#683535 (C++17) No.1653 Squarefree

提出ソース

結果

問題	No.1653 Squarefree
ユーザー	chocorusk
提出日時	2021-07-27 19:44:45
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	TLE
実行時間	-
コード長	11,388 bytes
コンパイル時間	2,681 ms
コンパイル使用メモリ	214,620 KB
実行使用メモリ	26,496 KB
最終ジャッジ日時	2024-10-14 02:18:44
合計ジャッジ時間	8,967 ms
ジャッジサーバーID （参考情報）	judge2 / judge3

このコードへのチャレンジ
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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	TLE	-
testcase_01	--	-
testcase_02	--	-
testcase_03	--	-
testcase_04	--	-
testcase_05	--	-
testcase_06	--	-
testcase_07	--	-
testcase_08	--	-
testcase_09	--	-
testcase_10	--	-
testcase_11	--	-
testcase_12	--	-
testcase_13	--	-
testcase_14	--	-
testcase_15	--	-
testcase_16	--	-
testcase_17	--	-
testcase_18	--	-
testcase_19	--	-
testcase_20	--	-
testcase_21	--	-
testcase_22	--	-
testcase_23	--	-
testcase_24	--	-
testcase_25	--	-
testcase_26	--	-
testcase_27	--	-
testcase_28	--	-
testcase_29	--	-
testcase_30	--	-
testcase_31	--	-
testcase_32	--	-
testcase_33	--	-
testcase_34	--	-
testcase_35	--	-
testcase_36	--	-
testcase_37	--	-
testcase_38	--	-
testcase_39	--	-
testcase_40	--	-

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ソースコード

raw source code

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

namespace inner {

using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;

template <typename T>
T gcd(T a, T b) {
  while (b) swap(a %= b, b);
  return a;
}

uint64_t gcd_impl(uint64_t n, uint64_t m) {
  constexpr uint64_t K = 5;
  for (int i = 0; i < 80; ++i) {
    uint64_t t = n - m;
    uint64_t s = n - m * K;
    bool q = t < m;
    bool p = t < m * K;
    n = q ? m : t;
    m = q ? t : m;
    if (m == 0) return n;
    n = p ? n : s;
  }
  return gcd_impl(m, n % m);
}

uint64_t gcd_pre(uint64_t n, uint64_t m) {
  for (int i = 0; i < 4; ++i) {
    uint64_t t = n - m;
    bool q = t < m;
    n = q ? m : t;
    m = q ? t : m;
    if (m == 0) return n;
  }
  return gcd_impl(n, m);
}

uint64_t gcd_fast(uint64_t n, uint64_t m) {
  return n > m ? gcd_pre(n, m) : gcd_pre(m, n);
}

template <typename T = int32_t>
T inv(T a, T p) {
  T b = p, x = 1, y = 0;
  while (a) {
    T q = b % a;
    swap(a, b /= a);
    swap(x, y -= q * x);
  }
  assert(b == 1);
  return y < 0 ? y + p : y;
}

template <typename T = int32_t, typename U = int64_t>
T modpow(T a, U n, T p) {
  T ret = 1;
  for (; n; n >>= 1, a = U(a) * a % p)
    if (n & 1) ret = U(ret) * a % p;
  return ret;
}

}  // namespace inner

using namespace std;

unsigned long long rng() {
  static unsigned long long x_ = 88172645463325252ULL;
  x_ = x_ ^ (x_ << 7);
  return x_ = x_ ^ (x_ >> 9);
}
using namespace std;

struct ArbitraryLazyMontgomeryModInt {
  using mint = ArbitraryLazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static u32 mod;
  static u32 r;
  static u32 n2;

  static u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static void set_mod(u32 m) {
    assert(m < (1 << 30));
    assert((m & 1) == 1);
    mod = m;
    n2 = -u64(m) % m;
    r = get_r();
    assert(r * mod == 1);
  }

  u32 a;

  ArbitraryLazyMontgomeryModInt() : a(0) {}
  ArbitraryLazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

  static u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }

  mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  mint operator+(const mint &b) const { return mint(*this) += b; }
  mint operator-(const mint &b) const { return mint(*this) -= b; }
  mint operator*(const mint &b) const { return mint(*this) *= b; }
  mint operator/(const mint &b) const { return mint(*this) /= b; }
  bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  mint operator-() const { return mint() - mint(*this); }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = ArbitraryLazyMontgomeryModInt(t);
    return (is);
  }

  mint inverse() const { return pow(mod - 2); }

  u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static u32 get_mod() { return mod; }
};
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::mod;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::r;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::n2;

using namespace std;

struct montgomery64 {
  using mint = montgomery64;
  using i64 = int64_t;
  using u64 = uint64_t;
  using u128 = __uint128_t;

  static u64 mod;
  static u64 r;
  static u64 n2;

  static u64 get_r() {
    u64 ret = mod;
    for (i64 i = 0; i < 5; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static void set_mod(u64 m) {
    assert(m < (1LL << 62));
    assert((m & 1) == 1);
    mod = m;
    n2 = -u128(m) % m;
    r = get_r();
    assert(r * mod == 1);
  }

  u64 a;

  montgomery64() : a(0) {}
  montgomery64(const int64_t &b) : a(reduce((u128(b) + mod) * n2)){};

  static u64 reduce(const u128 &b) {
    return (b + u128(u64(b) * u64(-r)) * mod) >> 64;
  }

  mint &operator+=(const mint &b) {
    if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  mint &operator-=(const mint &b) {
    if (i64(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  mint &operator*=(const mint &b) {
    a = reduce(u128(a) * b.a);
    return *this;
  }

  mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  mint operator+(const mint &b) const { return mint(*this) += b; }
  mint operator-(const mint &b) const { return mint(*this) -= b; }
  mint operator*(const mint &b) const { return mint(*this) *= b; }
  mint operator/(const mint &b) const { return mint(*this) /= b; }
  bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  mint operator-() const { return mint() - mint(*this); }

  mint pow(u128 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = montgomery64(t);
    return (is);
  }

  mint inverse() const { return pow(mod - 2); }

  u64 get() const {
    u64 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static u64 get_mod() { return mod; }
};
typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2;


namespace fast_factorize {
using u64 = uint64_t;

template <typename mint>
bool miller_rabin(u64 n, vector<u64> as) {
  if (mint::get_mod() != n) mint::set_mod(n);
  u64 d = n - 1;
  while (~d & 1) d >>= 1;
  mint e{1}, rev{int64_t(n - 1)};
  for (u64 a : as) {
    if (n <= a) break;
    u64 t = d;
    mint y = mint(a).pow(t);
    while (t != n - 1 && y != e && y != rev) {
      y *= y;
      t *= 2;
    }
    if (y != rev && t % 2 == 0) return false;
  }
  return true;
}

bool is_prime(u64 n) {
  if (~n & 1) return n == 2;
  if (n <= 1) return false;
  if (n < (1LL << 30))
    return miller_rabin<ArbitraryLazyMontgomeryModInt>(n, {2, 7, 61});
  else
    return miller_rabin<montgomery64>(
        n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}

template <typename mint, typename T>
T pollard_rho(T n) {
  if (~n & 1) return 2;
  if (is_prime(n)) return n;
  if (mint::get_mod() != n) mint::set_mod(n);
  mint R, one = 1;
  auto f = [&](mint x) { return x * x + R; };
  auto rnd = [&]() { return rng() % (n - 2) + 2; };
  while (1) {
    mint x, y, ys, q = one;
    R = rnd(), y = rnd();
    T g = 1;
    constexpr int m = 128;
    for (int r = 1; g == 1; r <<= 1) {
      x = y;
      for (int i = 0; i < r; ++i) y = f(y);
      for (int k = 0; g == 1 && k < r; k += m) {
        ys = y;
        for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
        g = inner::gcd_fast(q.get(), n);
      }
    }
    if (g == n) do
        g = inner::gcd_fast((x - (ys = f(ys))).get(), n);
      while (g == 1);
    if (g != n) return g;
  }
  exit(1);
}

bool inner_factorize(u64 n) {
  if (n <= 1) return true;
  u64 p;
  if (n <= (1LL << 30))
    p = pollard_rho<ArbitraryLazyMontgomeryModInt>(n);
  else
    p = pollard_rho<montgomery64>(n);
  if (p == n) return true;
  if(inner::gcd_fast(p, n/p)>1) return false;
  auto l = inner_factorize(p);
  if(!l) return false;
  auto r = inner_factorize(n / p);
  return r;
}

bool factorize(u64 n) {
  return inner_factorize(n);
}

}  // namespace fast_factorize
using fast_factorize::factorize;
using fast_factorize::is_prime;
using namespace std;

namespace fastio {
static constexpr int SZ = 1 << 17;
char ibuf[SZ], obuf[SZ];
int pil = 0, pir = 0, por = 0;

struct Pre {
  char num[40000];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i * 4 + j] = n % 10 + '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
}
inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

inline void rd(char& c) { c = ibuf[pil++]; }
template <typename T>
inline void rd(T& x) {
  if (pil + 32 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if (c == '-') {
    minus = 1;
    c = ibuf[pil++];
  }
  x = 0;
  while (c >= '0') {
    x = x * 10 + (c & 15);
    c = ibuf[pil++];
  }
  if (minus) x = -x;
}
inline void rd() {}
template <typename Head, typename... Tail>
inline void rd(Head& head, Tail&... tail) {
  rd(head);
  rd(tail...);
}

inline void wt(char c) { obuf[por++] = c; }
template <typename T>
inline void wt(T x) {
  if (por > SZ - 32) flush();
  if (!x) {
    obuf[por++] = '0';
    return;
  }
  if (x < 0) {
    obuf[por++] = '-';
    x = -x;
  }
  int i = 12;
  char buf[16];
  while (x >= 10000) {
    memcpy(buf + i, pre.num + (x % 10000) * 4, 4);
    x /= 10000;
    i -= 4;
  }
  if (x < 100) {
    if (x < 10) {
      wt(char('0' + char(x)));
    } else {
      uint32_t q = (uint32_t(x) * 205) >> 11;
      uint32_t r = uint32_t(x) - q * 10;
      obuf[por + 0] = '0' + q;
      obuf[por + 1] = '0' + r;
      por += 2;
    }
  } else {
    if (x < 1000) {
      memcpy(obuf + por, pre.num + (x << 2) + 1, 3);
      por += 3;
    } else {
      memcpy(obuf + por, pre.num + (x << 2), 4);
      por += 4;
    }
  }
  memcpy(obuf + por, buf + i + 4, 12 - i);
  por += 12 - i;
}

inline void wt() {}
template <typename Head, typename... Tail>
inline void wt(Head head, Tail... tail) {
  wt(head);
  wt(tail...);
}
template <typename T>
inline void wtn(T x) {
  wt(x, '\n');
}

struct Dummy {
  Dummy() { atexit(flush); }
} dummy;

}  // namespace fastio
using fastio::rd;
using fastio::wt;
using fastio::wtn;
int main() {
    using ll=long long;
  ll l, r;
  cin>>l>>r;
  const int MAX=20000010;
    bitset<MAX> isprime;
    for(int i=3; i<MAX; i++, i++) isprime[i]=1;
    isprime[2]=1;
    for(int i=3; i<MAX; i++){
        if(isprime[i]){
            for(int j=(i<<1); j<MAX; j+=i) isprime[j]=0;
        }
    }
    ll x[1000010];
    bitset<MAX> sqf;
    for(ll i=l; i<=r; i++){
		x[i-l]=i;
		sqf[i-l]=1;
	}
	for(ll p=2; p<MAX; p++){
		if(!isprime[p]) continue;
		for(ll i=(l+p-1)/p*p; i<=r; i+=p){
			int e=0;
			while(x[i-l]%p==0){
				x[i-l]/=p;
				e++;
			}
			if(e>1) sqf[i-l]=0;
		}
	}
	int ans=0;
	for(ll i=l; i<=r; i++){
		if(!sqf[i-l]) continue;
        if(x[i-l]==1){
            ans++;
            continue;
        }
		if(factorize(x[i-l])) ans++;
	}
  cout<<ans<<endl;
}

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結果

テストケース

ソースコード