#887517 (C++14) No.2358 xy+yz+zx=N

• 問題: No.2358 xy+yz+zx=N
• ユーザー: rokahikou1
• 提出日時: 2023-07-06 00:11:40
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 28 ms / 2,000 ms
• コード長: 13,982 bytes
• コンパイル時間: 2,240 ms
• コンパイル使用メモリ: 193,832 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-07-19 18:30:12
• 合計ジャッジ時間: 3,081 ms
• ジャッジサーバーID （参考情報）: judge1 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	27 ms; 5,376 KB
testcase_09	AC	28 ms; 5,376 KB
testcase_10	AC	24 ms; 5,376 KB
testcase_11	AC	24 ms; 5,376 KB
testcase_12	AC	18 ms; 5,376 KB

コンパイルメッセージ

main.cpp: In function 'std::pair<long long int, long long int> math::crt2(const std::pair<long long int, long long int>&, const std::pair<long long int, long long int>&)':
main.cpp:359:10: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  359 |     auto [r1, m1] = rm1;
      |          ^
main.cpp:360:10: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  360 |     auto [r2, m2] = rm2;
      |          ^
main.cpp: In function 'long long int math::garner(const std::vector<std::pair<long long int, long long int> >&)':
main.cpp:382:14: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  382 |         auto [r, m] = rm[i];
      |              ^
main.cpp: In function 'long long int math::garner_mod(std::vector<std::pair<long long int, long long int> >, long long int)':
main.cpp:403:14: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  403 |         auto [r, m] = rm[i];
      |              ^
main.cpp: In function 'void solve()':
main.cpp:497:14: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  497 |     for(auto [x, y, z] : ans) {
      |              ^

ソースコード

#pragma region Macros
#include <bits/stdc++.h>
#define rep(i, n) for(int(i) = 0; (i) < (n); (i)++)
#define rrep(i, n) for(int(i) = (n)-1; (i) >= 0; (i)--)
#define FOR(i, m, n) for(int(i) = (m); (i) < (n); (i)++)
#define ROF(i, m, n) for(int(i) = (n)-1; (i) >= (m); (i)--)
#define ALL(v) (v).begin(), (v).end()
#define LLA(v) (v).rbegin(), (v).rend()
#define SZ(v) (int)(v).size()
#define INT(...)     \
    int __VA_ARGS__; \
    read(__VA_ARGS__)
#define LL(...)     \
    ll __VA_ARGS__; \
    read(__VA_ARGS__)
#define DOUBLE(...)     \
    double __VA_ARGS__; \
    read(__VA_ARGS__)
#define CHAR(...)     \
    char __VA_ARGS__; \
    read(__VA_ARGS__)
#define STRING(...)     \
    string __VA_ARGS__; \
    read(__VA_ARGS__)
#define VEC(type, name, size) \
    vector<type> name(size);  \
    read(name)
#define VEC2(type, name, height, width)                     \
    vector<vector<type>> name(height, vector<type>(width)); \
    read(name)
#define DVEC(type, name1, name2, size)     \
    vector<type> name1(size), name2(size); \
    read(name1, name2)
#define TVEC(type, name1, name2, name3, size)           \
    vector<type> name1(size), name2(size), name3(size); \
    read(name1, name2, name3)
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const int INF = 1 << 30;
const ll LINF = 1LL << 60;
const int MOD = 1e9 + 7;
const char newl = '\n';
const int dx[] = {1, 0, -1, 0};
const int dy[] = {0, 1, 0, -1};
template <class T> inline bool between(T x, T l, T r) {
    return l <= x && x < r;
}
template <class T> inline vector<T> make_vec(size_t a, T val) {
    return vector<T>(a, val);
}
template <class... Ts> inline auto make_vec(size_t a, Ts... ts) {
    return vector<decltype(make_vec(ts...))>(a, make_vec(ts...));
}
void read() {}
template <class T> inline void read(T &a) { cin >> a; }
template <class T, class S> inline void read(pair<T, S> &p) {
    read(p.first), read(p.second);
}
template <class T> inline void read(vector<T> &v) {
    for(auto &&a : v)
        read(a);
}
template <class T, class U> inline void read(vector<T> &a, vector<U> &b) {
    for(int i = 0; i < a.size(); i++) {
        read(a[i]);
        read(b[i]);
    }
}
template <class T, class U, class V>
inline void read(vector<T> &a, vector<U> &b, vector<V> &c) {
    for(int i = 0; i < a.size(); i++) {
        read(a[i]);
        read(b[i]);
        read(c[i]);
    }
}
template <class Head, class... Tail>
inline void read(Head &head, Tail &...tail) {
    read(head), read(tail...);
}
template <class T> void _write(const T &a) { cout << a; }
template <class T, class U> void _write(const std::pair<T, U> &a) { cout << a.first << ' ' << a.second; }
template <class T> void write(const T &a) {
    _write(a);
    cout << newl;
}
template <class T> void write(const vector<T> &a) {
    for(int i = 0; i < a.size(); i++) {
        _write(a[i]);
        cout << (i + 1 == a.size() ? newl : ' ');
    }
}
template <class Head, class... Tail>
void write(const Head &head, const Tail &...tail) {
    _write(head);
    cout << ' ';
    write(tail...);
}
template <class T> void writel(const T &a) { cout << a << '\n'; }
template <class T> void writel(const vector<T> &a) {
    for(int i = 0; i < a.size(); i++) {
        _write(a[i]);
        cout << newl;
    }
}
template <class Head, class... Tail>
void writel(const Head &head, const Tail &...tail) {
    _write(head);
    cout << newl;
    write(tail...);
}
template <class T> void _debug(const T &a) { cerr << a; }
template <class T, class U> void _debug(const std::pair<T, U> &a) { cerr << a.first << ' ' << a.second; }
template <class T> void debug(const T &a) {
    _debug(a);
    cerr << newl;
}
template <class T> void debug(const vector<T> &a) {
    for(int i = 0; i < a.size(); i++) {
        _debug(a[i]);
        cerr << (i + 1 == a.size() ? newl : ' ');
    }
}
template <class Head, class... Tail>
void debug(const Head &head, const Tail &...tail) {
    _debug(head);
    cerr << ' ';
    debug(tail...);
}
template <class T> void debugl(const T &a) { cerr << a << '\n'; }
template <class T> void debugl(const vector<T> &a) {
    for(int i = 0; i < a.size(); i++) {
        _debug(a[i]);
        cerr << newl;
    }
}
template <class Head, class... Tail>
void debugl(const Head &head, const Tail &...tail) {
    _debug(head);
    cerr << newl;
    debug(tail...);
}
template <class T> auto sum(const vector<T> &a) {
    return accumulate(ALL(a), T(0));
}
template <class T> auto min(const vector<T> &a) { return *min_element(ALL(a)); }
template <class T> auto max(const vector<T> &a) { return *max_element(ALL(a)); }
template <class T, class U> void msort(vector<T> &a, vector<U> &b) {
    assert(a.size() == b.size());
    vector<pair<T, U>> ab(a.size());
    for(int i = 0; i < a.size(); i++)
        ab[i] = {a[i], b[i]};
    sort(ALL(ab));
    for(int i = 0; i < a.size(); i++) {
        a[i] = ab[i].first;
        b[i] = ab[i].second;
    }
}
template <class T, class U, class V>
void msort(vector<T> &a, vector<U> &b, vector<V> &c) {
    assert(a.size() == b.size() && b.size() == c.size());
    vector<tuple<T, U, V>> abc(a.size());
    for(int i = 0; i < a.size(); i++)
        abc[i] = {a[i], b[i], c[i]};
    sort(ALL(abc));
    for(int i = 0; i < a.size(); i++) {
        a[i] = get<0>(abc[i]);
        b[i] = get<1>(abc[i]);
        c[i] = get<2>(abc[i]);
    }
}
template <class T, class U> inline bool chmax(T &a, U b) {
    if(a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T, class U> inline bool chmin(T &a, U b) {
    if(a > b) {
        a = b;
        return 1;
    }
    return 0;
}
int digit(ll a) {
    ll ret = 0;
    while(a && ++ret)
        a /= 10;
    return ret;
}
int digit_sum(ll a) {
    ll ret = 0;
    while(a) {
        ret += a % 10;
        a /= 10;
    }
    return ret;
}
ll llpow(ll a, ll n) {
    ll ret = 1;
    rep(i, n) ret *= a;
    return ret;
}
inline int bsf(int v) { return __builtin_ctz(v); } // 最下位の1が下から何番目か
inline int bsf(ll v) { return __builtin_ctzll(v); }
inline int bsr(int v) {
    return 31 - __builtin_clz(v);
} // 最上位の1が下から何番目か
inline int bsr(ll v) { return 63 - __builtin_clzll(v); }
inline int lsb(int v) { return v & -v; }      // 最下位の1だけ残す
inline ll lsb(ll v) { return v & -v; }
inline int msb(int v) { return 1 << bsr(v); } // 最上位の1だけ残す
inline ll msb(ll v) { return 1LL << bsr(v); }
struct IO {
    IO() {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout << fixed << setprecision(10);
    }
} io;
#pragma endregion

namespace math {

std::set<long long> divisor(long long n) {
    std::set<long long> ret;
    for(long long i = 1; i * i <= n; i++) {
        if(n % i == 0) {
            ret.insert(i);
            if(i * i != n)
                ret.insert(n / i);
        }
    }
    return ret;
}

// 素数篩＋素因数分解
// 初期化O(N),素因数分解O(logN)
// たくさん素因数分解するときはこっち
struct Sieve {
    int N;
    std::vector<int> sieve;
    std::vector<int> primes;
    Sieve(int n) : N(n), sieve(n + 1) { init(); }
    void init() {
        std::iota(sieve.begin(), sieve.end(), 0);
        for(int i = 2; i * i <= N; i++) {
            if(sieve[i] < i)
                continue;
            for(int j = i * i; j <= N; j += i) {
                if(sieve[j] == j)
                    sieve[j] = i;
            }
        }
        for(int i = 2; i <= N; i++) {
            if(is_prime(i)) primes.push_back(i);
        }
    }

    bool is_prime(int x) {
        assert(x <= N);
        if(x == 1)
            return false;
        return sieve[x] == x;
    }

    std::map<long long, int> prime_factorize(int n) {
        assert(n <= N);
        std::map<long long, int> ret;
        while(n > 1) {
            ret[sieve[n]]++;
            n = n / sieve[n];
        }
        return ret;
    }

    std::map<long long, int> prime_factorize_large(long long n) {
        std::map<long long, int> ret;
        for(auto p : primes) {
            while(n % p == 0) {
                ret[p]++;
                n /= p;
            }
        }
        if(n > 1) ret[n] = 1;
        return ret;
    }
};

// 素因数分解
// O(sqrt(N))
std::map<long long, int> prime_factor(long long n) {
    std::map<long long, int> ret;
    for(long long i = 2; i * i <= n; i++) {
        while(n % i == 0) {
            ret[i]++;
            n /= i;
        }
    }
    if(n != 1)
        ret[n] = 1;
    return ret;
}

long long mod_pow(long long x, long long n, long long mod) {
    if(n == 0)
        return 1;
    long long res = mod_pow(x * x % mod, n / 2, mod);
    if(n & 1)
        res = res * x % mod;
    return res;
}

long long euler_phi(long long n) {
    long long ret = n;
    for(long long i = 2; i * i <= n; i++) {
        if(n % i == 0) {
            ret -= ret / i;
            while(n % i == 0)
                n /= i;
        }
    }
    if(n > 1)
        ret -= ret / n;
    return ret;
}

long long extgcd(long long a, long long b, long long &x, long long &y) {
    if(b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    long long d = extgcd(b, a % b, y, x);
    y -= a / b * x;
    return d;
}

long long mod_inv(long long a, long long mod) {
    long long b = mod, u = 1, v = 0;
    while(b) {
        long long t = a / b;
        std::swap(a -= t * b, b);
        std::swap(u -= t * b, v);
    }
    u %= mod;
    if(u < 0)
        u += mod;
    return u;
}

std::pair<long long, long long>
crt2(const std::pair<long long, long long> &rm1,
     const std::pair<long long, long long> &rm2) {
    long long p, q;
    auto [r1, m1] = rm1;
    auto [r2, m2] = rm2;
    long long d = extgcd(r1, m2, p, q);
    if((r2 - r1) % d != 0)
        return {0, -1};
    long long m = m1 * (m2 / d);
    long long tmp = (r2 - r1) / d * p % (m2 / d);
    long long c = (r1 + m1 * tmp);
    long long r = (c % m + m) % m;
    return {r, m};
}

/**
 * @brief  Garnerのアルゴリズム. x % m[i] == b[i] % m[i]を満たす最小のxを求める.
 *
 * @param rm {あまり,法}の配列. !!法はすべて互いに素!!
 * @return long long x % m[i] == b[i] % m[i]を満たす最小のx.
 */
long long garner(const std::vector<std::pair<long long, long long>> &rm) {
    int n = rm.size();
    long long m_prod = 1;
    long long res = rm[0].first % rm[0].second;
    for(int i = 1; i < n; i++) {
        auto [r, m] = rm[i];
        m_prod *= rm[i - 1].second;
        long long t = (((r - res) * mod_inv(m_prod, m)) % m + m) % m;
        res += t * m_prod;
    }
    return res;
}

/**
 * @brief  Garnerのアルゴリズム. x % m[i] == b[i] % m[i]を満たす最小のxを求める.
 *
 * @param rm {あまり,法}の配列. !!法はすべて互いに素!!
 * @param mod 答えの法.
 * @return long long x % m[i] == b[i] % m[i]を満たす最小のx (mod M).
 */
long long garner_mod(std::vector<std::pair<long long, long long>> rm,
                     long long mod) {
    rm.emplace_back(0, mod);
    int n = rm.size();
    std::vector<long long> coffs(n, 1), constants(n, 0);
    for(int i = 0; i < n - 1; i++) {
        auto [r, m] = rm[i];
        long long t = ((r - constants[i]) * mod_inv(coffs[i], m) % m + m) & m;
        for(int j = i + 1; j < n; j++) {
            (constants[j] += coffs[j] * t) %= rm[j].second;
            (coffs[j] *= m) %= rm[j].second;
        }
    }
    return constants.back();
}

long long floor_div(long long a, long long b) {
    assert(b != 0);
    if(b < 0)
        a = -a, b = -b;
    return a >= 0 ? a / b : (a - (b - 1)) / b;
}

long long ceil_div(long long a, long long b) {
    assert(b != 0);
    if(b < 0)
        a = -a, b = -b;
    return a >= 0 ? (a + b - 1) / b : a / b;
}

int bit_length(long long x) {
    assert(x >= 0);
    int ret = 0;
    while(x > 0) {
        ret++;
        x /= 2;
    }
    return ret;
}

long long ll_sqrt(long long x) {
    long long ret = sqrt(x) - 1;
    while((ret + 1) * (ret + 1) <= x)
        ret++;
    return ret;
}

// multiple of d in [left,right],left>0
long long cmul(long long left, long long right, long long d) {
    if(left == 0)
        return right / d;
    return right / d - (left - 1) / d;
}

// multiple of d in [left,right]
long long count_multiple(long long left, long long right, long long d) {
    if(right < 0)
        return cmul(-right, -left, d);
    if(left > 0)
        return cmul(left, right, d);
    return cmul(0, right, d) + cmul(0, -left, d) + 1;
}

}; // namespace math

using namespace math;

void solve() {
    INT(N);
    int rn = ll_sqrt(N);
    vector<tuple<int, int, int>> ans;
    for(int x = 0; x <= rn; x++) {
        for(int y = x; y <= rn; y++) {
            if(x == 0 && y == 0) continue;
            if((N - x * y) % (x + y) == 0) {
                int z = (N - x * y) / (x + y);
                if(z >= y) {
                    if(x != y && y != z) {
                        ans.emplace_back(x, 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);
                    } else if(x == y && y == z) {
                        ans.emplace_back(x, y, z);
                    } else if(x == y) {
                        ans.emplace_back(x, y, z);
                        ans.emplace_back(x, z, y);
                        ans.emplace_back(z, x, y);
                    } else {
                        ans.emplace_back(x, y, z);
                        ans.emplace_back(y, x, z);
                        ans.emplace_back(y, z, x);
                    }
                }
            }
        }
    }
    write(ans.size());
    for(auto [x, y, z] : ans) {
        write(x, y, z);
    }
}

int main() {
    int t = 1;
    // cin >> t;
    while(t--) {
        solve();
    }
}