#1025013 (C++17) No.2953 Maximum Right Triangle

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結果

問題	No.2953 Maximum Right Triangle
ユーザー	dyktr_06
提出日時	2024-11-08 21:47:54
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	15,701 bytes
コンパイル時間	2,835 ms
コンパイル使用メモリ	234,956 KB
実行使用メモリ	5,248 KB
最終ジャッジ日時	2024-11-08 21:48:00
合計ジャッジ時間	3,269 ms
ジャッジサーバーID （参考情報）	judge5 / judge2
このコードへのチャレンジ
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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	2 ms 5,248 KB
testcase_02	AC	2 ms 5,248 KB
testcase_03	AC	2 ms 5,248 KB
testcase_04	AC	2 ms 5,248 KB
testcase_05	AC	2 ms 5,248 KB
testcase_06	AC	2 ms 5,248 KB
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ソースコード

raw source code
#include <bits/stdc++.h>

using namespace std;

#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(n) for(int i = 0; i < (int)(n); ++i)
#define rep2(i, n) for(int i = 0; i < (int)(n); ++i)
#define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define Sort(a) (sort((a).begin(), (a).end()))
#define RSort(a) (sort((a).rbegin(), (a).rend()))
#define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end()))

typedef long long int ll;
typedef unsigned long long ul;
typedef long double ld;
typedef vector<int> vi;
typedef vector<long long> vll;
typedef vector<char> vc;
typedef vector<string> vst;
typedef vector<double> vd;
typedef vector<long double> vld;
typedef pair<long long, long long> P;
using i128 = __int128_t;

template<class T> long long sum(const T &a){ return accumulate(a.begin(), a.end(), 0LL); }
template<class T> auto min(const T &a){ return *min_element(a.begin(), a.end()); }
template<class T> auto max(const T &a){ return *max_element(a.begin(), a.end()); }

const long long MINF = 0x7fffffffffff;
const long long INF = 0x1fffffffffffffff;
const long long MOD = 998244353;
const long double EPS = 1e-9;
const long double PI = acos(-1);

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; }

template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p){ is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for(T &in : v) is >> in; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; }

template <typename T>
long long binary_search(long long ok, long long ng, T check){
    while(abs(ok - ng) > 1){
        long long mid = (ok + ng) / 2;
        if(check(mid)) ok = mid;
        else ng = mid;
    }
    return ok;
}

template <typename T>
long double binary_search_real(long double ok, long double ng, T check, int iter = 100){
    for(int i = 0; i < iter; ++i){
        long double mid = (ok + ng) / 2;
        if(check(mid)) ok = mid;
        else ng = mid;
    }
    return ok;
}

template <typename T>
long long trisum(T a, T b){
    long long res = ((b - a + 1) * (a + b)) / 2;
    return res;
}

template <typename T>
T intpow(T x, int n){
    T ret = 1;
    while(n > 0) {
        if(n & 1) (ret *= x);
        (x *= x);
        n >>= 1;
    }
    return ret;
}

template <typename T>
T getReminder(T a, T b){
    if(b == 0) return -1;
    if(a >= 0 && b > 0){
        return a % b;
    } else if(a < 0 && b > 0){
        return ((a % b) + b) % b;
    } else if(a >= 0 && b < 0){
        return a % b;
    } else{
        return (abs(b) - abs(a % b)) % b;
    }
}

template<class T, class U> inline T vin(T &vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; }
template<class T> inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; }
template<class... T> void in(T&... a){ (cin >> ... >> a); }
void out(){ cout << '\n'; }
template<class T, class... Ts> void out(const T &a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T, class U> void inGraph(vector<vector<T>> &G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } }

namespace Geometry{
    using T = long long;
    const T INFT = 9e18;
    inline constexpr int type(T x, T y){
        if(!x && !y) return 0;
        if(y < 0 || (y == 0 && x > 0)) return -1;
        return 1;
    }

    T absT(T x){
        if(x < 0) return -x;
        return x;
    }

    struct Point{
        T x, y;
        Point(T X = 0, T Y = 0) : x(X), y(Y){}

        inline bool operator==(const Point &other) const {
            return ((x == other.x) && (y == other.y));
        }
        inline bool operator!=(const Point &other) const {
            return ((x != other.x) || (y != other.y));
        }
        inline bool operator<(const Point &other) const {
            int L = type(x, y), R = type(other.x, other.y);
            if(L != R) return L < R;
            if(x * other.y == other.x * y) return abs(x + y) < abs(other.x + other.y);
            return x * other.y > other.x * y;
        }
        inline bool operator>(const Point &other) const {
            int L = type(x, y), R = type(other.x, other.y);
            if(L != R) return L > R;
            if(x * other.y == other.x * y) return abs(x + y) > abs(other.x + other.y);
            return x * other.y < other.x * y;
        }
        inline Point operator+() const noexcept { return *this; }
        inline Point operator-() const noexcept { return Point(-x, -y); }
        inline Point operator+(const Point &p) const { return Point(x + p.x, y + p.y); }
        inline Point operator-(const Point &p) const { return Point(x - p.x, y - p.y); }
        inline Point &operator+=(const Point &p) { return x += p.x, y += p.y, *this; }
        inline Point &operator-=(const Point &p) { return x -= p.x, y -= p.y, *this; }
        inline T operator*(const Point &p) const { return x * p.x + y * p.y; }
        inline Point &operator*=(const T &k) { return x *= k, y *= k, *this; }
        inline Point operator*(const T &k) { return (*this *= k); }
        // floor
        inline Point &operator/=(const T &k) { return x /= k, y /= k, *this; }
        inline Point operator/(const T &k) { return (*this /= k); }
        friend inline istream &operator>>(istream &is, Point &p) noexcept {
            is >> p.x >> p.y;
            return is;
        }
        friend inline ostream &operator<<(ostream &os, const Point &p) noexcept { return os << p.x << " " << p.y; }
    };

    bool angle_equal(const Point &p, const Point &q){
        int L = type(p.x, p.y), R = type(q.x, q.y);
        if(L != R) return false;
        return p.x * q.y == q.x * p.y;
    }

    long double rad2deg(long double rad){
        return rad * (long double) 180 / acos(-1);
    }

    long double deg2rad(long double deg){
        return deg * acosl(-1) / (long double) 180;
    }

    Point rotate(Point &p, long double deg){
        complex<T> comp(p.x, p.y);
        comp *= exp(complex<T>(.0, deg2rad(deg)));
        return Point(comp.real(), comp.imag());
    }

    T cross(const Point &p, const Point &q){
        return p.x * q.y - p.y * q.x;
    }

    T dot(const Point &p, const Point &q){
        return p.x * q.x + p.y * q.y;
    }

    T manhattanDist(const Point &p, const Point &q){
        return absT(p.x - q.x) + absT(p.y - q.y);
    }

    // 2乗
    T dist(const Point &p, const Point &q){
        return (p.x - q.x) * (p.x - q.x) + (p.y - q.y) * (p.y - q.y);
    }

    // 線分 p1-p2 と線分 q1-q2
    bool intersection(const Point &p1, const Point &p2, const Point &q1, const Point &q2){
        T a = cross(p2 - p1, q1 - p1);
        T b = cross(p2 - p1, q2 - p1);
        T c = cross(q2 - q1, p1 - q1);
        T d = cross(q2 - q1, p2 - q1);
        if(a == 0 && b == 0){
            T e = dot(p2 - p1, q1 - p1);
            T f = dot(p2 - p1, q2 - p1);
            if(e > f) swap(e, f);
            return e <= dist(p1, p2) && 0 <= f;
        }
        return a * b <= 0 && c * d <= 0;
    }

    // 2倍
    T polygonArea(const vector<Point> &points){
        const int n = points.size();
        T res = 0;
        for(int i = 0; i < n - 1; i++){
            res += cross(points[i], points[i + 1]);
        }
        res += cross(points[n - 1], points[0]);
        return absT(res);
    }

    vector<Point> convexHull(vector<Point> points){
        vector<Point> U, L, res;
        sort(points.begin(), points.end(), [](Point p, Point q){
            return (p.x != q.x ? p.x < q.x : p.y < q.y);
        });
        points.erase(unique(points.begin(), points.end()), points.end());
        const int n = points.size();
        if((int) points.size() <= 2){
            return points;
        }

        // lower
        for(int i = 0; i < n; i++){
            int j = L.size();
            // 傾きで左回りかをチェック
            while(j >= 2 && cross(L[j - 1] - L[j - 2], points[i] - L[j - 2]) <= 0){
                L.pop_back();
                j--;
            }
            L.push_back(points[i]);
        }

        // upper
        for(int i = n - 1; i >= 0; i--){
            int j = U.size();
            while(j >= 2 && cross(U[j - 1] - U[j - 2], points[i] - U[j - 2]) <= 0){
                U.pop_back();
                j--;
            }
            U.push_back(points[i]);
        }

        res = L;
        for(int i = 1; i < (int) U.size() - 1; i++){
            res.push_back(U[i]);
        }
        return res;
    }

    // 点が領域外部: 0, 内部: 1, 境界上: 2
    int inCcwConvex(Point p, const vector<Point> &points) {
        const int n = points.size();
        T cr1 = cross(points[1] - points[0], p - points[0]);
        T cr2 = cross(points[n - 1] - points[0], p - points[0]);
        if(cr1 < 0 || 0 < cr2){
            return 0;
        }

        int l = 1, r = n - 1;
        while(abs(r - l) > 1){
            int mid = (l + r) / 2;
            if(cross(p - points[0], points[mid] - points[0]) >= 0){
                r = mid;
            } else{
                l = mid;
            }
        }

        T cr = cross(points[l] - p, points[r] - p);
        if(cr == 0){
            return 2;
        } else if(cr > 0){
            if(cr1 == 0 || cr2 == 0){
                return 2;
            } else{
                return 1;
            }
        } else{
            return 0;
        }
    }

    pair<T, pair<int, int>> closestPair(vector<Point> &points){
        const int n = points.size();
        assert(n >= 2);
        vector<pair<Point, int>> sortp(n);
        for(int i = 0; i < n; i++){
            sortp[i] = {points[i], i};
        }

        sort(sortp.begin(), sortp.end(), [](pair<Point, int> p, pair<Point, int> q){
            return (p.first.x != q.first.x ? p.first.x < q.first.x : p.first.y < q.first.y);
        });

        int ans1 = -1, ans2 = -1;
        T min_dist = INFT;
        auto dfs = [&](auto &self, int l, int r) -> T {
            if(r - l <= 1){
                return INFT;
            }
            int mid = (l + r) / 2;
            T d = min(self(self, l, mid), self(self, mid, r));
            vector<pair<Point, int>> tmp;
            for(int i = l; i < r; i++){
                T dx = sortp[mid].first.x - sortp[i].first.x;
                if(dx * dx < d){
                    tmp.push_back(sortp[i]);
                }
            }
            sort(tmp.begin(), tmp.end(), [](pair<Point, int> p, pair<Point, int> q){
                return p.first.y < q.first.y;
            });
            for(int i = 0; i < (int) tmp.size(); i++){
                for(int j = i + 1; j < (int) tmp.size(); j++){
                    T dy = tmp[j].first.y - tmp[i].first.y;
                    if(dy * dy >= d){
                        break;
                    }
                    T td = dist(tmp[i].first, tmp[j].first);
                    if(td < d){
                        d = td;
                        if(d < min_dist){
                            min_dist = d;
                            ans1 = tmp[i].second;
                            ans2 = tmp[j].second;
                        }
                    }
                }
            }
            return d;
        };
        dfs(dfs, 0, n);
        return {min_dist, {ans1, ans2}};
    }

    pair<T, pair<int, int>> furthestPair(vector<Point> &points){
        const int n = points.size();
        assert(n >= 2);
        vector<Point> convex = convexHull(points);
        const int m = convex.size();

        map<pair<T, T>, int> mp;
        for(int i = 0; i < n; i++){
            mp[{points[i].x, points[i].y}] = i;
        }

        vector<int> idx(m);
        for(int i = 0; i < m; i++){
            idx[i] = mp[{convex[i].x, convex[i].y}];
        }

        if(m == 1){
            return {dist(points[0], points[1]), {0, 1}};
        }else if(m == 2){
            return {dist(convex[0], convex[1]), {idx[0], idx[1]}};
        }

        auto compare = [](Point p, Point q){
            return p.x != q.x ? p.x < q.x : p.y < q.y;
        };

        int i = 0, j = 0;
        for(int k = 0; k < m; k++){
            if(compare(convex[k], convex[i])) i = k;
            if(compare(convex[j], convex[k])) j = k;
        }

        int i0 = i, j0 = j;
        T max_dist = 0;
        int ans1 = -1, ans2 = -1;
        while(i != j0 || j != i0){
            T d = dist(convex[i], convex[j]);
            if(d > max_dist){
                max_dist = d;
                ans1 = idx[i];
                ans2 = idx[j];
            }
            if(cross(convex[(i + 1) % m] - convex[i], convex[(j + 1) % m] - convex[j]) < 0){
                i = (i + 1) % m;
            }else{
                j = (j + 1) % m;
            }
        }
        return {max_dist, {ans1, ans2}};
    }
}

ll T;

void input(){
    in(T);
}

void solve(){
    ll d, x, y; in(d, x, y);
    ll dx = -y, dy = x;
    ll g = __gcd(abs(dx), abs(dy));
    dx /= g, dy /= g;
    auto fx1 = [&](ll z){
        ll nx = x + dx * z;
        ll ny = y + dy * z;
        return 0 <= nx && nx <= d && 0 <= ny && ny <= d;
    };
    auto fx2 = [&](ll z){
        ll nx = x - dx * z;
        ll ny = y - dy * z;
        return 0 <= nx && nx <= d && 0 <= ny && ny <= d;
    };
    ll ok1 = binary_search(0, d + 1, fx1), ok2 = binary_search(0, d + 1, fx2);
    if(ok1 == 0 && ok2 == 0){
    	out(0);
    	return;
    }
    ll ans = max(Geometry::polygonArea({{0, 0}, {x, y}, {x + dx * ok1, y + dy * ok1}}), Geometry::polygonArea({{0, 0}, {x, y}, {x - dx * ok2, y - dy * ok2}}));
    out(ans);
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(20);

    T = 1;
    input();
    while(T--) solve();
}
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結果

テストケース

ソースコード
