#1029703 (C++17(gcc12)) No.2979 直角三角形の個数

提出ソース
結果

問題	No.2979 直角三角形の個数
ユーザー	NyaanNyaan
提出日時	2024-12-03 01:13:28
言語	C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
結果	TLE
実行時間	-
コード長	16,261 bytes
コンパイル時間	3,060 ms
コンパイル使用メモリ	268,616 KB
実行使用メモリ	18,684 KB
最終ジャッジ日時	2024-12-03 01:13:57
合計ジャッジ時間	27,961 ms
ジャッジサーバーID （参考情報）	judge3 / judge5
このコードへのチャレンジ
（要ログイン）
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 13,640 KB
testcase_01	AC	2 ms 13,636 KB
testcase_02	AC	2 ms 17,380 KB
testcase_03	AC	2 ms 13,636 KB
testcase_04	AC	1 ms 6,816 KB
testcase_05	AC	2 ms 6,816 KB
testcase_06	AC	2 ms 6,820 KB
testcase_07	AC	1 ms 6,816 KB
testcase_08	AC	2 ms 6,816 KB
testcase_09	AC	1 ms 6,816 KB
testcase_10	AC	3 ms 6,820 KB
testcase_11	AC	2 ms 6,816 KB
testcase_12	AC	5 ms 6,820 KB
testcase_13	AC	4 ms 6,820 KB
testcase_14	AC	22 ms 6,820 KB
testcase_15	AC	22 ms 6,820 KB
testcase_16	AC	74 ms 6,816 KB
testcase_17	AC	195 ms 6,820 KB
testcase_18	AC	625 ms 6,816 KB
testcase_19	AC	869 ms 6,824 KB
testcase_20	AC	2,768 ms 6,816 KB
testcase_21	TLE	-
testcase_22	TLE	-
testcase_23	TLE	-
testcase_24	AC	2 ms 6,816 KB
testcase_25	AC	2 ms 6,820 KB
testcase_26	AC	2 ms 6,816 KB
testcase_27	AC	10 ms 6,820 KB
testcase_28	TLE	-
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
// 埋め込まずに通そうとしたけど O(N^{3/4}) から落ちません。助けて！

/**
 * date   : 2024-12-03 01:12:50
 * author : Nyaan
 */

#define NDEBUG

using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tr2/dynamic_bitset>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility

namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  constexpr P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(T &v) {
  return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
  vector<vector<T>> ret;
  vector<T> v;
  auto dfs = [&](auto rc, int i) -> void {
    if (i == (int)a.size()) {
      ret.push_back(v);
      return;
    }
    for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
  };
  dfs(dfs, 0);
  return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
  T res = I;
  for (; n; f(a = a * a), n >>= 1) {
    if (n & 1) f(res = res * a);
  }
  return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
  return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
T Rev(const T &v) {
  T res = v;
  reverse(begin(res), end(res));
  return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
  using U = typename T::value_type;
  if(v.empty()) return {};
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      res[j][i] = v[i][j];
    }
  }
  return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
  using U = typename T::value_type;
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      if (clockwise) {
        res[W - 1 - j][i] = v[i][j];
      } else {
        res[j][H - 1 - i] = v[i][j];
      }
    }
  }
  return res;
}

}  // namespace Nyaan


// bit operation

namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan


// inout

namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan


// debug


#ifdef NyaanDebug
#define trc(...) (void(0))
#endif
#ifndef NyaanDebug
#define trc(...) (void(0))
#endif

#ifndef NyaanLocal
#define trc2(...) (void(0))
#endif


// macro

#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)


namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }


//





using namespace std;

// floor(sqrt(n)) を返す (ただし n が負の場合は 0 を返す)
long long isqrt(long long n) {
  if (n <= 0) return 0;
  long long x = sqrt(n);
  while ((x + 1) * (x + 1) <= n) x++;
  while (x * x > n) x--;
  return x;
}


namespace EnumerateQuotientImpl {
long long fast_div(long long a, long long b) { return 1.0 * a / b; };
long long slow_div(long long a, long long b) { return a / b; };
}  // namespace EnumerateQuotientImpl

// { (q, l, r) : forall x in (l,r], floor(N/x) = q }
// を引数に取る関数f(q, l, r)を渡す。範囲が左に半開なのに注意
// 商は小さい方から走査する
template <typename T, typename F>
void enumerate_quotient(T N, const F& f) {
  T sq = isqrt(N);

#define FUNC(d)                       \
  T upper = N, quo = 0;               \
  while (upper > sq) {                \
    T thres = d(N, (++quo + 1));      \
    f(quo, thres, upper);             \
    upper = thres;                    \
  }                                   \
  while (upper > 0) {                 \
    f(d(N, upper), upper - 1, upper); \
    upper--;                          \
  }

  if (N <= 1e12) {
    FUNC(EnumerateQuotientImpl::fast_div);
  } else {
    FUNC(EnumerateQuotientImpl::slow_div);
  }
#undef FUNC
}

/**
 *  @brief 商の列挙
 */








// Prime Sieve {2, 3, 5, 7, 11, 13, 17, ...}
vector<int> prime_enumerate(int N) {
  vector<bool> sieve(N / 3 + 1, 1);
  for (int p = 5, d = 4, i = 1, sqn = sqrt(N); p <= sqn; p += d = 6 - d, i++) {
    if (!sieve[i]) continue;
    for (int q = p * p / 3, r = d * p / 3 + (d * p % 3 == 2), s = 2 * p,
             qe = sieve.size();
         q < qe; q += r = s - r)
      sieve[q] = 0;
  }
  vector<int> ret{2, 3};
  for (int p = 5, d = 4, i = 1; p <= N; p += d = 6 - d, i++)
    if (sieve[i]) ret.push_back(p);
  while (!ret.empty() && ret.back() > N) ret.pop_back();
  return ret;
}


// f(n, p, c) : n = pow(p, c), f is multiplicative function

template <typename T, T (*f)(int, int, int)>
struct enamurate_multiplicative_function {
  enamurate_multiplicative_function(int _n)
      : ps(prime_enumerate(_n)), a(_n + 1, T()), n(_n), p(ps.size()) {}

  vector<T> run() {
    a[1] = 1;
    dfs(-1, 1, 1);
    return a;
  }

 private:
  vector<int> ps;
  vector<T> a;
  int n, p;
  void dfs(int i, long long x, T y) {
    a[x] = y;
    if (y == T()) return;
    for (int j = i + 1; j < p; j++) {
      long long nx = x * ps[j];
      long long dx = ps[j];
      if (nx > n) break;
      for (int c = 1; nx <= n; nx *= ps[j], dx *= ps[j], ++c) {
        dfs(j, nx, y * f(dx, ps[j], c));
      }
    }
  }
};

/**
 * @brief 乗法的関数の列挙
 */


namespace multiplicative_function {
template <typename T>
T moebius(int, int, int c) {
  return c == 0 ? 1 : c == 1 ? -1 : 0;
}
template <typename T>
T sigma0(int, int, int c) {
  return c + 1;
}
template <typename T>
T sigma1(int n, int p, int) {
  return (n - 1) / (p - 1) + n;
}
template <typename T>
T totient(int n, int p, int) {
  return n - n / p;
}
}  // namespace multiplicative_function

template <typename T>
static constexpr vector<T> mobius_function(int n) {
  enamurate_multiplicative_function<T, multiplicative_function::moebius<T>> em(
      n);
  return em.run();
}

template <typename T>
static constexpr vector<T> sigma0(int n) {
  enamurate_multiplicative_function<T, multiplicative_function::sigma0<T>> em(
      n);
  return em.run();
}

template <typename T>
static constexpr vector<T> sigma1(int n) {
  enamurate_multiplicative_function<T, multiplicative_function::sigma1<T>> em(
      n);
  return em.run();
}

template <typename T>
static constexpr vector<T> totient(int n) {
  enamurate_multiplicative_function<T, multiplicative_function::totient<T>> em(
      n);
  return em.run();
}

/**
 * @brief 有名な乗法的関数
 * @docs docs/multiplicative-function/mf-famous-series.md
 */


using namespace Nyaan;

ll naive(ll N) {
  ll ans = 0;
  rep1(m, N) rep1(n, m - 1) {
    ll s = m * (m + n) * 2;
    if (s > N) break;
    if (gcd(m, n) != 1) continue;
    ans += N / s;
  }
  return ans;
}

// 1 + 2 + ... + x
ll C2(ll x) { return x * (x + 1) / 2; }

ll calc(ll N) {
  N /= 2;
  ll sq = sqrt(N) + 3;
  vi mo = mobius_function<int>(sq);
  vl v(sq);

  static map<ll, ll> mp;

  auto f = [&](ll x) {
    if (mp.count(x)) return mp[x];
    ll s = 0;
    enumerate_quotient(x, [&](ll z, ll L, ll R) {
      // z, m in (L, R]
      enumerate_quotient(z, [&](ll q, ll l, ll r) {
        ll ml = max(L + 1, l / 2 + 1);
        ll mr = min(r, R) + 1;
        if (ml < mr) {
          ll t = 0;
          // -sum_{ml <= m < mr} max(l, m)
          ll p = clamp(l, ml, mr);
          // [ml, p) は l, [p, mr) は m
          t -= (p - ml) * l;
          t -= C2(mr - 1) - C2(p - 1);
          // sum_{ml <= m < mr} min(r, 2m-1)
          p = clamp(r / 2 + 1, ml, mr);
          // [ml, p) は 2m-1, [p, mr) は r
          t += (C2(p - 1) - C2(ml - 1)) * 2 - (p - ml);
          t += (mr - p) * r;
          s += q * t;
        }
      });
    });
    return mp[x] = s;
  };

  rep1(i, sq - 1) {
    ll x = N / (i * i);
    if (x == 0) break;
    v[i] = f(x);
  }
  ll ans = 0;
  rep(i, sq) ans += v[i] * mo[i];
  return ans;
}

void q() {
  inl(N);
  ll ans = 0, sgn = 1;
  while (N) ans += calc(N) * sgn, sgn = -sgn, N /= 2;
  out(ans);
}

void Nyaan::solve() {
  int t = 1;
  // in(t);
  while (t--) q();
}
yukicoder

結果

テストケース

ソースコード
