結果

問題 No.2384 Permutations of Permutations
ユーザー hari64hari64
提出日時 2023-07-27 10:15:19
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 4 ms / 2,000 ms
コード長 10,255 bytes
コンパイル時間 3,632 ms
コンパイル使用メモリ 234,432 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-04-14 22:46:05
合計ジャッジ時間 4,508 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,816 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 2 ms
6,940 KB
testcase_03 AC 2 ms
6,944 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 4 ms
6,940 KB
testcase_06 AC 3 ms
6,940 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 2 ms
6,944 KB
testcase_09 AC 2 ms
6,940 KB
testcase_10 AC 3 ms
6,944 KB
testcase_11 AC 3 ms
6,944 KB
testcase_12 AC 3 ms
6,940 KB
testcase_13 AC 3 ms
6,944 KB
testcase_14 AC 3 ms
6,940 KB
testcase_15 AC 3 ms
6,944 KB
testcase_16 AC 2 ms
6,944 KB
testcase_17 AC 3 ms
6,940 KB
testcase_18 AC 3 ms
6,940 KB
testcase_19 AC 2 ms
6,944 KB
testcase_20 AC 2 ms
6,940 KB
testcase_21 AC 3 ms
6,940 KB
testcase_22 AC 2 ms
6,940 KB
testcase_23 AC 3 ms
6,940 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#ifndef hari64
#include <bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#define debug(...)
#else
#include "../../util/viewer.hpp"
#define debug(...) viewer::_debug(__LINE__, #__VA_ARGS__, __VA_ARGS__)
#endif
// clang-format off
using namespace std;
using ll = long long; using ld = long double;
using pii = pair<int, int>; using pll = pair<ll, ll>;
template <typename T> using vc = vector<T>;
template <typename T> using vvc = vector<vc<T>>;
template <typename T> using vvvc = vector<vvc<T>>;
using vi = vc<int>; using vll = vc<ll>; using vpii = vc<pii>; using vpll = vc<pll>;
using vvi = vc<vi>; using vvll = vc<vll>; using vvpi = vc<vpii>; using vvpll = vc<vpll>;
#define OVERLOAD4(_1,_2,_3,_4,name,...) name
#define OVERLOAD3(_1,_2,_3,name,...) name
#define REP1(n) for(ll i=0;i<n;++i)
#define REP2(i,n) for(ll i=0;i<n;++i)
#define REP3(i,a,b) for(ll i=a;i<b;++i)
#define REP4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define REP(...) OVERLOAD4(__VA_ARGS__,REP4,REP3,REP2,REP1)(__VA_ARGS__)
#define RREP1(n) for(ll i=n;i--;)
#define RREP2(i,n) for(ll i=n;i--;)
#define RREP3(i,a,b) for(ll i=b;i-->(a);)
#define RREP4(i,a,b,c) for(ll i=(a)+((b)-(a)-1)/(c)*(c);i>=(a);i-=c)
#define RREP(...) OVERLOAD4(__VA_ARGS__,RREP4,RREP3,RREP2,RREP1)(__VA_ARGS__)
#define EACH1(i,a) for(auto&&i:a)
#define EACH2(x,y,a) for(auto&&[x,y]:a)
#define EACH3(x,y,z,a) for(auto&&[x,y,z]:a)
#define EACH(...) OVERLOAD4(__VA_ARGS__,EACH3,EACH2,EACH1)(__VA_ARGS__)
#define ALL1(i) begin(i),end(i)
#define ALL2(i,a) begin(i),begin(i)+a
#define ALL3(i,a,b) begin(i)+a,begin(i)+b
#define ALL(...) OVERLOAD3(__VA_ARGS__,ALL3,ALL2,ALL1)(__VA_ARGS__)
#define RALL1(i) (i).rbegin(),(i).rend()
#define RALL2(i,k) (i).rbegin(),(i).rbegin()+k
#define RALL3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define RALL(...) OVERLOAD3(__VA_ARGS__,RALL3,RALL2,RALL1)(__VA_ARGS__)
constexpr int INF = 1001001001; constexpr long long INFll = 1001001001001001001;
template <class T> bool chmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
template <class T> bool chmin(T& a, const T& b) { return a > b ? a = b, 1 : 0; }
// clang-format on

// 9:25~

// clang-format off
namespace internal{template<class T>using is_signed_int128=typename conditional<is_same<T,__int128_t>::value||is_same<T,__int128>::value,true_type,false_type>::type;template<class T>using is_unsigned_int128=typename conditional<is_same<T,__uint128_t>::value||is_same<T,unsigned __int128>::value,true_type,false_type>::type;template<class T>using is_integral=typename conditional<std::is_integral<T>::value||is_signed_int128<T>::value||is_unsigned_int128<T>::value,true_type,false_type>::type;
template<class T>using is_signed_int=typename conditional<(is_integral<T>::value&&is_signed<T>::value)||is_signed_int128<T>::value,true_type,false_type>::type;template<class T>using is_unsigned_int=typename conditional<(is_integral<T>::value&&is_unsigned<T>::value)||is_unsigned_int128<T>::value,true_type,false_type>::type;template<class T>using is_signed_int_t=enable_if_t<is_signed_int<T>::value>;template<class T>using is_unsigned_int_t=enable_if_t<is_unsigned_int<T>::value>;
constexpr long long safe_mod(long long x,long long m){x%=m;if(x<0)x+=m;return x;}struct barrett{unsigned int _m;unsigned long long im;explicit barrett(unsigned int m):_m(m),im((unsigned long long)(-1)/m+1){}unsigned int umod()const{return _m;}unsigned int mul(unsigned int a,unsigned int b)const{unsigned long long z=a;z*=b;unsigned long long x=(unsigned long long)(((unsigned __int128)(z)*im)>>64);unsigned int v=(unsigned int)(z-x*_m);if(_m<=v)v+=_m;return v;}};
constexpr long long pow_mod_constexpr(long long x,long long n,int m){if(m==1)return 0;unsigned int _m=(unsigned int)(m);unsigned long long r=1;unsigned long long y=safe_mod(x,m);while(n){if(n&1)r=(r*y)%_m;y=(y*y)%_m;n>>=1;}return r;}constexpr pair<long long,long long>inv_gcd(long long a,long long b){a=safe_mod(a,b);if(a==0)return{b,0};long long s=b,t=a;long long m0=0,m1=1;while(t){long long u=s/t;s-=t*u;m0-=m1*u;auto tmp=s;s=t;t=tmp;tmp=m0;m0=m1;m1=tmp;}if(m0<0)m0+=b/s;return{s,m0};}
constexpr bool is_prime_constexpr(int n){if(n<=1)return false;if(n==2||n==7||n==61)return true;if(n%2==0)return false;long long d=n-1;while(d%2==0)d/=2;constexpr long long bases[3]={2,7,61};for(long long a:bases){long long t=d;long long y=pow_mod_constexpr(a,t,n);while(t!=n-1&&y!=1&&y!=n-1){y=y*y%n;t<<=1;}if(y!=n-1&&t%2==0)return false;}return true;}template<int n>constexpr bool is_prime=is_prime_constexpr(n);} // namespace internal
template<int m>struct static_modint{using mint=static_modint;static constexpr int mod(){return m;}static mint raw(int v){mint x;x._v=v;return x;}static_modint():_v(0){}template<class T,internal::is_signed_int_t<T>* =nullptr>static_modint(T v){long long x=(long long)(v%(long long)(umod()));if(x<0)x+=umod();_v=(unsigned int)(x);}template<class T,internal::is_unsigned_int_t<T>* =nullptr>static_modint(T v){_v=(unsigned int)(v%umod());}unsigned int val()const{return _v;}
mint&operator++(){_v++;if(_v==umod())_v=0;return*this;}mint&operator--(){if(_v==0)_v=umod();_v--;return*this;}mint operator++(int){mint result=*this;++*this;return result;}mint operator--(int){mint result=*this;--*this;return result;}mint&operator+=(const mint&rhs){_v+=rhs._v;if(_v>=umod())_v-=umod();return*this;}mint&operator-=(const mint&rhs){_v-=rhs._v;if(_v>=umod())_v+=umod();return*this;}
mint&operator*=(const mint&rhs){unsigned long long z=_v;z*=rhs._v;_v=(unsigned int)(z%umod());return*this;}mint&operator/=(const mint&rhs){return*this=*this*rhs.inv();}mint operator+()const{return*this;}mint operator-()const{return mint()-*this;}mint pow(long long n)const{assert(0<=n);mint x=*this,r=1;while(n){if(n&1)r*=x;x*=x;n>>=1;}return r;}mint inv()const{if(prime){assert(_v);return pow(umod()-2);}else{auto eg=internal::inv_gcd(_v,m);assert(eg.first==1);return eg.second;}}
friend mint operator+(const mint&lhs,const mint&rhs){return mint(lhs)+=rhs;}friend mint operator-(const mint&lhs,const mint&rhs){return mint(lhs)-=rhs;}friend mint operator*(const mint&lhs,const mint&rhs){return mint(lhs)*=rhs;}friend mint operator/(const mint&lhs,const mint&rhs){return mint(lhs)/=rhs;}friend bool operator==(const mint&lhs,const mint&rhs){return lhs._v==rhs._v;}friend bool operator!=(const mint&lhs,const mint&rhs){return lhs._v!=rhs._v;}
friend ostream&operator<<(ostream&os,const mint&rhs){return os<<rhs._v;}friend istream&operator>>(istream&is,mint&rhs){long long v;is>>v;v%=(long long)(umod());if(v<0)v+=umod();;rhs._v=(unsigned int)v;return is;}static constexpr bool prime=internal::is_prime<m>;private:unsigned int _v;static constexpr unsigned int umod(){return m;}};
constexpr int MOD = 998244353;using mint=static_modint<MOD>;vector<mint>mint_factorial={mint(1)};/*n>1e8 ⇒ fast_modfact(deprecated)*/mint modfact(int n){assert(n<=100000000);if(int(mint_factorial.size())<=n){for(int i=mint_factorial.size();i<=n;i++){mint next=mint_factorial.back()*i;mint_factorial.push_back(next);}}return mint_factorial[n];}
/*x s.t. x^2 ≡ a (mod Prime) or -1*/mint modsqrt(mint a){long long p=mint::mod();if(a.val()==1)return a;if(a.pow((p-1)>>1).val()!=1)return -1;mint b=1,one=1;while(b.pow((p-1)>>1).val()==1)b+=one;long long m=p-1,e=0;while(m%2==0)m>>=1,e++;mint x=a.pow((m-1)>>1);mint y=a*x*x;x*=a;mint z=b.pow(m);while(y!=1){long long j=0;mint t=y;while(t!=one)j++,t*=t;z=z.pow(1ll<<(e-j-1));x*=z;z*=z;y*=z;e=j;}return x;}mint nCk(int n,int k){if(k<0||n<k)return mint(0);return modfact(n)*(modfact(k)).inv()*modfact(n-k).inv();}
/*min x s.t. a^x ≡ b (mod M) or -1*/int modlog(mint a,mint b){if(gcd(a.mod(),a.val())!=1){cout<<"\033[1;31mCAUTION: m must be coprime to a.\033[0m"<<endl;assert(false);}long long m=mint::mod();long long sq=round(sqrt(m))+1;unordered_map<long long,long long>ap;mint re=a;for(long long r=1;r<sq;r++){if(ap.find(re.val())==ap.end())ap[re.val()]=r;re*=a;}mint A=a.inv().pow(sq);re=b;for(mint q=0;q.val()<sq;q++){if(re==1&&q!=0)return(q*sq).val();if(ap.find(re.val())!=ap.end())return(q*sq+ap[re.val()]).val();re*=A;}return-1;};
// clang-format on

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N, K;
    cin >> N >> K;

    if (N == 2) {
        cout << 1 << endl;
        return 0;
    }
    if (N != 6) {
        cout << mint(K) * modfact(N - K) << endl;
        return 0;
    }

    assert(N == 6);
    mint ans = mint(K) * modfact(N - K);  // 内部自己同型

    vi Pn({0, 1, 2, 3, 4, 5});
    vvi Sn;
    map<vi, int> revSn;

    do {
        Sn.push_back(Pn);
        revSn[Pn] = Sn.size() - 1;
    } while (next_permutation(ALL(Pn)));

    const vvi base = {
        {1, 0, 3, 2, 5, 4},  //
        {3, 4, 5, 0, 1, 2},  //
        {2, 3, 0, 1, 5, 4},  //
        {1, 0, 5, 4, 3, 2},  //
        {3, 2, 1, 0, 5, 4},  //
    };

    auto prod = [&](const vi& self, const vi& rhs) -> vi {
        vi ret(6, -1);
        REP(i, 6) ret[i] = self[rhs[i]];
        return ret;
    };

    // 外部自己同型群の代表
    vi G(Sn.size(), -1);
    REP(i, int(Sn.size())) {
        vi s = Sn[i];
        vi res = {0, 1, 2, 3, 4, 5};

        bool ok = false;
        do {
            ok = true;
            for (int i = 0; i < N - 1; i++) {
                if (s[i] > s[i + 1]) {
                    swap(s[i], s[i + 1]);
                    res = prod(res, base[i]);
                    ok = false;
                }
            }
        } while (!ok);
        G[i] = revSn.at(res);
    }
    debug(G);

    vi fromVec(6);
    REP(i, 6) {
        if (i + 1 < K) {
            fromVec[i] = i + 1;
        } else if (i + 1 == K) {
            fromVec[i] = 0;
        } else {
            fromVec[i] = i;
        }
    }
    debug(fromVec);

    do {
        vi now = fromVec;
        vi revPn(6);
        REP(i, 6) revPn[Pn[i]] = i;
        now = prod(now, revPn);
        now = prod(Pn, now);
        now = Sn[G[revSn[now]]];
        bool ok = true;
        REP(i, 6) {
            if (i + 1 < K) {
                if (now[i] != i + 1) ok = false;
            } else if (i + 1 == K) {
                if (now[i] != 0) ok = false;
            }
        }
        debug(ok);
        if (ok) ans++;
    } while (next_permutation(ALL(Pn)));

    cout << ans << endl;

    return 0;
}
0