結果

問題 No.1626 三角形の構築
ユーザー rniyarniya
提出日時 2023-01-15 16:28:29
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 6,862 bytes
コンパイル時間 2,344 ms
コンパイル使用メモリ 216,588 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-06-09 04:25:45
合計ジャッジ時間 3,673 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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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 2 ms
5,248 KB
testcase_01 WA -
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 1 ms
5,376 KB
testcase_04 AC 1 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 WA -
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 2 ms
5,376 KB
testcase_11 WA -
testcase_12 AC 2 ms
5,376 KB
testcase_13 WA -
testcase_14 WA -
testcase_15 WA -
testcase_16 WA -
testcase_17 WA -
testcase_18 WA -
testcase_19 WA -
testcase_20 WA -
testcase_21 WA -
testcase_22 AC 2 ms
5,376 KB
testcase_23 AC 2 ms
5,376 KB
testcase_24 AC 3 ms
5,376 KB
testcase_25 AC 1 ms
5,376 KB
testcase_26 WA -
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 # 

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define ALL(x) (x).begin(), (x).end()
#ifdef LOCAL
#include "debug.hpp"
#else
#define debug(...) void(0)
#endif

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (size_t i = 0; i < v.size(); i++) {
        os << v[i] << (i + 1 == v.size() ? "" : " ");
    }
    return os;
}

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
long long MSK(int n) { return (1LL << n) - 1; }

template <class T> T ceil(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? x / y : (x - y + 1) / y);
}

template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <typename T> void mkuni(vector<T>& v) {
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
}
template <typename T> int lwb(const vector<T>& v, const T& x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); }

const int INF = (1 << 30) - 1;
const long long IINF = (1LL << 60) - 1;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const int MOD = 998244353;
// const int MOD = 1000000007;

#include <numeric>
#include <tuple>
#include <vector>

namespace elementary_math {

template <typename T> std::vector<T> divisor(T n) {
    std::vector<T> res;
    for (T i = 1; i * i <= n; i++) {
        if (n % i == 0) {
            res.emplace_back(i);
            if (i * i != n) res.emplace_back(n / i);
        }
    }
    return res;
}

template <typename T> std::vector<std::pair<T, int>> prime_factor(T n) {
    std::vector<std::pair<T, int>> res;
    for (T p = 2; p * p <= n; p++) {
        if (n % p == 0) {
            res.emplace_back(p, 0);
            while (n % p == 0) {
                res.back().second++;
                n /= p;
            }
        }
    }
    if (n > 1) res.emplace_back(n, 1);
    return res;
}

std::vector<int> osa_k(int n) {
    std::vector<int> min_factor(n + 1, 0);
    for (int i = 2; i <= n; i++) {
        if (min_factor[i]) continue;
        for (int j = i; j <= n; j += i) {
            if (!min_factor[j]) {
                min_factor[j] = i;
            }
        }
    }
    return min_factor;
}

std::vector<int> prime_factor(const std::vector<int>& min_factor, int n) {
    std::vector<int> res;
    while (n > 1) {
        res.emplace_back(min_factor[n]);
        n /= min_factor[n];
    }
    return res;
}

long long modpow(long long x, long long n, long long mod) {
    assert(0 <= n && 1 <= mod && mod < (1LL << 31));
    if (mod == 1) return 0;
    x %= mod;
    long long res = 1;
    while (n > 0) {
        if (n & 1) res = res * x % mod;
        x = x * x % mod;
        n >>= 1;
    }
    return res;
}

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

long long inv_mod(long long a, long long mod) {
    assert(1 <= mod);
    long long x, y;
    if (extgcd(a, mod, x, y) != 1) return -1;
    return (mod + x % mod) % mod;
}

template <typename T> T euler_phi(T n) {
    auto pf = prime_factor(n);
    T res = n;
    for (const auto& p : pf) {
        res /= p.first;
        res *= p.first - 1;
    }
    return res;
}

std::vector<int> euler_phi_table(int n) {
    std::vector<int> res(n + 1, 0);
    iota(res.begin(), res.end(), 0);
    for (int i = 2; i <= n; i++) {
        if (res[i] != i) continue;
        for (int j = i; j <= n; j += i) res[j] = res[j] / i * (i - 1);
    }
    return res;
}

// minimum i > 0 s.t. x^i \equiv 1 \pmod{m}
template <typename T> T order(T x, T m) {
    T n = euler_phi(m);
    auto cand = divisor(n);
    sort(cand.begin(), cand.end());
    for (auto& i : cand) {
        if (modpow(x, i, m) == 1) {
            return i;
        }
    }
    return -1;
}

template <typename T> std::vector<std::tuple<T, T, T>> quotient_ranges(T n) {
    std::vector<std::tuple<T, T, T>> res;
    T m = 1;
    for (; m * m <= n; m++) res.emplace_back(m, m, n / m);
    for (; m >= 1; m--) {
        T l = n / (m + 1) + 1, r = n / m;
        if (l <= r and std::get<1>(res.back()) < l) res.emplace_back(l, r, n / l);
    }
    return res;
}

}  // namespace elementary_math

ll SQRT(ll x) {
    ll lb = 0, ub = INF;
    while (ub - lb > 1) {
        ll mid = (ub + lb) >> 1;
        (mid * mid <= x ? lb : ub) = mid;
    }
    return lb;
}

void solve() {
    int S, T;
    cin >> S >> T;

    if (T & 1) {
        cout << 0 << '\n';
        return;
    }
    ll s = T / 2, prod = 1LL * S * S;
    if (prod % s != 0) {
        cout << 0 << '\n';
        return;
    }
    prod /= s;
    auto facs = elementary_math::prime_factor(S);
    for (auto& p : facs) p.second *= 2;
    vector<vector<ll>> ans;
    auto dfs = [&](auto self, int d, ll cur) -> void {
        if (d == (int)facs.size()) {
            ll c = s - cur;
            if (c <= 0) return;
            if (c * 3 <= T) return;
            if (prod % cur != 0) return;
            ll SUM = T - c, PROD = prod / cur;
            PROD -= s * s - SUM * s;
            ll tmp = SUM * SUM - 4 * PROD;
            if (tmp < 0) return;
            ll r = SQRT(tmp);
            if (r * r != tmp) return;
            if ((SUM + r) & 1) return;
            ll a = (SUM + r) >> 1, b = SUM - a;
            if (a <= 0 or b <= 0) return;
            if (a > c or b > c) return;
            vector<ll> v = {a, b, c};
            sort(v.begin(), v.end());
            ans.emplace_back(v);
            return;
        }
        ll nxt = cur, p = facs[d].first;
        for (int i = 0; i < facs[d].second; i++, nxt *= p) self(self, d + 1, nxt);
    };
    dfs(dfs, 0, 1);

    cout << ans.size() << '\n';
    for (auto& t : ans) cout << t << '\n';
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int t;
    cin >> t;
    for (; t--;) solve();
    return 0;
}
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