結果

問題 No.1626 三角形の構築
ユーザー oteraotera
提出日時 2021-06-19 16:52:40
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 94 ms / 2,000 ms
コード長 6,890 bytes
コンパイル時間 2,948 ms
コンパイル使用メモリ 232,544 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-10-12 11:30:06
合計ジャッジ時間 4,397 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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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 AC 4 ms
5,248 KB
testcase_02 AC 5 ms
5,248 KB
testcase_03 AC 4 ms
5,248 KB
testcase_04 AC 3 ms
5,248 KB
testcase_05 AC 4 ms
5,248 KB
testcase_06 AC 5 ms
5,248 KB
testcase_07 AC 4 ms
5,248 KB
testcase_08 AC 5 ms
5,248 KB
testcase_09 AC 5 ms
5,248 KB
testcase_10 AC 4 ms
5,248 KB
testcase_11 AC 5 ms
5,248 KB
testcase_12 AC 3 ms
5,248 KB
testcase_13 AC 3 ms
5,248 KB
testcase_14 AC 5 ms
5,248 KB
testcase_15 AC 4 ms
5,248 KB
testcase_16 AC 5 ms
5,248 KB
testcase_17 AC 4 ms
5,248 KB
testcase_18 AC 4 ms
5,248 KB
testcase_19 AC 5 ms
5,248 KB
testcase_20 AC 4 ms
5,248 KB
testcase_21 AC 5 ms
5,248 KB
testcase_22 AC 5 ms
5,248 KB
testcase_23 AC 4 ms
5,248 KB
testcase_24 AC 35 ms
5,248 KB
testcase_25 AC 94 ms
5,248 KB
testcase_26 AC 7 ms
5,248 KB
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 # 

/**
 *    author:  otera
 *    created: 19.06.2021 16:12:22 
**/
#include<bits/stdc++.h>
using namespace std;

using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned;
#define repa(i, n) for(int i = 0; i < n; ++ i)
#define repb(i, a, b) for(int i = a; i < b; ++ i)
#define repc(i, a, b, c) for(int i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, repc, repb, repa)(__VA_ARGS__)
#define rep1a(i, n) for(int i = 0; i <= n; ++ i)
#define rep1b(i, a, b) for(int i = a; i <= b; ++ i)
#define rep1c(i, a, b, c) for(int i = a; i <= b; i += c)
#define rep1(...) overload4(__VA_ARGS__, rep1c, rep1b, rep1a)(__VA_ARGS__)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define per1(i,n) for(int i=n;i>=1;i--)
typedef pair<int, int> P;
typedef pair<ll, ll> LP;
#define pb push_back
#define eb emplace_back
#define fr first
#define sc second
#define all(c) c.begin(),c.end()
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define Sort(a) sort(all(a))
#define Rev(a) reverse(all(a))
#define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a))
#define si(c) (int)(c).size()
inline ll popcnt(ull a){ return __builtin_popcountll(a); }
#define tpow(n) (1LL<<(n))
#define unless(A) if(!(A))
ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
ll intpow(ll a, ll b, ll m) {ll ans = 1; while(b){ if(b & 1) (ans *= a) %= m; (a *= a) %= m; b /= 2; } return ans; }
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define vec(type,name,...) vector<type>name(__VA_ARGS__)
#define VEC(type,name,size) vector<type>name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,w) vector<vector<type>>name(h,vector<type>(w));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
template<class T> void scan(T& a){ cin >> a; }
template<class T> void scan(vector<T>& a){ for(auto&& i : a) scan(i); }
void in(){}
template <class Head, class... Tail> void in(Head& head, Tail&... tail){ scan(head); in(tail...); }
void print(){ cout << ' '; }
template<class T> void print(const T& a){ cout << a; }
template<class T> void print(const vector<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout << ' '; print(*i); } }
int out(){ cout << '\n'; return 0; }
template<class T> int out(const T& t){ print(t); cout << '\n'; return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); cout << ' '; out(tail...); return 0; }
#define CHOOSE(a) CHOOSE2 a
#define CHOOSE2(a0,a1,a2,a3,a4,x,...) x
#define debug_1(x1) cout<<#x1<<": "<<x1<<endl
#define debug_2(x1,x2) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<endl
#define debug_3(x1,x2,x3) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<endl
#define debug_4(x1,x2,x3,x4) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<", "#x4<<": "<<x4<<endl
#define debug_5(x1,x2,x3,x4,x5) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<", "#x4<<": "<<x4<<", "#x5<<": "<<x5<<endl
#ifdef DEBUG
#define debug(...) CHOOSE((__VA_ARGS__,debug_5,debug_4,debug_3,debug_2,debug_1,~))(__VA_ARGS__)
#define dump(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); }
#else
#define debug(...)
#define dump(...)
#endif

#define int long long

const ll MAX = 1'000'000'000;

map<ll, int> p_f(ll n) {
    map<ll, int> ret;
    for(int i = 2; i * i <= n; ++ i) {
        if(n % i == 0) {
            int exp = 0;
            while(n % i == 0) {
                ++ exp;
                n /= i;
            }
            ret[i] = exp;
        }
    }
    if(n != 1) ret[n] = 1;
    return ret;
}

void solve() {
    LL(s, t);
    auto pfs = p_f(s);
    auto pft = p_f(t);
    // s^2 * 16 / tを素因数分解
    ll ss = 16LL * s * s;
    if(ss % t != 0) {
        out(0);
        return;
    }
    ll all = ss / t;
    map<ll, int> pfa;
    for(auto [p, e]: pfs) {
        pfa[p] += 2 * e;
    }
    pfa[2] += 4;
    for(auto [p, e]: pft) {
        pfa[p] -= e;
    }
    vc<pair<ll, int>> pf;
    for(auto [p, e]: pfa) {
        if(e > 0) {
            pf.eb(p, e);
        }
    }
    int sz = si(pf);
    vc<ll> div;
    auto rec = [&](auto &&self, ll now, int pos) -> void {
        if(pos == sz) {
            div.eb(now);
            return;
        }
        ll p = pf[pos].fr, e = pf[pos].sc;
        rep(i, e + 1) {
            self(self, now, pos + 1);
            now *= p;
        }
    };
    rec(rec, 1LL, 0);
    Sort(div);
    vc<tuple<ll, ll, ll>> ans;
    for(ll x: div) {
        ll res = all / x;
        // y * (t - x - y) = res
        ll D = (t - x) * (t - x) - 4LL * res;
        if(D < 0) continue;
        ll sq = sqrt((ld)D);
        for(int i = max(sq - 10, 0LL); i <= sq + 10; ++ i) {
            if(i * i == D) {
                rep(_, 2) {
                    ll y2 = t - x + (_ == 0 ? i : -i);
                    unless(y2 % 2 == 0) continue;
                    ll y = y2 / 2;
                    ll z = t - x - y;
                    unless((t - x) % 2 == 0 and (t - y) % 2 == 0 and (t - z) % 2 == 0) continue;
                    ll a = (t - x) / 2, b = (t - y) / 2, c = (t - z) / 2;
                    unless(a > 0 and b > 0 and c > 0) continue;
                    unless(a <= MAX and b <= MAX and c <= MAX) continue;
                    vc<ll> now = {a, b, c}; Sort(now);
                    a = now[0], b = now[1], c = now[2];
                    unless(a + b > c) continue;
                    ans.eb(a, b, c);
                }
                break;
            }
        }
    }
    Uniq(ans);
    out(si(ans));
    rep(i, si(ans)) {
        ll a = get<0>(ans[i]), b = get<1>(ans[i]), c = get<2>(ans[i]);
        out(a, b, c);
    }
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    // cout << fixed << setprecision(20);
    INT(t); rep(i, t)solve();
    // solve();
    return 0;
}
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