結果

問題 No.2081 Make a Test Case of GCD Subset
ユーザー hari64hari64
提出日時 2022-09-08 15:09:24
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 12,750 bytes
コンパイル時間 3,398 ms
コンパイル使用メモリ 236,208 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-05-03 11:13:26
合計ジャッジ時間 6,592 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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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 WA -
testcase_01 WA -
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ソースコード

diff # 

// これは不正解のはず

#include <bits/stdc++.h>  // clang-format off
using namespace std;constexpr int INF=1001001001;constexpr long long INFll=1001001001001001001;namespace viewer{using s=string;template<class T>s f(T i){s S=i==INF||i==INFll?"inf":to_string(i);return s(max(0,3-int(S.size())),' ')+S;}
template<class T>auto v(T&x,s&&e)->decltype(cerr<<x){return cerr<<x<<e;}void v(int x,s&&e){cerr<<f(x)<<e;}void v(long long x,s&&e){cerr<<f(x)<<e;}void v(float x,s&&e){cerr<<fixed<<setprecision(5)<<x<<e;}void v(double x,s&&e){cerr<<fixed<<setprecision(5)<<x<<e;}void v(long double x,s&&e){cerr<<fixed<<setprecision(5)<<x<<e;}
template<class T,class U>void v(const pair<T,U>&p,s&&e="\n"){cerr<<"(";v(p.first,", ");v(p.second,")"+e);}template<class T,class U>void v(const tuple<T,U>&t,s&&e="\n"){cerr<<"(";v(get<0>(t),", ");v(get<1>(t),")"+e);}template<class T,class U,class V>void v(const tuple<T,U,V>&t,s&&e="\n"){cerr<<"(";v(get<0>(t),", ");v(get<1>(t),", ");v(get<2>(t),")"+e);}template<class T,class U,class V,class W>void v(const tuple<T,U,V,W>&t,s&&e="\n"){cerr<<"(";v(get<0>(t),", ");v(get<1>(t),", ");v(get<2>(t),", ");v(get<3>(t),")"+e);}
template<class T>void v(const vector<T>&vx,s);template<class T>auto ve(int,const vector<T>&vx)->decltype(cerr<<vx[0]){cerr<<"{";for(const T&x:vx)v(x,",");return cerr<<"}\n";}template<class T>auto ve(bool,const vector<T>&vx){cerr<<"{\n";for(const T&x:vx)cerr<<"  ",v(x,",");cerr<<"}\n";}template<class T>void v(const vector<T>&vx,s){ve(0,vx);}
template<class T>void v(const deque<T>&q,s&&e){v(vector<T>(q.begin(),q.end()),e);}template<class T,class C>void v(const set<T,C>&S,s&&e){v(vector<T>(S.begin(),S.end()),e);}template<class T,class C>void v(const multiset<T,C>&S,s&&e){v(vector<T>(S.begin(),S.end()),e);}template<class T>void v(const unordered_set<T>&S,s&&e){v(vector<T>(S.begin(),S.end()),e);}
template<class T,class U,class V>void v(const priority_queue<T,U,V>&p,s&&e){priority_queue<T,U,V>q=p;vector<T>z;while(!q.empty()){z.push_back(q.top());q.pop();}v(z,e);}template<class T,class U>void v(const map<T,U>&m,s&&e){cerr<<"{"<<(m.empty()?"":"\n");for(const auto&kv:m){cerr<<"  [";v(kv.first,"");cerr<<"] : ";v(kv.second,"");cerr<<"\n";}cerr<<"}"+e;}
template<class T>void _view(int n,s&S,T&var){cerr<<"\033[1;32m"<<n<<"\033[0m: \033[1;36m"<<S<<"\033[0m = ";v(var,"\n");}template<class T>void grid(T _){}void grid(const vector<vector<bool>>&vvb){cerr<<"\n";for(const vector<bool>&vb:vvb){for(const bool&b:vb)cerr<<(b?".":"#");cerr<<"\n";}}
void _debug(int,s){}template<typename H,typename... T>void _debug(int n,s S,const H&h,const T&... t){int i=0,cnt=0;for(;i<int(S.size());i++){if(S[i]=='(')cnt++;if(S[i]==')')cnt--;if(cnt==0&&S[i]==',')break;}if(i==int(S.size()))_view(n,S,h);else{s S1=S.substr(0,i),S2=S.substr(i+2);if(S2=="\"grid\""){cerr<<"\033[1;32m"<<n<<"\033[0m: \033[1;36m"<<S1<<"\033[0m = ";grid(h);}else _view(n,S1,h),_debug(n,S2,t...);}}}
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;} // https://rsk0315.hatenablog.com/entry/2021/01/18/065720
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;};
#ifndef hari64
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#define debug(...)
#else
#define debug(...) viewer::_debug(__LINE__, #__VA_ARGS__, __VA_ARGS__)
#endif  // clang-format on

// O(NloglogN)
vector<bool> prime_table(int n) {
    assert(n >= 1);
    vector<bool> isp(n + 1, false);
    if (n == 1) return isp;
    isp[2] = 1;
    for (int i = 3; i <= n; i += 2) isp[i] = true;
    for (int p = 3; p * p <= n; p += 2)
        if (isp[p])
            for (int q = p * p; q <= n; q += (p << 1)) isp[q] = false;
    return isp;
}

template <class T>
T gcd(vector<T>& Xs) {
    T ret = abs(Xs[0]);
    for (T x : Xs) ret = gcd(ret, abs(x));
    return ret;
}

template <class T>
vector<T> divisors(T n) {
    vector<T> ret;
    for (T i = 1; i * i <= n; i++) {
        if (n % i == 0) {
            ret.push_back(i);
            if (i * i != n) ret.push_back(n / i);
        }
    }
    sort(begin(ret), end(ret));
    return ret;
}

void check_slow(const int M, const vector<int>& ans) {
    int cnt = 0;
    for (int bit = 1; bit < (1 << int(ans.size())); bit++) {
        vector<int> temp;
        for (int i = 0; i < int(ans.size()); i++) {
            if (bit & (1 << i)) {
                temp.push_back(ans[i]);
            }
        }
        if (gcd(temp) >= 2) {
            cnt++;
        }
    }
    assert(cnt == M);
}

void check_fast(const int M, const vector<int>& ans) {
    vector<mint> dp(100000 + 1, 0);
    for (auto& a : ans) {
        for (auto& d : divisors(a)) {
            if (d == 1) {
                continue;
            }
            dp[d]++;
        }
    }
    for (int i = 100000; i > 1; i--) {
        dp[i] = mint(2).pow(dp[i].val()) - 1;
        for (int j = 2 * i; j <= 100000; j += i) {
            dp[i] -= dp[j];
        }
    }
    assert(mint(M).val() == accumulate(dp.begin(), dp.end(), mint(0)).val());
}

void check(const int M, const vector<int>& ans) {
    vector<int> ans2 = ans;
    sort(ans2.begin(), ans2.end());
    ans2.erase(unique(ans2.begin(), ans2.end()), ans2.end());
    assert(ans.size() == ans2.size());
    assert(*min_element(ans.begin(), ans.end()) >= 1);
    assert(*max_element(ans.begin(), ans.end()) <= 100000);
    if (M <= 10) {
        check_slow(M, ans);
    }
    check_fast(M, ans);
}

int get_prime(vector<bool>& isp) {
    for (int i = 0; i < 100000; i++) {
        if (isp[i]) {
            isp[i] = false;
            return i;
        }
    }
    assert(false);
}

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

    vector<bool> isp = prime_table(100000);

    int M;
    cin >> M;
    assert(0 <= M && M < 998244353);
    if (M == 0) {
        M = 998244353;
    }
    vector<int> ans;
    vector<int> coefs(__builtin_popcount(M));

    //  大きい数字になるといけないので、各グループのベースとなる素数はあらかじめ確保しておく
    for (auto& e : coefs) {
        e = get_prime(isp);
    }
    // bit毎に考える
    for (int bit = 0; bit <= 30; bit++) {
        if (M & (1 << bit)) {
            vector<int> temp;

            // 別々の素数を用意し、
            for (int i = 0; i < bit; i++) {
                temp.push_back(get_prime(isp));
            }

            // 最初に用意したベースを乗算する
            for (auto& p : temp) {
                p *= coefs.back();
            }
            coefs.pop_back();

            // 空集合の分を加える
            temp.push_back(get_prime(isp));

            ans.insert(ans.end(), temp.begin(), temp.end());
        }
    }

    check(M, ans);

    cout << ans.size() + 1 << endl;
    for (auto& elem : ans) cout << elem << ' ';
    cout << ans.back() << endl;

    return 0;
}
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