結果

問題 No.2358 xy+yz+zx=N
ユーザー OnjoujiToki
提出日時 2023-07-08 12:57:06
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 33 ms / 2,000 ms
コード長 6,775 bytes
コンパイル時間 1,311 ms
コンパイル使用メモリ 138,512 KB
最終ジャッジ日時 2025-02-15 08:56:30
ジャッジサーバーID
（参考情報） 		judge1 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 10
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

diff #
プレゼンテーションモードにする

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdint>
#include <cstring>
#include <ctime>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <unordered_map>
#include <unordered_set>
using namespace std;
template <int mod>
struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ModInt &operator^=(long long p) {  // quick_pow here:3
    ModInt res = 1;
    for (; p; p >>= 1) {
      if (p & 1) res *= *this;
      *this *= *this;
    }
    return *this = res;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  ModInt operator^(long long p) const { return ModInt(*this) ^= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  explicit operator int() const { return x; }  // added by QCFium
  ModInt operator=(const int p) {
    x = p;
    return ModInt(*this);
  }  // added by QCFium
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      a -= t * b;
      std::swap(a, b);
      u -= t * v;
      std::swap(u, v);
    }
    return ModInt(u);
  }
  friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &p) {
    return os << p.x;
  }
  friend std::istream &operator>>(std::istream &is, ModInt<mod> &a) {
    long long x;
    is >> x;
    a = ModInt<mod>(x);
    return (is);
  }
};
template <typename T>
struct SegmentTree {
  using Monoid = typename T::Monoid;
  explicit SegmentTree(int n) : SegmentTree(std::vector<Monoid>(n, T::id())) {}
  explicit SegmentTree(const std::vector<Monoid> &a) : n(a.size()), sz(1) {
    while (sz < n) sz <<= 1;
    data.assign(sz << 1, T::id());
    std::copy(a.begin(), a.end(), data.begin() + sz);
    for (int i = sz - 1; i > 0; --i) {
      data[i] = T::merge(data[i << 1], data[(i << 1) + 1]);
    }
  }
  void set(int idx, const Monoid val) {
    idx += sz;
    data[idx] = val;
    while (idx >>= 1)
      data[idx] = T::merge(data[idx << 1], data[(idx << 1) + 1]);
  }
  Monoid get(int left, int right) const {
    Monoid res_l = T::id(), res_r = T::id();
    for (left += sz, right += sz; left < right; left >>= 1, right >>= 1) {
      if (left & 1) res_l = T::merge(res_l, data[left++]);
      if (right & 1) res_r = T::merge(data[--right], res_r);
    }
    return T::merge(res_l, res_r);
  }
  Monoid operator[](const int idx) const { return data[idx + sz]; }
 private:
  const int n;
  int sz;  // sz + 原数组坐标 = 线段树里的编号，1 based
  std::vector<Monoid> data;
};
namespace monoid {
template <typename T>
struct RangeMinimumQuery {
  using Monoid = T;
  static constexpr Monoid id() { return std::numeric_limits<Monoid>::max(); }
  static Monoid merge(const Monoid &a, const Monoid &b) {
    return std::min(a, b);
  }
};
template <typename T>
struct RangeMaximumQuery {
  using Monoid = T;
  static constexpr Monoid id() { return std::numeric_limits<Monoid>::lowest(); }
  static Monoid merge(const Monoid &a, const Monoid &b) {
    return std::max(a, b);
  }
};
template <typename T>
struct RangeSumQuery {
  using Monoid = T;
  static constexpr Monoid id() { return 0; }
  static Monoid merge(const Monoid &a, const Monoid &b) { return a + b; }
};
}  // namespace monoid
template <typename T>
struct DSU {
  std::vector<T> f, siz;
  DSU(int n) : f(n), siz(n, 1) { std::iota(f.begin(), f.end(), 0); }
  T leader(T x) {
    while (x != f[x]) x = f[x] = f[f[x]];
    return x;
  }
  bool same(T x, T y) { return leader(x) == leader(y); }
  bool merge(T x, T y) {
    x = leader(x);
    y = leader(y);
    if (x == y) return false;
    siz[x] += siz[y];
    f[y] = x;
    return true;
  }
  T size(int x) { return siz[leader(x)]; }
};
std::vector<bool> prime_table(int n) {
  std::vector<bool> prime(n + 1, true);
  if (n >= 0) prime[0] = false;
  if (n >= 1) prime[1] = false;
  for (int i = 2; i * i <= n; i++) {
    if (!prime[i]) continue;
    for (int j = i * i; j <= n; j += i) {
      prime[j] = false;
    }
  }
  return prime;
}
std::vector<int> enumerate_primes(int n) {
  if (n <= 1) return {};
  auto d = prime_table(n);
  std::vector<int> primes;
  primes.reserve(count(begin(d), end(d), true));
  for (int i = 0; i < d.size(); i++) {
    if (d[i]) primes.push_back(i);
  }
  return primes;
}
void solve() {
  int n;
  std::cin >> n;
  std::vector<std::tuple<int, int, int>> ans;
  // when one is zero
  //
  for (int x = 1; x <= sqrt(n); x++) {
    if (n % x == 0) {
      ans.emplace_back(0, x, n / x);
      if (x != n / x) ans.emplace_back(0, n / x, x);
      ans.emplace_back(n / x, 0, x);
      if (x != n / x) ans.emplace_back(x, 0, n / x);
      ans.emplace_back(x, n / x, 0);
      if (x != n / x) ans.emplace_back(n / x, x, 0);
    }
  }
  // xy + yz + xz = n
  // n - xy = (x + y)z
  for (int x = 1; x <= sqrt(n); x++) {
    for (int y = x; y <= sqrt(n); y++) {
      if ((n - x * y) % (x + y) == 0) {
        int z = (n - x * y) / (x + y);
        if (z < x or z < y) continue;
        // x <= y <= z
        ans.emplace_back(x, y, z);
        if (x == y and x != z) {
          // x == y < z;
          ans.emplace_back(x, z, y);
          ans.emplace_back(z, x, y);
        } else if (x != y and y == z) {
          // x < y == z
          ans.emplace_back(z, x, y);
          ans.emplace_back(z, y, x);
        } else if (x == y and y == z)
          continue;
        else {
          assert(x != y and y != z);
          ans.emplace_back(x, z, y);
          ans.emplace_back(y, x, z);
          ans.emplace_back(y, z, x);
          ans.emplace_back(z, x, y);
          ans.emplace_back(z, y, x);
        }
      }
    }
  }
  std::cout << ans.size() << '\n';
  for (auto &[x, y, z] : ans) std::cout << x << ' ' << y << ' ' << z << '\n';
}
int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  int t = 1;
  while (t--) solve();
  return 0;
}
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