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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#319684#4056. 进制转换hos_lyric100 ✓605ms179744kbC++146.8kb2024-02-03 02:31:272024-02-03 02:31:27

Judging History

你现在查看的是最新测评结果

  • [2024-02-03 02:31:27]
  • 评测
  • 测评结果:100
  • 用时:605ms
  • 内存:179744kb
  • [2024-02-03 02:31:27]
  • 提交

answer

// virtual after solving this as ucup, sorry (this code is written during virtual)

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;


constexpr int E = 50;
constexpr int F = 30;
Int two[E + 1], thr[F + 1];

int calc2(Int n) {
  int ret = 0;
  for (; n; n >>= 1) ret += (n & 1);
  return ret;
}
int calc3(Int n) {
  int ret = 0;
  for (; n; n /= 3) ret += n % 3;
  return ret;
}

Int N;
Mint X, Y, Z;

int main() {
  two[0] = thr[0] = 1;
  for (int e = 1; e <= E; ++e) two[e] = two[e - 1] * 2;
  for (int f = 1; f <= F; ++f) thr[f] = thr[f - 1] * 3;
  
  for (; ~scanf("%lld%u%u%u", &N, &X.x, &Y.x, &Z.x); ) {
    ++N;
    
    vector<Mint> YY(E + 1), ZZ(2 * F + 1);
    YY[0] = ZZ[0] = 1;
    for (int e = 1; e <= E; ++e) YY[e] = YY[e - 1] * Y;
    for (int f = 1; f <= 2 * F; ++f) ZZ[f] = ZZ[f - 1] * Z;
    
    int e = 0, f = 0;
    vector<Int> ns{0, 1};
    vector<Mint> ws{1};
    for (; !(N < two[e] * thr[f]); ) {
      const int len = ws.size();
      vector<Int> nns{0};
      vector<Mint> wws;
      int ee = e, ff = f;
      auto add = [&](Int l, Int r, Mint w) -> void {
// cerr<<"  [add] "<<l<<" "<<r<<" "<<w<<endl;
        assert(nns.back() == l);
        if (l % two[ee] != 0 && l % thr[ff] != 0) {
          nns.back() = r;
          wws.back() += w;
        } else {
          nns.push_back(r);
          wws.push_back(w);
        }
      };
      if (two[e] <= thr[f]) {
        ++ee;
        for (int a = 0; a < 2; ++a) {
          const Int shift = two[e] * thr[f] * a;
          const Mint x = X.pow(shift);
          for (int i = 0; i < len; ++i) {
            add(shift + ns[i], shift + ns[i + 1], x * YY[(shift + ns[i]) / two[e] % 2] * ws[i]);
          }
        }
      } else {
        ++ff;
        for (int b = 0; b < 3; ++b) {
          const Int shift = two[e] * thr[f] * b;
          const Mint x = X.pow(shift);
          for (int i = 0; i < len; ++i) {
            add(shift + ns[i], shift + ns[i + 1], x * ZZ[(shift + ns[i]) / thr[f] % 3] * ws[i]);
          }
        }
      }
      e = ee;
      f = ff;
      ns.swap(nns);
      ws.swap(wws);
cerr<<"e="<<e<<" f="<<f<<" "<<two[e]<<" "<<thr[f]<<" "<<ws.size()<<endl;
// cerr<<ns<<endl<<ws<<endl;
    }
    
    const int len = ws.size();
    Mint ans = 0;
    for (int i = 0; i < len; ++i) {
      if (ns[i + 1] <= N) {
        ans += YY[calc2(ns[i] / two[e])] * ZZ[calc3(ns[i] / thr[f])] * ws[i];
      } else {
        Mint x = X.pow(ns[i]);
        for (Int n = ns[i]; n < N; ++n) {
          ans += x * YY[calc2(n)] * ZZ[calc3(n)];
          x *= X;
        }
        break;
      }
    }
    ans -= 1;
    printf("%u\n", ans.x);
#ifdef LOCAL
if(N<=1'000'000){
 Mint brt=0;
 for(Int n=1;n<N;++n)brt+=X.pow(n)*Y.pow(calc2(n))*Z.pow(calc3(n));
 if(brt!=ans){
  cerr<<"FAIL N="<<N<<" "<<X<<" "<<Y<<" "<<Z<<": "<<brt<<" "<<ans<<endl;
  if(N<=100)for(Int n=0;n<two[e]*thr[f];++n)cerr<<n<<": "<<X.pow(n)<<" "<<Y.pow(calc2(n))<<" "<<Z.pow(calc3(n))<<": "<<X.pow(n)*Y.pow(calc2(n))*Z.pow(calc3(n))<<endl;
 }
 assert(brt==ans);
}
#endif
  }
  return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 5
Accepted
time: 0ms
memory: 4336kb

input:

9134097 778012792 263448561 839843856

output:

887680205

result:

ok 1 number(s): "887680205"

Test #2:

score: 5
Accepted
time: 1ms
memory: 4068kb

input:

9896386 2948513 263418583 271155379

output:

853292631

result:

ok 1 number(s): "853292631"

Test #3:

score: 5
Accepted
time: 1ms
memory: 4072kb

input:

9150910 827328107 842171962 39947937

output:

534921610

result:

ok 1 number(s): "534921610"

Test #4:

score: 5
Accepted
time: 564ms
memory: 179120kb

input:

9586674634211 1 1 58301262

output:

13306748

result:

ok 1 number(s): "13306748"

Test #5:

score: 5
Accepted
time: 593ms
memory: 178856kb

input:

9774917720998 1 1 609549524

output:

825025220

result:

ok 1 number(s): "825025220"

Test #6:

score: 5
Accepted
time: 605ms
memory: 178516kb

input:

9765239207265 422503033 1 719749187

output:

993518920

result:

ok 1 number(s): "993518920"

Test #7:

score: 5
Accepted
time: 513ms
memory: 178444kb

input:

9732354736444 277693641 1 501293609

output:

77844778

result:

ok 1 number(s): "77844778"

Test #8:

score: 5
Accepted
time: 17ms
memory: 9192kb

input:

9004409828 377918953 449219487 26422407

output:

110868569

result:

ok 1 number(s): "110868569"

Test #9:

score: 5
Accepted
time: 13ms
memory: 9312kb

input:

9579878149 820453354 218842704 133154415

output:

727248713

result:

ok 1 number(s): "727248713"

Test #10:

score: 5
Accepted
time: 14ms
memory: 9168kb

input:

9475807443 305433821 391589421 170059051

output:

372839725

result:

ok 1 number(s): "372839725"

Test #11:

score: 5
Accepted
time: 120ms
memory: 56644kb

input:

484758270277 372146623 410538257 35340632

output:

575284574

result:

ok 1 number(s): "575284574"

Test #12:

score: 5
Accepted
time: 107ms
memory: 53936kb

input:

473458173541 864158404 220259603 529747800

output:

610487662

result:

ok 1 number(s): "610487662"

Test #13:

score: 5
Accepted
time: 121ms
memory: 55100kb

input:

459992983903 359742981 983942229 552405867

output:

81366483

result:

ok 1 number(s): "81366483"

Test #14:

score: 5
Accepted
time: 112ms
memory: 56540kb

input:

462331701308 665849375 563297194 141092054

output:

774987426

result:

ok 1 number(s): "774987426"

Test #15:

score: 5
Accepted
time: 493ms
memory: 179744kb

input:

9061635042931 746632077 302662913 559990819

output:

274721229

result:

ok 1 number(s): "274721229"

Test #16:

score: 5
Accepted
time: 543ms
memory: 178760kb

input:

9653325901537 559549569 638292572 474780356

output:

418906016

result:

ok 1 number(s): "418906016"

Test #17:

score: 5
Accepted
time: 547ms
memory: 178440kb

input:

9640271229478 619740479 644097590 907038757

output:

936646026

result:

ok 1 number(s): "936646026"

Test #18:

score: 5
Accepted
time: 526ms
memory: 178364kb

input:

9781711161203 988850684 154464719 995932763

output:

166841144

result:

ok 1 number(s): "166841144"

Test #19:

score: 5
Accepted
time: 494ms
memory: 179160kb

input:

9156325004698 915375188 316066096 217969045

output:

306877956

result:

ok 1 number(s): "306877956"

Test #20:

score: 5
Accepted
time: 590ms
memory: 179708kb

input:

9042535293051 906265264 156788435 622201740

output:

397975092

result:

ok 1 number(s): "397975092"