struct dfs_low_context: dfs_time_context<graph> {
using base = dfs_time_context<graph>;
big_vector<int> low;
dfs_low_context(graph const& g): base(g), low(g.n()) {}
void on_enter(node_index v) {
base::on_enter(v);
low[v] = base::tin[v];
}
void on_return_from_child(node_index v, edge_index e) {
node_index u = base::g->edge(e).traverse(v);
low[v] = std::min(low[v], low[u]);
}
void on_back_edge(node_index v, edge_index e) {
node_index u = base::g->edge(e).traverse(v);
low[v] = std::min(low[v], base::tin[u]);
}
void on_forward_cross_edge(node_index v, edge_index e) {
node_index u = base::g->edge(e).traverse(v);
low[v] = std::min(low[v], base::tin[u]);
}
};
}
#line 1 "cp-algo/structures/csr.hpp"
#line 4 "cp-algo/structures/csr.hpp"
#include <algorithm>
#include <numeric>
#line 7 "cp-algo/structures/csr.hpp"
#include <span>
namespace cp_algo::structures {
template<class datatype>
struct csr {
csr(): head{0} { }
void new_row() {
head.push_back(head.back());
}
void push(datatype const& value) {
data.push_back(value);
head.back()++;
}
template<typename... Args>
void emplace(Args&&... args) {
data.emplace_back(std::forward<Args>(args)...);
head.back()++;
}
void reserve_rows(int n) {
head.reserve(n + 1);
}
void reserve_data(size_t n) {
data.reserve(n);
}
void reverse_rows() {
std::ranges::reverse(data);
std::adjacent_difference(head.begin(), head.end(), head.begin());
std::ranges::reverse(head | std::views::drop(1));
std::partial_sum(head.begin(), head.end(), head.begin());
}
size_t size() const { return head.size() - 1; }
size_t total_size() const { return data.size(); }
auto operator[](this auto&& self, auto row) {
return std::span(self.data).subspan(self.head[row], self.head[row + 1] - self.head[row]);
}
auto rows(this auto&& self) {
return std::views::iota(size_t(0), self.size())
| std::views::transform([&self](auto i) { return self[i]; });
}
big_vector<int> head;
big_vector<datatype> data;
};
}
#line 7 "cp-algo/graph/tarjan.hpp"
#include <cassert>
#line 9 "cp-algo/graph/tarjan.hpp"
namespace cp_algo::graph {
// Add stack and components collection
template<graph_type graph>
struct tarjan_context: dfs_low_context<graph> {
using base = dfs_low_context<graph>;
std::stack<int> stack;
structures::csr<node_index> components;
tarjan_context(graph const& g): base(g) {
components.reserve_data(g.n());
}
void on_enter(node_index v) {
base::on_enter(v);
stack.push(v);
}
void collect(node_index v) {
components.new_row();
node_index u;
do {
u = stack.top();
stack.pop();
base::state[u] = blocked;
components.push(u);
} while(u != v);
}
};
template<graph_type graph>
struct exit_context: tarjan_context<graph> {
using tarjan_context<graph>::tarjan_context;
void on_exit(node_index v) {
if (this->low[v] == this->tin[v]) {
this->collect(v);
}
}
};
// Tarjan's algorithm for Strongly Connected Components
// returns components in reverse topological order
template<digraph_type graph>
auto strongly_connected_components(graph const& g) {
return dfs<exit_context>(g).components;
}
// Tarjan's algorithm for Two-Edge-Connected Components
template<undirected_graph_type graph>
auto two_edge_connected_components(graph const& g) {
return dfs<exit_context>(g).components;
}
template<undirected_graph_type graph>
struct bcc_context: tarjan_context<graph> {
using base = tarjan_context<graph>;
using base::base;
void on_return_from_child(node_index v, edge_index e) {
base::on_return_from_child(v, e);
node_index u = base::g->edge(e).traverse(v);
if (base::low[u] >= base::tin[v]) {
base::collect(u);
base::components.push(v);
}
}
void on_exit(node_index v) {
if (std::empty(base::g->outgoing(v))) {
base::collect(v);
}
}
};
// Tarjan's algorithm for Biconnected Components (vertex-biconnected)
template<undirected_graph_type graph>
auto biconnected_components(graph const& g) {
return dfs<bcc_context>(g).components;
}
}
#line 7 "verify/graph/bcc.test.cpp"
#include <bits/stdc++.h>
using namespace std;
using namespace cp_algo::graph;
void solve() {
int n, m;
cin >> n >> m;
graph g(n);
g.read_edges(m);
auto comps = biconnected_components(g);
cout << size(comps) << '\n';
for(auto const& comp: comps.rows()) {
cout << size(comp) << ' ';
for(auto v: comp) {
cout << v << ' ';
}
cout << '\n';
}
}
signed main() {
//freopen("input.txt", "r", stdin);
ios::sync_with_stdio(0);
cin.tie(0);
int t = 1;
//cin >> t;
while(t--) {
solve();
}
}
Test cases
| Env | Name | Status | Elapsed | Memory |
|---|---|---|---|---|
| g++ | example_00 |
AC |
6 ms | 6 MB |
| g++ | example_01 |
AC |
6 ms | 6 MB |
| g++ | example_02 |
AC |
6 ms | 6 MB |
| g++ | large_cycle_00 |
AC |
249 ms | 51 MB |
| g++ | max_line_clique_00 |
AC |
68 ms | 39 MB |
| g++ | max_random_00 |
AC |
270 ms | 46 MB |
| g++ | max_random_2_00 |
AC |
201 ms | 42 MB |
| g++ | max_random_2_01 |
AC |
267 ms | 42 MB |
| g++ | max_random_2_02 |
AC |
215 ms | 42 MB |
| g++ | max_star_00 |
AC |
94 ms | 46 MB |
| g++ | max_tree_00 |
AC |
233 ms | 44 MB |
| g++ | min_00 |
AC |
7 ms | 6 MB |
| g++ | min_01 |
AC |
7 ms | 6 MB |
| g++ | min_02 |
AC |
7 ms | 6 MB |
| g++ | random_1_00 |
AC |
223 ms | 37 MB |
| g++ | random_2_00 |
AC |
228 ms | 39 MB |
| g++ | random_2_01 |
AC |
89 ms | 28 MB |
| g++ | random_2_02 |
AC |
85 ms | 29 MB |
| g++ | small_random_1_00 |
AC |
6 ms | 6 MB |
| g++ | small_random_2_00 |
AC |
7 ms | 6 MB |
| g++ | small_random_2_01 |
AC |
7 ms | 6 MB |
| g++ | small_random_2_02 |
AC |
7 ms | 6 MB |