#683427 (C++17(gcc12)) No.1626 三角形の構築

• 問題: No.1626 三角形の構築
• ユーザー: 👑 null
• 提出日時: 2021-07-26 20:27:00
• 言語: C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
• 結果: CE (最新)
  AC
  (最初)
• 実行時間: -
• コード長: 7,912 bytes
• コンパイル時間: 30,132 ms
• コンパイル使用メモリ: 6,820 KB
• 最終ジャッジ日時: 2025-01-23 09:45:54
• ジャッジサーバーID （参考情報）: judge5 / judge1

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ソースコード

/*
このコード、と～おれ!
Be accepted!
∧＿∧　
（｡･ω･｡)つ━☆・*。
⊂　　 ノ 　　　・゜+.
　しーＪ　　　°。+ *´¨)
 　　　　　　　　　.· ´¸.·*´¨) ¸.·*¨)
          　　　　　　　　　　(¸.·´ (¸.·'* ☆
*/

#include <cstdio>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstring>
#include <vector>
#include <numeric>
#include <iostream>
#include <random>
#include <map>
#include <unordered_map>
#include <queue>
#include <regex>
#include <functional>
#include <complex>
#include <list>
#include <cassert>
#include <iomanip>
#include <set>
#include <stack>
#include <bitset>
#include <array>
#include <chrono>

//#pragma GCC target("arch=skylake-avx512")
#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse4")
#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define repeat(i, n, m) for(int i = n; i < (m); ++i)
#define rep(i, n) for(int i = 0; i < (n); ++i)
#define printynl(a) printf(a ? "yes\n" : "no\n")
#define printyn(a) printf(a ? "Yes\n" : "No\n")
#define printYN(a) printf(a ? "YES\n" : "NO\n")
#define printim(a) printf(a ? "possible\n" : "imposible\n")
#define printdb(a) printf("%.50lf\n", a)
#define printLdb(a) printf("%.50Lf\n", a)
#define printdbd(a) printf("%.16lf\n", a)
#define prints(s) printf("%s\n", s.c_str())
#define all(x) (x).begin(), (x).end()
#define deg_to_rad(deg) (((deg)/360.0L)*2.0L*PI)
#define rad_to_deg(rad) (((rad)/2.0L/PI)*360.0L)
#define Please return
#define AC 0
#define manhattan_dist(a, b, c, d) (abs(a - c) + abs(b - d))

using ll = long long;
using ull = unsigned long long;

constexpr int INF = 1073741823;
constexpr int MINF = -1073741823;
constexpr ll LINF = ll(4661686018427387903);
constexpr ll MOD = 1e9 + 7;
constexpr ll mod = 998244353;
constexpr long double eps = 1e-6;
const long double PI = acosl(-1.0L);

using namespace std;

void scans(string& str) {
    char c;
    str = "";
    scanf("%c", &c);
    if (c == '\n')scanf("%c", &c);
    while (c != '\n' && c != -1 && c != ' ') {
        str += c;
        scanf("%c", &c);
    }
}

void scanc(char& str) {
    char c;
    scanf("%c", &c);
    if (c == -1)return;
    while (c == '\n') {
        scanf("%c", &c);
    }
    str = c;
}

double acot(double x) {
    return PI / 2 - atan(x);
}

ll LSB(ll n) { return (n & (-n)); }

template<typename T>
inline T chmin(T& a, const T& b) {
    if (a > b)a = b;
    return a;
}

template<typename T>
inline T chmax(T& a, const T& b) {
    if (a < b)a = b;
    return a;
}

//cpp_int
#if __has_include(<boost/multiprecision/cpp_int.hpp>)
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
using namespace boost::multiprecision;
#else
using cpp_int = ll;
#endif

//atcoder library
#if __has_include(<atcoder/all>)
#include <atcoder/all>
//using namespace atcoder;
#endif

/*
    random_device seed_gen;
    mt19937 engine(seed_gen());
    uniform_int_distribution dist(1, 100);
*/


/*----------------------------------------------------------------------------------*/

ll sq(ll n) {
    ll ng = -1, ok = 3 * 1e9;
    while (abs(ng - ok) > 1) {
        ll mid = (ok + ng) / 2;
        if (mid * mid >= n)ok = mid;
        else ng = mid;
    }
    if (ok * ok == n)return ok;
    else return -1;
}

struct Miller {
    const vector<long long> v = { 2 , 7 , 61 }; // < 4,759,123,141
    // x^k (mod m)
    long long modpow(long long x, long long k, long long m) {
        long long res = 1;
        while (k) {
            if (k & 1) {
                res = res * x % m;
            }
            k /= 2;
            x = x * x % m;
        }
        return res;
    }
    // check if n is prime
    bool check(long long n) {
        if (n < 2) {
            return false;
        }
        long long d = n - 1;
        long long s = 0;
        while (d % 2 == 0) {
            d /= 2;
            s++;
        }
        for (long long a : v) {
            if (a == n) {
                return true;
            }
            if (modpow(a, d, n) != 1) {
                bool ok = true;
                for (long long r = 0; r < s; r++) {
                    if (modpow(a, d * (1LL << r), n) == n - 1) {
                        ok = false;
                        break;
                    }
                }
                if (ok) {
                    return false;
                }
            }
        }
        return true;
    }
};

struct Rho {
    mt19937 mt;
    Miller miller;
    long long c;
    Rho() {
        mt.seed(clock());
    }
    inline long long f(long long x, long long n) {
        return (x * x + c) % n;
    }
    long long check(long long n) {
        if (n == 4) {
            return 2;
        }
        c = mt() % n;
        long long x = mt() % n;
        long long y = x;
        long long d = 1;
        while (d == 1) {
            x = f(x, n);
            y = f(f(y, n), n);
            d = gcd(abs(x - y), n);
        }
        if (d == n) {
            return -1;
        }
        return d;
    }
    vector<long long> factor(long long n) {
        if (n <= 1) {
            return {};
        }
        if (miller.check(n)) {
            return { n };
        }
        long long res = -1;
        while (res == -1) {
            res = check(n);
        }
        vector<long long> fa = factor(res);
        vector<long long> fb = factor(n / res);
        fa.insert(fa.end(), fb.begin(), fb.end());
        return fa;
    }
};

Rho rho;

void dfs(const map<ll, ll>& f, ll num, const map<ll, ll>::iterator &ite, vector<ll> &d) {
    if (ite == f.end()) {
        d.push_back(num);
        return;
    }
    rep(i, ite->second + 1) {
        dfs(f, num, next(ite), d);
        num *= ite->first;
    }
}

vector<ll> divisor(ll n) {
    map<ll, ll> mp;
    for (const auto& aa : rho.factor(n))++mp[aa];
    vector<ll>ret;
    dfs(mp, 1, mp.begin(), ret);
    return ret;
}

#include "testlib.h"

int main(int argc, char **argv) {
    registerValidation(argc, argv);

    int T;
    T = inf.readInt(1, 20);
    inf.readEoln();
    while (T--) {
        ll s, t;
        s = inf.readInt(1, 750000000);
        inf.readSpace();
        t = inf.readLong(1ll, 3000000000ll);
        inf.readEoln();
        s *= 4;
        s = s * s;
        if (s % t) {
            puts("0");
            continue;
        }
        s /= t;
        vector<ll> d = divisor(s);
        ll a = -1, b = -1, c = -1, x = 0, y = 0, z = 0;
        set<multiset<ll>> ans;
        for (const auto& aa : d) {
            ll k = s / aa, r = t - aa;
            x = aa;
            if (r <= 0 or r * r - 4 * k < 0)continue;
            ll p = sq(r * r - 4 * k);
            if (p == -1)continue;
            if ((r - p) > 0 and (r - p) % 2 == 0) {
                y = (r - p) / 2;
                z = t - x - y;
                if ((x + y) % 2 or (y + z) % 2 or (z + x) % 2)continue;
                a = y + z;
                b = z + x;
                c = x + y;
                a /= 2;
                b /= 2;
                c /= 2;
                ans.insert({ a, b, c });
            }
            if ((r + p) > 0 and (r + p) % 2 == 0) {
                y = (r + p) / 2;
                z = t - x - y;
                if ((x + y) % 2 or (y + z) % 2 or (z + x) % 2)continue;
                a = y + z;
                b = z + x;
                c = x + y;
                a /= 2;
                b /= 2;
                c /= 2;
                ans.insert({ a, b, c });
            }
        }
        if (ans.size() == 0) {
            puts("0");
            continue;
        }
        printf("%d\n", (int)ans.size());
        for (const auto& aa : ans) {
            for (const auto& aaa : aa)printf("%lld ", aaa);
            puts("");
        }
    }
inf.readEof();
    Please AC;
}