#1029873 (C++14) 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	👑 hos.lyric
提出日時	2024-12-04 04:29:36
言語	C++14 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	2,122 ms / 4,000 ms
コード長	4,893 bytes
コンパイル時間	1,738 ms
コンパイル使用メモリ	155,236 KB
実行使用メモリ	168,908 KB
最終ジャッジ日時	2024-12-04 04:29:54
合計ジャッジ時間	12,722 ms
ジャッジサーバーID （参考情報）	judge3 / judge4

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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	AC	146 ms 167,732 KB
testcase_01	AC	145 ms 167,680 KB
testcase_02	AC	177 ms 167,680 KB
testcase_03	AC	143 ms 167,680 KB
testcase_04	AC	143 ms 167,740 KB
testcase_05	AC	144 ms 167,796 KB
testcase_06	AC	143 ms 167,680 KB
testcase_07	AC	146 ms 167,808 KB
testcase_08	AC	151 ms 167,680 KB
testcase_09	AC	149 ms 167,680 KB
testcase_10	AC	177 ms 167,680 KB
testcase_11	AC	144 ms 167,668 KB
testcase_12	AC	148 ms 167,808 KB
testcase_13	AC	151 ms 167,808 KB
testcase_14	AC	154 ms 167,680 KB
testcase_15	AC	153 ms 167,808 KB
testcase_16	AC	158 ms 167,780 KB
testcase_17	AC	156 ms 167,808 KB
testcase_18	AC	199 ms 167,808 KB
testcase_19	AC	170 ms 167,808 KB
testcase_20	AC	228 ms 167,968 KB
testcase_21	AC	286 ms 168,064 KB
testcase_22	AC	1,589 ms 168,872 KB
testcase_23	AC	1,665 ms 168,876 KB
testcase_24	AC	149 ms 167,680 KB
testcase_25	AC	142 ms 167,680 KB
testcase_26	AC	144 ms 167,680 KB
testcase_27	AC	147 ms 167,680 KB
testcase_28	AC	2,122 ms 168,908 KB

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ソースコード

raw source code

#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")


// cannot use count
// no move constructor (==> use pointer for merge tech)
// unordered_set by value: __gnu_pbds::null_type
// no erase(iterator)
#include <ext/pb_ds/assoc_container.hpp>
using __gnu_pbds::gp_hash_table;

// https://codeforces.com/blog/entry/62393
#include <chrono>
struct Hash {
  static uint64_t splitmix64(uint64_t x) {
    // http://xorshift.di.unimi.it/splitmix64.c
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM = std::chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
  size_t operator()(const pair<int, int> &a) const {
    return operator()((uint64_t)a.first << 32 | a.second);
  }
};
template <class K> using Set = gp_hash_table<K, __gnu_pbds::null_type, Hash>;
template <class K, class V> using Map = gp_hash_table<K, V, Hash>;


inline long long divide(long long a, int b) {
  return a / b;
}
inline long long divide(long long a, long long b) {
  return a / b;
}

// quo[i - 1] < x <= quo[i] <=> floor(N/x) = quo[len - i]  (1 <= i <= len - 1)
struct Quotients {
  long long N;
  int N2;
  int len;
  Quotients(long long N_ = 0) : N(N_) {
    N2 = sqrt(static_cast<long double>(N));
    len = 2 * N2 + ((static_cast<long long>(N2) * (N2 + 1) <= N) ? 1 : 0);
  }
  long long operator[](int i) const {
    return (i <= N2) ? i : divide(N, len - i);
  }
  int indexOf(long long x) const {
    return (x <= N2) ? x : (len - divide(N, x));
  }
  friend std::ostream &operator<<(std::ostream &os, const Quotients &quo) {
    os << "[";
    for (int i = 0; i < quo.len; ++i) {
      if (i > 0) os << ", ";
      os << quo[i];
    }
    os << "]";
    return os;
  }
};


/*
  k (m^2-n^2, 2mn, m^2+n^2)
  
  \sum[k,m,n] [gcd(m, n) = 1] [m != n (mod 2)] [1 <= n < m] [2km(m+n) <= N]
  = \sum[k,m,n] (\sum[d] [d | m] [d | n] \mu(d)) [m != n (mod 2)] [1 <= n < m] [km(m+n) <= N/2]
  = \sum[d] [2 !| d] \mu(d) \sum[k,m,n] [m != n (mod 2)] [1 <= n < m] [km(m+n) <= N/2/d^2]
*/

constexpr int K = 40'000'000;
int small[K + 1];
void init() {
  for (Int m = 1; m * (m + 1) <= K; ++m) {
    for (Int n = (m & 1) + 1; m * (m + n) <= K && n < m; n += 2) {
      ++small[m * (m + n)];
    }
  }
  for (Int k = 1; k <= K; ++k) small[k] += small[k - 1];
}

Map<Int, Int> cache1;
Int solve1(Int N) {
  if (N <= K) return small[N];
  auto it = cache1.find(N);
  if (it != cache1.end()) return it->second;
  const Quotients quo(N);
  Int ret = 0;
  for (Int m = 1; m * (m + 1) <= N; ++m) {
    ret += ((min(N / m, 2 * m - 1) + 1) / 2 - (m + 1) / 2);
  }
  return cache1[N] = ret;
}

Map<Int, Int> cache;
Int solve(Int N) {
  auto it = cache.find(N);
  if (it != cache.end()) return it->second;
  const Quotients quo(N);
  Int ret = 0;
  for (int i = 1; i < quo.len; ++i) {
    ret += (quo[i] - quo[i - 1]) * solve1(quo[quo.len - i]);
  }
  return cache[N] = ret;
}

constexpr int LIM = 1'000'010;
int lpf[LIM], moe[LIM];

int main() {
  for (int p = 2; p < LIM; ++p) lpf[p] = p;
  for (int n = 1; n < LIM; ++n) moe[n] = 1;
  for (int p = 2; p < LIM; ++p) if (lpf[p] == p) {
    for (int n = p; n < LIM; n += p) {
      chmin(lpf[n], p);
      moe[n] = -moe[n];
    }
  }
  for (int d = 2; d*d < LIM; ++d) if (moe[d]) {
    for (int n = d*d; n < LIM; n += d*d) moe[n] = 0;
  }
// pv(moe,moe+31);
  
  init();
  
  Int N;
  for (; ~scanf("%lld", &N); ) {
    N /= 2;
    Int ans = 0;
    for (Int d = 1; d*d <= N; d += 2) if (moe[d]) {
      ans += moe[d] * solve(N / (d*d));
    }
    printf("%lld\n", ans);
  }
  return 0;
}

yukicoder

結果

テストケース

ソースコード