CP-Algorithms Library
This documentation is automatically generated by competitive-verifier/competitive-verifier
Counting Eulerian Circuits (verify/linalg/euler_circs.test.cpp)
- View this file on GitHub
- Last update: 2025-05-31 15:35:36+02:00
- Problem: https://judge.yosupo.jp/problem/counting_eulerian_circuits
Depends on
- cp-algo/linalg/matrix.hpp
- cp-algo/linalg/vector.hpp
- cp-algo/math/combinatorics.hpp
- cp-algo/math/common.hpp
- cp-algo/number_theory/modint.hpp
- cp-algo/random/rng.hpp
- cp-algo/util/big_alloc.hpp
- cp-algo/util/checkpoint.hpp
- cp-algo/util/simd.hpp
Code
// @brief Counting Eulerian Circuits
#define PROBLEM "https://judge.yosupo.jp/problem/counting_eulerian_circuits"
#pragma GCC optimize("Ofast,unroll-loops")
#include <bits/stdc++.h>
#include "blazingio/blazingio.min.hpp"
#include "cp-algo/math/combinatorics.hpp"
#include "cp-algo/linalg/matrix.hpp"
using namespace std;
using namespace cp_algo::math;
using namespace cp_algo::linalg;
const int64_t mod = 998244353;
using base = modint<mod>;
void solve() {
int n, m;
cin >> n >> m;
matrix<base> a(n);
int r = 0;
vector<int> indeg(n), outdeg(n);
for(int i = 0; i < m; i++) {
int u, v;
cin >> u >> v;
a[u][v] -= 1;
a[v][v] += 1;
outdeg[u]++;
indeg[v]++;
r = v;
}
a[r][r] = fact<base>(indeg[r] - 1);
for(int i = 0; i < n; i++) {
if(i == r) {
continue;
}
if(indeg[i] != outdeg[i]) {
cout << 0 << "\n";
return;
}
if(indeg[i] != 0) {
a[i] *= fact<base>(indeg[i] - 1);
} else {
a[i][i] = 1;
}
a[r][i] = a[i][r] = 0;
}
cout << a.det() << "\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/linalg/euler_circs.test.cpp"
// @brief Counting Eulerian Circuits
#define PROBLEM "https://judge.yosupo.jp/problem/counting_eulerian_circuits"
#pragma GCC optimize("Ofast,unroll-loops")
#include <bits/stdc++.h>
#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;
#line 41 "blazingio/blazingio.min.hpp"
#include $a(<arm_neon.h>,<immintrin.h>)
#line 43 "blazingio/blazingio.min.hpp"
#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/math/combinatorics.hpp"
#line 1 "cp-algo/math/common.hpp"
#line 6 "cp-algo/math/common.hpp"
namespace cp_algo::math {
#ifdef CP_ALGO_MAXN
const int maxn = CP_ALGO_MAXN;
#else
const int maxn = 1 << 19;
#endif
const int magic = 64; // threshold for sizes to run the naive algo
auto bpow(auto const& x, auto n, auto const& one, auto op) {
if(n == 0) {
return one;
} else {
auto t = bpow(x, n / 2, one, op);
t = op(t, t);
if(n % 2) {
t = op(t, x);
}
return t;
}
}
auto bpow(auto x, auto n, auto ans) {
return bpow(x, n, ans, std::multiplies{});
}
template<typename T>
T bpow(T const& x, auto n) {
return bpow(x, n, T(1));
}
inline constexpr auto inv2(auto x) {
assert(x % 2);
std::make_unsigned_t<decltype(x)> y = 1;
while(y * x != 1) {
y *= 2 - x * y;
}
return y;
}
}
#line 5 "cp-algo/math/combinatorics.hpp"
#include <ranges>
namespace cp_algo::math {
// fact/rfact/small_inv are caching
// Beware of usage with dynamic mod
template<typename T>
T fact(auto n) {
static std::vector<T> F(maxn);
static bool init = false;
if(!init) {
F[0] = T(1);
for(int i = 1; i < maxn; i++) {
F[i] = F[i - 1] * T(i);
}
init = true;
}
return F[n];
}
// Only works for modint types
template<typename T>
T rfact(auto n) {
static std::vector<T> F(maxn);
static bool init = false;
if(!init) {
int t = (int)std::min<int64_t>(T::mod(), maxn) - 1;
F[t] = T(1) / fact<T>(t);
for(int i = t - 1; i >= 0; i--) {
F[i] = F[i + 1] * T(i + 1);
}
init = true;
}
return F[n];
}
template<typename T, int base>
T pow_fixed(int n) {
static std::vector<T> prec_low(1 << 16);
static std::vector<T> prec_high(1 << 16);
static bool init = false;
if(!init) {
init = true;
prec_low[0] = prec_high[0] = T(1);
T step_low = T(base);
T step_high = bpow(T(base), 1 << 16);
for(int i = 1; i < (1 << 16); i++) {
prec_low[i] = prec_low[i - 1] * step_low;
prec_high[i] = prec_high[i - 1] * step_high;
}
}
return prec_low[n & 0xFFFF] * prec_high[n >> 16];
}
template<typename T>
std::vector<T> bulk_invs(auto const& args) {
std::vector<T> res(std::size(args), args[0]);
for(size_t i = 1; i < std::size(args); i++) {
res[i] = res[i - 1] * args[i];
}
auto all_invs = T(1) / res.back();
for(size_t i = std::size(args) - 1; i > 0; i--) {
res[i] = all_invs * res[i - 1];
all_invs *= args[i];
}
res[0] = all_invs;
return res;
}
template<typename T>
T small_inv(auto n) {
static auto F = bulk_invs<T>(std::views::iota(1, maxn));
return F[n - 1];
}
template<typename T>
T binom_large(T n, auto r) {
assert(r < maxn);
T ans = 1;
for(decltype(r) i = 0; i < r; i++) {
ans = ans * T(n - i) * small_inv<T>(i + 1);
}
return ans;
}
template<typename T>
T binom(auto n, auto r) {
if(r < 0 || r > n) {
return T(0);
} else if(n >= maxn) {
return binom_large(T(n), r);
} else {
return fact<T>(n) * rfact<T>(r) * rfact<T>(n - r);
}
}
}
#line 1 "cp-algo/linalg/matrix.hpp"
#line 1 "cp-algo/random/rng.hpp"
#line 5 "cp-algo/random/rng.hpp"
namespace cp_algo::random {
uint64_t rng() {
static std::mt19937_64 rng(
std::chrono::steady_clock::now().time_since_epoch().count()
);
return rng();
}
}
#line 1 "cp-algo/linalg/vector.hpp"
#line 1 "cp-algo/number_theory/modint.hpp"
#line 6 "cp-algo/number_theory/modint.hpp"
namespace cp_algo::math {
template<typename modint, typename _Int>
struct modint_base {
using Int = _Int;
using UInt = std::make_unsigned_t<Int>;
static constexpr size_t bits = sizeof(Int) * 8;
using Int2 = std::conditional_t<bits <= 32, int64_t, __int128_t>;
using UInt2 = std::conditional_t<bits <= 32, uint64_t, __uint128_t>;
constexpr static Int mod() {
return modint::mod();
}
constexpr static Int remod() {
return modint::remod();
}
constexpr static UInt2 modmod() {
return UInt2(mod()) * mod();
}
constexpr modint_base() = default;
constexpr modint_base(Int2 rr) {
to_modint().setr(UInt((rr + modmod()) % mod()));
}
modint inv() const {
return bpow(to_modint(), mod() - 2);
}
modint operator - () const {
modint neg;
neg.r = std::min(-r, remod() - r);
return neg;
}
modint& operator /= (const modint &t) {
return to_modint() *= t.inv();
}
modint& operator *= (const modint &t) {
r = UInt(UInt2(r) * t.r % mod());
return to_modint();
}
modint& operator += (const modint &t) {
r += t.r; r = std::min(r, r - remod());
return to_modint();
}
modint& operator -= (const modint &t) {
r -= t.r; r = std::min(r, r + remod());
return to_modint();
}
modint operator + (const modint &t) const {return modint(to_modint()) += t;}
modint operator - (const modint &t) const {return modint(to_modint()) -= t;}
modint operator * (const modint &t) const {return modint(to_modint()) *= t;}
modint operator / (const modint &t) const {return modint(to_modint()) /= t;}
// Why <=> doesn't work?..
auto operator == (const modint &t) const {return to_modint().getr() == t.getr();}
auto operator != (const modint &t) const {return to_modint().getr() != t.getr();}
auto operator <= (const modint &t) const {return to_modint().getr() <= t.getr();}
auto operator >= (const modint &t) const {return to_modint().getr() >= t.getr();}
auto operator < (const modint &t) const {return to_modint().getr() < t.getr();}
auto operator > (const modint &t) const {return to_modint().getr() > t.getr();}
Int rem() const {
UInt R = to_modint().getr();
return R - (R > (UInt)mod() / 2) * mod();
}
constexpr void setr(UInt rr) {
r = rr;
}
constexpr UInt getr() const {
return r;
}
// Only use these if you really know what you're doing!
static UInt modmod8() {return UInt(8 * modmod());}
void add_unsafe(UInt t) {r += t;}
void pseudonormalize() {r = std::min(r, r - modmod8());}
modint const& normalize() {
if(r >= (UInt)mod()) {
r %= mod();
}
return to_modint();
}
void setr_direct(UInt rr) {r = rr;}
UInt getr_direct() const {return r;}
protected:
UInt r;
private:
constexpr modint& to_modint() {return static_cast<modint&>(*this);}
constexpr modint const& to_modint() const {return static_cast<modint const&>(*this);}
};
template<typename modint>
concept modint_type = std::is_base_of_v<modint_base<modint, typename modint::Int>, modint>;
template<modint_type modint>
decltype(std::cin)& operator >> (decltype(std::cin) &in, modint &x) {
typename modint::UInt r;
auto &res = in >> r;
x.setr(r);
return res;
}
template<modint_type modint>
decltype(std::cout)& operator << (decltype(std::cout) &out, modint const& x) {
return out << x.getr();
}
template<auto m>
struct modint: modint_base<modint<m>, decltype(m)> {
using Base = modint_base<modint<m>, decltype(m)>;
using Base::Base;
static constexpr Base::Int mod() {return m;}
static constexpr Base::UInt remod() {return m;}
auto getr() const {return Base::r;}
};
template<typename Int = int>
struct dynamic_modint: modint_base<dynamic_modint<Int>, Int> {
using Base = modint_base<dynamic_modint<Int>, Int>;
using Base::Base;
static Base::UInt m_reduce(Base::UInt2 ab) {
if(mod() % 2 == 0) [[unlikely]] {
return typename Base::UInt(ab % mod());
} else {
typename Base::UInt2 m = typename Base::UInt(ab) * imod();
return typename Base::UInt((ab + m * mod()) >> Base::bits);
}
}
static Base::UInt m_transform(Base::UInt a) {
if(mod() % 2 == 0) [[unlikely]] {
return a;
} else {
return m_reduce(a * pw128());
}
}
dynamic_modint& operator *= (const dynamic_modint &t) {
Base::r = m_reduce(typename Base::UInt2(Base::r) * t.r);
return *this;
}
void setr(Base::UInt rr) {
Base::r = m_transform(rr);
}
Base::UInt getr() const {
typename Base::UInt res = m_reduce(Base::r);
return std::min(res, res - mod());
}
static Int mod() {return m;}
static Int remod() {return 2 * m;}
static Base::UInt imod() {return im;}
static Base::UInt2 pw128() {return r2;}
static void switch_mod(Int nm) {
m = nm;
im = m % 2 ? inv2(-m) : 0;
r2 = static_cast<Base::UInt>(static_cast<Base::UInt2>(-1) % m + 1);
}
// Wrapper for temp switching
auto static with_mod(Int tmp, auto callback) {
struct scoped {
Int prev = mod();
~scoped() {switch_mod(prev);}
} _;
switch_mod(tmp);
return callback();
}
private:
static thread_local Int m;
static thread_local Base::UInt im, r2;
};
template<typename Int>
Int thread_local dynamic_modint<Int>::m = 1;
template<typename Int>
dynamic_modint<Int>::Base::UInt thread_local dynamic_modint<Int>::im = -1;
template<typename Int>
dynamic_modint<Int>::Base::UInt thread_local dynamic_modint<Int>::r2 = 0;
}
#line 1 "cp-algo/util/big_alloc.hpp"
#line 6 "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;
}
};
}
#line 1 "cp-algo/util/simd.hpp"
#include <experimental/simd>
#line 7 "cp-algo/util/simd.hpp"
namespace cp_algo {
template<typename T, size_t len>
using simd [[gnu::vector_size(len * sizeof(T))]] = T;
using i64x4 = simd<int64_t, 4>;
using u64x4 = simd<uint64_t, 4>;
using u32x8 = simd<uint32_t, 8>;
using i32x4 = simd<int32_t, 4>;
using u32x4 = simd<uint32_t, 4>;
using i16x4 = simd<int16_t, 4>;
using u8x32 = simd<uint8_t, 32>;
using dx4 = simd<double, 4>;
[[gnu::target("avx2")]] inline dx4 abs(dx4 a) {
return a < 0 ? -a : a;
}
// https://stackoverflow.com/a/77376595
// works for ints in (-2^51, 2^51)
static constexpr dx4 magic = dx4() + (3ULL << 51);
[[gnu::target("avx2")]] inline i64x4 lround(dx4 x) {
return i64x4(x + magic) - i64x4(magic);
}
[[gnu::target("avx2")]] inline dx4 to_double(i64x4 x) {
return dx4(x + i64x4(magic)) - magic;
}
[[gnu::target("avx2")]] inline dx4 round(dx4 a) {
return dx4{
std::nearbyint(a[0]),
std::nearbyint(a[1]),
std::nearbyint(a[2]),
std::nearbyint(a[3])
};
}
[[gnu::target("avx2")]] inline u64x4 low32(u64x4 x) {
return x & uint32_t(-1);
}
[[gnu::target("avx2")]] inline auto swap_bytes(auto x) {
return decltype(x)(__builtin_shufflevector(u32x8(x), u32x8(x), 1, 0, 3, 2, 5, 4, 7, 6));
}
[[gnu::target("avx2")]] inline u64x4 montgomery_reduce(u64x4 x, uint32_t mod, uint32_t imod) {
auto x_ninv = u64x4(_mm256_mul_epu32(__m256i(x), __m256i() + imod));
x += u64x4(_mm256_mul_epu32(__m256i(x_ninv), __m256i() + mod));
return swap_bytes(x);
}
[[gnu::target("avx2")]] inline u64x4 montgomery_mul(u64x4 x, u64x4 y, uint32_t mod, uint32_t imod) {
return montgomery_reduce(u64x4(_mm256_mul_epu32(__m256i(x), __m256i(y))), mod, imod);
}
[[gnu::target("avx2")]] inline u32x8 montgomery_mul(u32x8 x, u32x8 y, uint32_t mod, uint32_t imod) {
return u32x8(montgomery_mul(u64x4(x), u64x4(y), mod, imod)) |
u32x8(swap_bytes(montgomery_mul(u64x4(swap_bytes(x)), u64x4(swap_bytes(y)), mod, imod)));
}
[[gnu::target("avx2")]] inline dx4 rotate_right(dx4 x) {
static constexpr u64x4 shuffler = {3, 0, 1, 2};
return __builtin_shuffle(x, shuffler);
}
template<std::size_t Align = 32>
[[gnu::target("avx2")]] inline bool is_aligned(const auto* p) noexcept {
return (reinterpret_cast<std::uintptr_t>(p) % Align) == 0;
}
template<class Target>
[[gnu::target("avx2")]] inline Target& vector_cast(auto &&p) {
return *reinterpret_cast<Target*>(std::assume_aligned<alignof(Target)>(&p));
}
}
#line 1 "cp-algo/util/checkpoint.hpp"
#line 7 "cp-algo/util/checkpoint.hpp"
namespace cp_algo {
std::map<std::string, double> checkpoints;
template<bool final = false>
void checkpoint([[maybe_unused]] std::string const& msg = "") {
#ifdef CP_ALGO_CHECKPOINT
static double last = 0;
double now = (double)clock() / CLOCKS_PER_SEC;
double delta = now - last;
last = now;
if(msg.size() && !final) {
checkpoints[msg] += delta;
}
if(final) {
for(auto const& [key, value] : checkpoints) {
std::cerr << key << ": " << value * 1000 << " ms\n";
}
std::cerr << "Total: " << now * 1000 << " ms\n";
}
#endif
}
}
#line 15 "cp-algo/linalg/vector.hpp"
namespace cp_algo::linalg {
template<typename base, class Alloc = big_alloc<base>>
struct vec: std::basic_string<base, std::char_traits<base>, Alloc> {
using Base = std::basic_string<base, std::char_traits<base>, Alloc>;
using Base::Base;
vec(Base const& t): Base(t) {}
vec(Base &&t): Base(std::move(t)) {}
vec(size_t n): Base(n, base()) {}
vec(auto &&r): Base(std::ranges::to<Base>(r)) {}
static vec ei(size_t n, size_t i) {
vec res(n);
res[i] = 1;
return res;
}
auto operator-() const {
return *this | std::views::transform([](auto x) {return -x;});
}
auto operator *(base t) const {
return *this | std::views::transform([t](auto x) {return x * t;});
}
auto operator *=(base t) {
for(auto &it: *this) {
it *= t;
}
return *this;
}
virtual void add_scaled(vec const& b, base scale, size_t i = 0) {
if(scale != base(0)) {
for(; i < size(*this); i++) {
(*this)[i] += scale * b[i];
}
}
}
virtual vec const& normalize() {
return static_cast<vec&>(*this);
}
virtual base normalize(size_t i) {
return (*this)[i];
}
void read() {
for(auto &it: *this) {
std::cin >> it;
}
}
void print() const {
for(auto &it: *this) {
std::cout << it << " ";
}
std::cout << "\n";
}
static vec random(size_t n) {
vec res(n);
std::ranges::generate(res, random::rng);
return res;
}
// Concatenate vectors
vec operator |(vec const& t) const {
return std::views::join(std::array{
std::views::all(*this),
std::views::all(t)
});
}
// Generally, vec shouldn't be modified
// after its pivot index is set
std::pair<size_t, base> find_pivot() {
if(pivot == size_t(-1)) {
pivot = 0;
while(pivot < size(*this) && normalize(pivot) == base(0)) {
pivot++;
}
if(pivot < size(*this)) {
pivot_inv = base(1) / (*this)[pivot];
}
}
return {pivot, pivot_inv};
}
void reduce_by(vec &t) {
auto [pivot, pinv] = t.find_pivot();
if(pivot < size(*this)) {
add_scaled(t, -normalize(pivot) * pinv, pivot);
}
}
private:
size_t pivot = -1;
base pivot_inv;
};
template<math::modint_type base, class Alloc = big_alloc<base>>
struct modint_vec: vec<base, Alloc> {
using Base = vec<base, Alloc>;
using Base::Base;
modint_vec(Base const& t): Base(t) {}
modint_vec(Base &&t): Base(std::move(t)) {}
void add_scaled(Base const& b, base scale, size_t i = 0) override {
static_assert(base::bits >= 64, "Only wide modint types for linalg");
if(scale != base(0)) {
assert(Base::size() == b.size());
size_t n = size(*this);
u64x4 scaler = u64x4() + scale.getr();
if (is_aligned(&(*this)[0]) && is_aligned(&b[0])) // verify we're not in SSO
for(i -= i % 4; i + 3 < n; i += 4) {
auto &ai = vector_cast<u64x4>((*this)[i]);
auto bi = vector_cast<u64x4 const>(b[i]);
#ifdef __AVX2__
ai += u64x4(_mm256_mul_epu32(__m256i(scaler), __m256i(bi)));
#else
ai += scaler * bi;
#endif
}
for(; i < n; i++) {
(*this)[i].add_unsafe(b[i].getr_direct() * scale.getr());
}
if(++counter == 4) {
for(auto &it: *this) {
it.pseudonormalize();
}
counter = 0;
}
}
}
Base const& normalize() override {
for(auto &it: *this) {
it.normalize();
}
return *this;
}
base normalize(size_t i) override {
return (*this)[i].normalize();
}
private:
size_t counter = 0;
};
}
#line 7 "cp-algo/linalg/matrix.hpp"
#include <optional>
#line 11 "cp-algo/linalg/matrix.hpp"
namespace cp_algo::linalg {
enum gauss_mode {normal, reverse};
template<typename base_t, class _vec_t = std::conditional_t<
math::modint_type<base_t>,
modint_vec<base_t>,
vec<base_t>>>
struct matrix: std::vector<_vec_t> {
using vec_t = _vec_t;
using base = base_t;
using Base = std::vector<vec_t>;
using Base::Base;
matrix(size_t n): Base(n, vec_t(n)) {}
matrix(size_t n, size_t m): Base(n, vec_t(m)) {}
matrix(Base const& t): Base(t) {}
matrix(Base &&t): Base(std::move(t)) {}
template<std::ranges::input_range R>
matrix(R &&r): Base(std::ranges::to<Base>(std::forward<R>(r))) {}
size_t n() const {return size(*this);}
size_t m() const {return n() ? size(row(0)) : 0;}
void resize(size_t n, size_t m) {
Base::resize(n);
for(auto &it: *this) {
it.resize(m);
}
}
auto& row(size_t i) {return (*this)[i];}
auto const& row(size_t i) const {return (*this)[i];}
auto elements() {return *this | std::views::join;}
auto elements() const {return *this | std::views::join;}
matrix operator-() const {
return *this | std::views::transform([](auto x) {return vec_t(-x);});
}
matrix& operator+=(matrix const& t) {
for(auto [a, b]: std::views::zip(elements(), t.elements())) {
a += b;
}
return *this;
}
matrix& operator -=(matrix const& t) {
for(auto [a, b]: std::views::zip(elements(), t.elements())) {
a -= b;
}
return *this;
}
matrix operator+(matrix const& t) const {return matrix(*this) += t;}
matrix operator-(matrix const& t) const {return matrix(*this) -= t;}
matrix& operator *=(base t) {for(auto &it: *this) it *= t; return *this;}
matrix operator *(base t) const {return matrix(*this) *= t;}
matrix& operator /=(base t) {return *this *= base(1) / t;}
matrix operator /(base t) const {return matrix(*this) /= t;}
// Make sure the result is matrix, not Base
matrix& operator *=(matrix const& t) {return *this = *this * t;}
void read_transposed() {
for(size_t j = 0; j < m(); j++) {
for(size_t i = 0; i < n(); i++) {
std::cin >> (*this)[i][j];
}
}
}
void read() {
for(auto &it: *this) {
it.read();
}
}
void print() const {
for(auto const& it: *this) {
it.print();
}
}
static matrix block_diagonal(std::vector<matrix> const& blocks) {
size_t n = 0;
for(auto &it: blocks) {
assert(it.n() == it.m());
n += it.n();
}
matrix res(n);
n = 0;
for(auto &it: blocks) {
for(size_t i = 0; i < it.n(); i++) {
std::ranges::copy(it[i], begin(res[n + i]) + n);
}
n += it.n();
}
return res;
}
static matrix random(size_t n, size_t m) {
matrix res(n, m);
std::ranges::generate(res, std::bind(vec_t::random, m));
return res;
}
static matrix random(size_t n) {
return random(n, n);
}
static matrix eye(size_t n) {
matrix res(n);
for(size_t i = 0; i < n; i++) {
res[i][i] = 1;
}
return res;
}
// Concatenate matrices
matrix operator |(matrix const& b) const {
assert(n() == b.n());
matrix res(n(), m()+b.m());
for(size_t i = 0; i < n(); i++) {
res[i] = row(i) | b[i];
}
return res;
}
void assign_submatrix(auto viewx, auto viewy, matrix const& t) {
for(auto [a, b]: std::views::zip(*this | viewx, t)) {
std::ranges::copy(b, begin(a | viewy));
}
}
auto submatrix(auto viewx, auto viewy) const {
return *this | viewx | std::views::transform([viewy](auto const& y) {
return y | viewy;
});
}
matrix T() const {
matrix res(m(), n());
for(size_t i = 0; i < n(); i++) {
for(size_t j = 0; j < m(); j++) {
res[j][i] = row(i)[j];
}
}
return res;
}
matrix operator *(matrix const& b) const {
assert(m() == b.n());
matrix res(n(), b.m());
for(size_t i = 0; i < n(); i++) {
for(size_t j = 0; j < m(); j++) {
res[i].add_scaled(b[j], row(i)[j]);
}
}
return res.normalize();
}
vec_t apply(vec_t const& x) const {
return (matrix(1, x) * *this)[0];
}
matrix pow(uint64_t k) const {
assert(n() == m());
return bpow(*this, k, eye(n()));
}
matrix& normalize() {
for(auto &it: *this) {
it.normalize();
}
return *this;
}
template<gauss_mode mode = normal>
void eliminate(size_t i, size_t k) {
auto kinv = base(1) / row(i).normalize()[k];
for(size_t j = (mode == normal) * i; j < n(); j++) {
if(j != i) {
row(j).add_scaled(row(i), -row(j).normalize(k) * kinv);
}
}
}
template<gauss_mode mode = normal>
void eliminate(size_t i) {
row(i).normalize();
for(size_t j = (mode == normal) * i; j < n(); j++) {
if(j != i) {
row(j).reduce_by(row(i));
}
}
}
template<gauss_mode mode = normal>
matrix& gauss() {
for(size_t i = 0; i < n(); i++) {
eliminate<mode>(i);
}
return normalize();
}
template<gauss_mode mode = normal>
auto echelonize(size_t lim) {
return gauss<mode>().sort_classify(lim);
}
template<gauss_mode mode = normal>
auto echelonize() {
return echelonize<mode>(m());
}
size_t rank() const {
if(n() > m()) {
return T().rank();
}
return size(matrix(*this).echelonize()[0]);
}
base det() const {
assert(n() == m());
matrix b = *this;
b.echelonize();
base res = 1;
for(size_t i = 0; i < n(); i++) {
res *= b[i][i];
}
return res;
}
std::pair<base, matrix> inv() const {
assert(n() == m());
matrix b = *this | eye(n());
if(size(b.echelonize<reverse>(n())[0]) < n()) {
return {0, {}};
}
base det = 1;
for(size_t i = 0; i < n(); i++) {
det *= b[i][i];
b[i] *= base(1) / b[i][i];
}
return {det, b.submatrix(std::views::all, std::views::drop(n()))};
}
// Can also just run gauss on T() | eye(m)
// but it would be slower :(
auto kernel() const {
auto A = *this;
auto [pivots, free] = A.template echelonize<reverse>();
matrix sols(size(free), m());
for(size_t j = 0; j < size(pivots); j++) {
base scale = base(1) / A[j][pivots[j]];
for(size_t i = 0; i < size(free); i++) {
sols[i][pivots[j]] = A[j][free[i]] * scale;
}
}
for(size_t i = 0; i < size(free); i++) {
sols[i][free[i]] = -1;
}
return sols;
}
// [solution, basis], transposed
std::optional<std::array<matrix, 2>> solve(matrix t) const {
matrix sols = (*this | t).kernel();
if(sols.n() < t.m() || matrix(sols.submatrix(
std::views::drop(sols.n() - t.m()),
std::views::drop(m())
)) != -eye(t.m())) {
return std::nullopt;
} else {
return std::array{
matrix(sols.submatrix(std::views::drop(sols.n() - t.m()), std::views::take(m()))),
matrix(sols.submatrix(std::views::take(sols.n() - t.m()), std::views::take(m())))
};
}
}
// To be called after a gaussian elimination run
// Sorts rows by pivots and classifies
// variables into pivots and free
auto sort_classify(size_t lim) {
size_t rk = 0;
std::vector<size_t> free, pivots;
for(size_t j = 0; j < lim; j++) {
for(size_t i = rk + 1; i < n() && row(rk)[j] == base(0); i++) {
if(row(i)[j] != base(0)) {
std::swap(row(i), row(rk));
row(rk) = -row(rk);
}
}
if(rk < n() && row(rk)[j] != base(0)) {
pivots.push_back(j);
rk++;
} else {
free.push_back(j);
}
}
return std::array{pivots, free};
}
};
template<typename base_t>
auto operator *(base_t t, matrix<base_t> const& A) {return A * t;}
}
#line 8 "verify/linalg/euler_circs.test.cpp"
using namespace std;
using namespace cp_algo::math;
using namespace cp_algo::linalg;
const int64_t mod = 998244353;
using base = modint<mod>;
void solve() {
int n, m;
cin >> n >> m;
matrix<base> a(n);
int r = 0;
vector<int> indeg(n), outdeg(n);
for(int i = 0; i < m; i++) {
int u, v;
cin >> u >> v;
a[u][v] -= 1;
a[v][v] += 1;
outdeg[u]++;
indeg[v]++;
r = v;
}
a[r][r] = fact<base>(indeg[r] - 1);
for(int i = 0; i < n; i++) {
if(i == r) {
continue;
}
if(indeg[i] != outdeg[i]) {
cout << 0 << "\n";
return;
}
if(indeg[i] != 0) {
a[i] *= fact<base>(indeg[i] - 1);
} else {
a[i][i] = 1;
}
a[r][i] = a[i][r] = 0;
}
cout << a.det() << "\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 |
10 ms | 10 MB |
| g++ | example_01 |
AC |
9 ms | 10 MB |
| g++ | example_02 |
AC |
9 ms | 10 MB |
| g++ | example_03 |
AC |
9 ms | 10 MB |
| g++ | has_isolated_point_00 |
AC |
19 ms | 15 MB |
| g++ | has_isolated_point_01 |
AC |
20 ms | 15 MB |
| g++ | has_isolated_point_02 |
AC |
18 ms | 15 MB |
| g++ | has_isolated_point_03 |
AC |
20 ms | 15 MB |
| g++ | loops_00 |
AC |
20 ms | 15 MB |
| g++ | loops_01 |
AC |
15 ms | 13 MB |
| g++ | max_random_00 |
AC |
15 ms | 13 MB |
| g++ | max_random_01 |
AC |
15 ms | 13 MB |
| g++ | max_random_circuit_00 |
AC |
29 ms | 15 MB |
| g++ | max_random_circuit_01 |
AC |
29 ms | 15 MB |
| g++ | max_random_circuit_02 |
AC |
29 ms | 15 MB |
| g++ | max_random_circuit_03 |
AC |
28 ms | 15 MB |