#423316 (C++14) No.976 2 の 128 乗と M

提出ソース
結果

問題	No.976 2 の 128 乗と M
ユーザー	azz
提出日時	2020-01-31 21:29:50
言語	C++14 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	3 ms / 2,000 ms
コード長	13,954 bytes
コンパイル時間	2,539 ms
コンパイル使用メモリ	195,964 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-09-17 07:13:40
合計ジャッジ時間	4,085 ms
ジャッジサーバーID （参考情報）	judge5 / judge4
このコードへのチャレンジ
（要ログイン）
ファイルパターン	結果
sample	AC * 4
other	AC * 50
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

raw source code
#include <bits/stdc++.h>
using namespace std;

# define REP(i,n) for (int i=0;i<(n);++i)
# define rep(i,a,b) for(int i=a;i<(b);++i)
# define all(v) v.begin(),v.end()
# define showVector(v) REP(i,v.size()){cout << (v[i]) << " ";} cout << endl;
template<class T> inline bool chmin(T &a, T b){ if(a > b) { a = b; return true;} return false;}
template<class T> inline bool chmax(T &a, T b){ if(a < b) { a = b; return true;} return false;}
typedef long long int ll;
typedef pair<ll,ll> P_ii;
typedef pair<double,double> P_dd;

template<class T>
vector<T> make_vec(size_t a){
    return vector<T>(a);
}

template<class T, class... Ts>
auto make_vec(size_t a, Ts... ts){
  return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}

template<typename T,typename V>
typename enable_if<is_class<T>::value==0>::type
fill_v(T &t,const V &v){t=v;}

template<typename T,typename V>
typename enable_if<is_class<T>::value!=0>::type
fill_v(T &t,const V &v){
  for(auto &e:t) fill_v(e,v);
}

ll gcd(ll a, ll b) {
    if(a < b) swap(a,b);
    
    if(b == 0) return a;
    return gcd(b, a % b);
}

ll lcm(ll a, ll b){
    ll g = gcd(a,b);
    return (a/g)*b;
}

// 素数判定 O(√n)
bool is_prime(int n){
    for(int i = 2; i * i <= n; i++){
        if(n % i == 0) return false;
    }
    return true;
}

// 約数列挙 O(√n)
vector<ll> divisor(ll n){
    vector<ll> res;
    for(ll i = 1; i * i <= n; i++){
        if(n % i == 0){
            res.push_back(i);
            if(i != n / i) res.push_back(n / i);
        }
    }
    return res;
}

vector<pair<ll, ll> > prime_factorize(ll n) {
    vector<pair<ll, ll> > res;
    for (ll p = 2; p * p <= n; ++p) {
        if (n % p != 0) continue;
        ll num = 0;
        while (n % p == 0) { ++num; n /= p; }
        res.push_back(make_pair(p, num));
    }
    if (n != 1) res.push_back(make_pair(n, 1));
    return res;
}

// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const int mod = 1000000007;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x=0):x(x%mod){}
  mint& operator+=(const mint a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator-=(const mint a) {
    if ((x += mod-a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res+=a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res-=a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res*=a;
  }
  mint pow(ll t) const {
    if (!t) return 1;
    mint a = pow(t>>1);
    a *= a;
    if (t&1) a *= *this;
    return a;
  }
 
  // for prime mod
  mint inv() const {
    return pow(mod-2);
  }
  mint& operator/=(const mint a) {
    return (*this) *= a.inv();
  }
  mint operator/(const mint a) const {
    mint res(*this);
    return res/=a;
  }
};

const int MOD = 1000000007;
const int inf=1e9+7;
const ll longinf=1LL<<60 ;

void addM(ll &a, ll b) {
    a += b;
    if (a >= MOD) a -= MOD;
}

void mulM(ll &a, ll b) {
    a = ((a%MOD)*(b%MOD))%MOD ;
}

ll powM(ll a,ll b) {
    ll ret = 1;
    ll tmp = a;
    while(b>0) {
        if((b&1)==1) ret = (ret * tmp) % MOD;
        tmp = (tmp * tmp) % MOD;
        b = b >> 1;
    }
    return ret;
}

// mod. m での a の逆元 a^{-1} を計算する
ll modinv(ll a, ll m) {
    ll b = m, u = 1, v = 0;
    while (b) {
        ll t = a / b;
        a -= t * b; swap(a, b);
        u -= t * v; swap(u, v);
    }
    u %= m;
    if (u < 0) u += m;
    return u;
}

// ラングレンス圧縮
vector<pair<char, int>> rang_com(string s){
  vector<pair<char, int>> ret;
  string t = s;
  t.erase(unique(all(t)), t.end());
  int now = 0;
  int pre = 0;
  for(auto ct : t){
    while(now < s.size() && s[now] == ct) now++;
    if(ret.size() == 0){
      ret.push_back({ct, now});
    } else {
      ret.push_back({ct, now - pre});
    }
    pre = now;
  }
  return ret;
}

namespace FFT{
  using dbl = double;
  using Int = long long;  

  struct num{
    dbl x,y;
    num(){x=y=0;}
    num(dbl x,dbl y):x(x),y(y){}
  };
  
  inline num operator+(num a,num b){
    return num(a.x+b.x,a.y+b.y);
  }
  inline num operator-(num a,num b){
    return num(a.x-b.x,a.y-b.y);
  }
  inline num operator*(num a,num b){
    return num(a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x);
  }
  inline num conj(num a){
    return num(a.x,-a.y);
  }
 
  int base=1;
  vector<num> rts={{0,0},{1,0}};
  vector<int> rev={0,1};
 
  const dbl PI=acosl(-1.0);
 
  void ensure_base(int nbase){
    if(nbase<=base) return;
 
    rev.resize(1<<nbase);
    for(int i=0;i<(1<<nbase);i++)
      rev[i]=(rev[i>>1]>>1)+((i&1)<<(nbase-1));
 
    rts.resize(1<<nbase);
    while(base<nbase){
      dbl angle=2*PI/(1<<(base+1));
      for(int i=1<<(base-1);i<(1<<base);i++){
        rts[i<<1]=rts[i];
        dbl angle_i=angle*(2*i+1-(1<<base));
        rts[(i<<1)+1]=num(cos(angle_i),sin(angle_i));
      }
      base++;
    }
  }
 
  void fft(vector<num> &a,int n=-1){
    if(n==-1) n=a.size();
    assert((n&(n-1))==0);
 
    int zeros=__builtin_ctz(n);
    ensure_base(zeros);
    int shift=base-zeros;
    for(int i=0;i<n;i++)
      if(i<(rev[i]>>shift))
        swap(a[i],a[rev[i]>>shift]);
 
    for(int k=1;k<n;k<<=1){
      for(int i=0;i<n;i+=2*k){
        for(int j=0;j<k;j++){
          num z=a[i+j+k]*rts[j+k];
          a[i+j+k]=a[i+j]-z;
          a[i+j]=a[i+j]+z;
        }
      }
    }
  }
 
  vector<num> fa;

  template<typename T>
  vector<Int> multiply(const vector<T> &a,const vector<T> &b){
    int need=a.size()+b.size()-1;
    int nbase=0;
    while((1<<nbase)<need) nbase++;
    ensure_base(nbase);
 
    int sz=1<<nbase;
    if(sz>(int)fa.size()) fa.resize(sz);
    for(int i=0;i<sz;i++){
      int x=(i<(int)a.size()?a[i]:0);
      int y=(i<(int)b.size()?b[i]:0);
      fa[i]=num(x,y);
    }
    fft(fa,sz);
 
    num r(0,-0.25/sz);
    for(int i=0;i<=(sz>>1);i++){
      int j=(sz-i)&(sz-1);
      num z=(fa[j]*fa[j]-conj(fa[i]*fa[i]))*r;
      if(i!=j)
        fa[j]=(fa[i]*fa[i]-conj(fa[j]*fa[j]))*r;
      fa[i]=z;
    }
    fft(fa,sz);
 
    vector<Int> res(need);
    for(int i=0;i<need;i++)
      res[i]=fa[i].x+0.5;
    
    return res;
  }
  
};

struct bigint {  
  using ll = long long; 
  using vll = vector<ll>;
  
  constexpr static ll base = 1000000000;
  constexpr static ll base_digits = 9;

  vll a;
  ll sign;

  bigint():sign(1){}

  bigint(ll v){*this=v;}

  bigint(const string &s){read(s);}

  void operator=(const bigint &v){
    sign=v.sign;
    a=v.a;
  }

  void operator=(ll v){
    sign=1;
    if(v<0) sign=-1,v=-v;
    for(;v>0;v=v/base) a.push_back(v%base);
  }

  bigint operator+(const bigint &v) const{
    if(sign==v.sign){
      bigint res=v;

      for(ll i=0,carry=0;i<(ll)max(a.size(),v.a.size())||carry;++i){
        if(i==(ll)res.a.size()) res.a.push_back(0);
        res.a[i]+=carry+(i<(ll)a.size()?a[i]:0);
        carry=res.a[i]>=base;
        if(carry) res.a[i]-=base;
      }
      return res;
    }
    return *this -(-v);
  }

  bigint operator-(const bigint &v) const{
    if(sign==v.sign){
      if(abs()>=v.abs()){
        bigint res=*this;
        for(ll i=0,carry=0;i<(ll)v.a.size()||carry;++i){
          res.a[i]-=carry+(i<(ll)v.a.size()?v.a[i]:0);
          carry=res.a[i]<0;
          if(carry) res.a[i]+=base;
        }
        res.trim();
        return res;
      }
      return -(v-*this);
    }
    return *this+(-v);
  }

  void operator*=(ll v){
    if(v<0) sign=-sign,v=-v;
    for(ll i=0,carry=0;i<(ll)a.size()|| carry;++i){
      if(i ==(ll)a.size()) a.push_back(0);
      ll cur=a[i] *(ll)v+carry;
      carry=(ll)(cur/base);
      a[i]=(ll)(cur%base);
      // asm("divl %%ecx" : "=a"(carry),"=d"(a[i]) : "A"(cur),"c"(base));
    }
    trim();
  }

  bigint operator*(ll v) const{
    bigint res=*this;
    res *=v;
    return res;
  }

  friend pair<bigint,bigint> divmod(const bigint &a1,const bigint &b1){
    ll norm=base/(b1.a.back()+1);   
    bigint a=a1.abs()*norm;
    bigint b=b1.abs()*norm;
    bigint q,r;
    q.a.resize(a.a.size());

    for(ll i=a.a.size()-1;i>=0;i--){
      r *=base;
      r+=a.a[i];
      ll s1=r.a.size()<=b.a.size() ? 0 : r.a[b.a.size()];
      ll s2=r.a.size()<=b.a.size()-1 ? 0 : r.a[b.a.size()-1];
      ll d=((ll)base*s1+s2)/b.a.back();
      r-=b*d;
      while(r<0) r+=b,--d;
      q.a[i]=d;
    }

    q.sign=a1.sign*b1.sign;
    r.sign=a1.sign;
    q.trim();
    r.trim();
    return make_pair(q,r/norm);
  }

  bigint operator/(const bigint &v) const{
    return divmod(*this,v).first;
  }

  bigint operator%(const bigint &v) const{
    return divmod(*this,v).second;
  }

  void operator/=(ll v){
    if(v<0) sign=-sign,v=-v;
    for(ll i=(ll)a.size()-1,rem=0;i>=0;--i){
      ll cur=a[i]+rem *(ll)base;
      a[i]=(ll)(cur/v);
      rem=(ll)(cur%v);
    }
    trim();
  }

  bigint operator/(ll v) const{
    bigint res=*this;
    res/=v;
    return res;
  }

  ll operator%(ll v) const{
    if(v<0) v=-v;
    ll m=0;
    for(ll i=a.size()-1;i>=0;--i) m=(a[i]+m *(ll)base)%v;
    return m*sign;
  }

  void operator+=(const bigint &v){
    *this=*this+v;
  }

  void operator-=(const bigint &v){
    *this=*this-v;
  }

  void operator*=(const bigint &v){
    *this=*this*v;
  }

  void operator/=(const bigint &v){
    *this=*this/v;
  }

  bool operator<(const bigint &v) const{
    if(sign!=v.sign) return sign<v.sign;
    if(a.size()!=v.a.size()) return a.size()*sign<v.a.size()*v.sign;
    for(ll i=a.size()-1;i>=0;i--)
      if(a[i]!=v.a[i]) return a[i]*sign<v.a[i]*sign;
    return false;
  }

  bool operator>(const bigint &v) const{
    return v<*this;
  }

  bool operator<=(const bigint &v) const{
    return !(v<*this);
  }

  bool operator>=(const bigint &v) const{
    return !(*this<v);
  }

  bool operator==(const bigint &v) const{
    return !(*this<v)&&!(v<*this);
  }

  bool operator!=(const bigint &v) const{
    return *this<v|| v<*this;
  }

  void trim(){
    while(!a.empty()&&!a.back()) a.pop_back();
    if(a.empty()) sign=1;
  }

  bool isZero() const{
    return a.empty()||(a.size()==1&&!a[0]);
  }

  bigint operator-() const{
    bigint res=*this;
    res.sign=-sign;
    return res;
  }

  bigint abs() const{
    bigint res=*this;
    res.sign*=res.sign;
    return res;
  }

  ll longValue() const{
    ll res=0;
    for(ll i=a.size()-1;i>=0;i--) res=res*base+a[i];
    return res*sign;
  }

  friend bigint gcd(const bigint &a,const bigint &b){
    return b.isZero() ? a : gcd(b,a%b);
  }

  friend bigint lcm(const bigint &a,const bigint &b){
    return a/gcd(a,b)*b;
  }

  void read(const string &s){
    sign=1;
    a.clear();
    ll pos=0;
    while(pos<(ll)s.size()&&(s[pos]=='-'|| s[pos]=='+')){
      if(s[pos]=='-') sign=-sign;
      ++pos;
    }
    for(ll i=s.size()-1;i>=pos;i-=base_digits){
      ll x=0;
      for(ll j=max(pos,i-base_digits+1);j<=i;j++) x=x*10+s[j]-'0';
      a.push_back(x);
    }
    trim();
  }

  friend istream &operator>>(istream &stream,bigint &v){
    string s;
    stream>>s;
    v.read(s);
    return stream;
  }

  friend ostream &operator<<(ostream &stream,const bigint &v){
    if(v.sign==-1) stream<<'-';
    stream<<(v.a.empty()?0:v.a.back());
    for(ll i=(ll)v.a.size()-2;i>=0;--i)
      stream<<setw(base_digits)<<setfill('0')<<v.a[i];
    return stream;
  }

  static vll convert_base(const vll &a,ll old_digits,ll new_digits){
    vll p(max(old_digits,new_digits)+1);
    p[0]=1;
    for(ll i=1;i<(ll)p.size();i++) p[i]=p[i-1]*10;
    vll res;
    ll cur=0;
    ll cur_digits=0;
    for(ll i=0;i<(ll)a.size();i++){
      cur+=a[i]*p[cur_digits];
      cur_digits+=old_digits;
      while(cur_digits>=new_digits){
        res.push_back(signed(cur%p[new_digits]));
        cur/=p[new_digits];
        cur_digits-=new_digits;
      }
    }
    res.push_back((signed)cur);
    while(!res.empty()&&!res.back()) res.pop_back();
    return res;
  }
  
  static vll karatsubaMultiply(const vll &a,const vll &b){
    ll n=a.size();
    vll res(n+n);
    if(n<=32){
      for(ll i=0;i<n;i++)
        for(ll j=0;j<n;j++)
          res[i+j]+=a[i]*b[j];
      return res;
    }

    ll k=n>>1;
    vll a1(a.begin(),a.begin()+k);
    vll a2(a.begin()+k,a.end());
    vll b1(b.begin(),b.begin()+k);
    vll b2(b.begin()+k,b.end());

    vll a1b1=karatsubaMultiply(a1,b1);
    vll a2b2=karatsubaMultiply(a2,b2);

    for(ll i=0;i<k;i++) a2[i]+=a1[i];
    for(ll i=0;i<k;i++) b2[i]+=b1[i];

    vll r=karatsubaMultiply(a2,b2);
    for(ll i=0;i<(ll)a1b1.size();i++) r[i]-=a1b1[i];
    for(ll i=0;i<(ll)a2b2.size();i++) r[i]-=a2b2[i];

    for(ll i=0;i<(ll)r.size();i++) res[i+k]+=r[i];
    for(ll i=0;i<(ll)a1b1.size();i++) res[i]+=a1b1[i];
    for(ll i=0;i<(ll)a2b2.size();i++) res[i+n]+=a2b2[i];
    return res;
  }
  
  bigint operator*(const bigint &v) const{
    constexpr static ll nbase = 10000;
    constexpr static ll nbase_digits = 4;
    
    vll a=convert_base(this->a,base_digits,nbase_digits);
    vll b=convert_base(v.a,base_digits,nbase_digits);

    /*
      while(a.size()<b.size()) a.push_back(0);
      while(b.size()<a.size()) b.push_back(0);
      while(a.size() &(a.size()-1)) a.push_back(0),b.push_back(0);
      vll c=karatsubaMultiply(a,b);
    */    

    if(a.empty()) a.push_back(0);
    if(b.empty()) b.push_back(0);    
    vll c=FFT::multiply(a,b);
    bigint res;
    res.sign=sign*v.sign;
    for(ll i=0,carry=0;i<(ll)c.size();i++){
      ll cur=c[i]+carry;
      res.a.push_back((ll)(cur%nbase));
      carry=(ll)(cur/nbase);
      if(i+1==(int)c.size()&&carry>0) c.push_back(0);
    }
    
    res.a=convert_base(res.a,nbase_digits,base_digits);
    res.trim();
    return res;
  }
};

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

  bigint m;
  cin >> m;

  bigint a = 1;
  REP(_, 128) a *= 2;

  cout << a % m << endl;

  return 0;
}
yukicoder

結果

ソースコード
