test/verify/convolution/yosupo-lcm-convolution.test.cpp

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• Last update: 2024-08-31 20:47:44+09:00
• Problem: https://judge.yosupo.jp/problem/lcm_convolution

Depends on

• 約数についてのゼータ変換/メビウス変換 (convolution/divisor-zeta-moebius-transform.hpp)
• math/external_gcd.hpp
• modint (math/modint.hpp)
• template/template.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/lcm_convolution"

#include "template/template.hpp"
#include "math/modint.hpp"
#include "convolution/divisor-zeta-moebius-transform.hpp"

using mint = modint998244353;

mint op(mint a, mint b) {
  return a + b;
}

mint invop(mint a, mint b) {
  return a - b;
}

int main() {
  ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
  int N; cin >> N;
  vector<mint>a(N+1); for(int i=0; i<N; i++) cin >> a[i+1];
  vector<mint>b(N+1); for(int i=0; i<N; i++) cin >> b[i+1];  

  vector<mint> za = divisor::zeta_transform_naive<mint,op>(a);
  vector<mint> zb = divisor::zeta_transform_naive<mint,op>(b);

  vector<mint> zc(N+1); for(int i=0; i<N+1; i++) zc[i] = za[i] * zb[i];

  vector<mint> c = divisor::moebius_transform_naive<mint,invop>(zc);
  for(int i=1; i<=N; i++) cout << c[i].val() << " \n"[i==N];
}

#line 1 "test/verify/convolution/yosupo-lcm-convolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/lcm_convolution"

#line 1 "template/template.hpp"
#include <iostream>
#include <cassert>
using namespace std;
using ll = long long;
template<class T> inline bool chmax(T& a, const T& b) {if (a<b) {a=b; return true;} return false;}
template<class T> inline bool chmin(T& a, const T& b) {if (b<a) {a=b; return true;} return false;}
const int INTINF = 1000001000;
const int INTMAX = 2147483647;
const ll LLMAX = 9223372036854775807;
const ll LLINF = 1000000000000000000;
#line 1 "math/modint.hpp"



#line 1 "math/external_gcd.hpp"



#include <tuple>

// g,x,y
template<typename T>
constexpr std::tuple<T, T, T> extendedGCD(T a, T b) {
    T x0 = 1, y0 = 0, x1 = 0, y1 = 1;
    while (b != 0) {
        T q = a / b;
        T r = a % b;
        a = b;
        b = r;
        
        T xTemp = x0 - q * x1;
        x0 = x1;
        x1 = xTemp;
        
        T yTemp = y0 - q * y1;
        y0 = y1;
        y1 = yTemp;
    }
    return {a, x0, y0};
}

#line 5 "math/modint.hpp"

template<int MOD>
struct static_modint {
    int value;

    constexpr explicit static_modint() : value(0) {}

    constexpr static_modint(long long v) {
        value = int(((v % MOD) + MOD) % MOD);
    }

    constexpr static_modint& operator+=(const static_modint& other) {
        if ((value += other.value) >= MOD) value -= MOD;
        return *this;
    }

    constexpr static_modint& operator-=(const static_modint& other) {
        if ((value -= other.value) < 0) value += MOD;
        return *this;
    }

    constexpr static_modint& operator*=(const static_modint& other) {
        value = int((long long)value * other.value % MOD);
        return *this;
    }

    constexpr static_modint operator+(const static_modint& other) const {
        return static_modint(*this) += other;
    }

    constexpr static_modint operator-(const static_modint& other) const {
        return static_modint(*this) -= other;
    }

    constexpr static_modint operator*(const static_modint& other) const {
        return static_modint(*this) *= other;
    }

    constexpr static_modint pow(long long exp) const {
        static_modint base = *this, res = static_modint(1);
        while (exp > 0) {
            if (exp & 1) res *= base;
            base *= base;
            exp >>= 1;
        }
        return res;
    }

    constexpr static_modint inv() const {
        //return pow(MOD - 2);
        int g,x,y;
        tie(g,x,y) = extendedGCD(value, MOD);
        assert(g==1);
        if (x < 0) {
            x += MOD;
        }
        //cerr << g << " " << x << " " << y << " " << value << endl;
        //assert((((long)x*value)%MOD + MOD)%MOD == 1);
        return x;
    }

    constexpr static_modint& operator/=(const static_modint& other) {
        return *this *= other.inv();
    }

    constexpr static_modint operator/(const static_modint& other) const {
        return static_modint(*this) /= other;
    }

    constexpr bool operator!=(const static_modint& other) const {
        return val() != other.val();
    }

    constexpr bool operator==(const static_modint& other) const {
        return val() == other.val();
    }

    int val() const {
      return this->value;
    }

    friend std::ostream& operator<<(std::ostream& os, const static_modint& mi) {
        return os << mi.value;
    }

    friend std::istream& operator>>(std::istream& is, static_modint& mi) {
        long long x;
        is >> x;
        mi = static_modint(x);
        return is;
    }
};

template <int mod>
using modint = static_modint<mod>;
using modint998244353  = modint<998244353>;
using modint1000000007 = modint<1000000007>;


#line 1 "convolution/divisor-zeta-moebius-transform.hpp"



#include <vector>
#include <map>

namespace divisor {
  // 約数についてのゼータ変換。 g_n = \Sigma_{m|n} f_m なる g を求める。
  template <typename T, T(*op)(T, T) >
  std::vector<T> zeta_transform_naive(const std::vector<T>& f) {
    int N = f.size() - 1;
    std::vector<T> g = f;

    for (int i = 1; i <= N; i++) {
      for (int j = 2 * i; j <= N; j += i) {
        g[j] = op(g[j], f[i]);
      }
    }

    return g;
  }

  // 約数についてのメビウス変換。 f_n = \Sigma_{m|n} g_m なる g を求める。
  template <typename T, T(*invop)(T, T)>
  std::vector<T> moebius_transform_naive(const std::vector<T>& f) {
    int N = f.size() - 1;
    std::vector<T> g = f;

    for (int i = 1; i <= N; i++) {
      for (int j = i * 2; j <= N; j += i) {
        g[j] = invop(g[j], g[i]);
      }
    }

    return g;
  }

  template <typename I, typename T, T(*op)(T, T)>
  std::map<I, T> zeta_transform(const std::map<I, T>& mp) {
    std::map<I, T> ret = mp;
    for (auto p2itr = mp.rbegin(); p2itr != mp.rend(); p2itr++) {
      for (auto p1itr = next(p2itr); p1itr != mp.rend(); p1itr++) {
        if ((*p2itr).first % (*p1itr).first == 0) {
          ret[(*p2itr).first] = op(ret[(*p2itr).first], ret[(*p1itr).first]);
        }
      }
    }

    return ret;
  }


  template <typename I, typename T, T(*op)(T, T)>
  std::map<I, T> moebius_transform(const std::map<I, T>& mp) {
    std::map<I, T> ret = mp;

    for (auto p1itr = ret.begin(); p1itr != ret.end(); p1itr++) {
      for (auto p2itr = next(p1itr); p2itr != ret.end(); p2itr++) {
        if ((*p2itr).first % (*p1itr).first == 0) {
          ret[(*p2itr).first] = invop(ret[(*p2itr).first], ret[(*p1itr).first]);
        }
      }
    }

    return ret;
  }
} // namespace divisor


#line 6 "test/verify/convolution/yosupo-lcm-convolution.test.cpp"

using mint = modint998244353;

mint op(mint a, mint b) {
  return a + b;
}

mint invop(mint a, mint b) {
  return a - b;
}

int main() {
  ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
  int N; cin >> N;
  vector<mint>a(N+1); for(int i=0; i<N; i++) cin >> a[i+1];
  vector<mint>b(N+1); for(int i=0; i<N; i++) cin >> b[i+1];  

  vector<mint> za = divisor::zeta_transform_naive<mint,op>(a);
  vector<mint> zb = divisor::zeta_transform_naive<mint,op>(b);

  vector<mint> zc(N+1); for(int i=0; i<N+1; i++) zc[i] = za[i] * zb[i];

  vector<mint> c = divisor::moebius_transform_naive<mint,invop>(zc);
  for(int i=1; i<=N; i++) cout << c[i].val() << " \n"[i==N];
}

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