結果
問題 | No.1175 Simultaneous Equations |
ユーザー |
👑 ![]() |
提出日時 | 2020-09-03 09:17:03 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 23 ms / 2,000 ms |
コード長 | 17,838 bytes |
コンパイル時間 | 3,568 ms |
コンパイル使用メモリ | 233,620 KB |
最終ジャッジ日時 | 2025-01-14 04:05:01 |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 11 |
ソースコード
//#define _GLIBCXX_DEBUG#include<bits/stdc++.h>using namespace std;#define endl '\n'#define lfs cout<<fixed<<setprecision(10)#define ALL(a) (a).begin(),(a).end()#define ALLR(a) (a).rbegin(),(a).rend()#define spa << " " <<#define fi first#define se second#define MP make_pair#define MT make_tuple#define PB push_back#define EB emplace_back#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)using ll = long long;using ld = long double;const ll MOD1 = 1e9+7;const ll MOD9 = 998244353;const ll INF = 1e18;using P = pair<ll, ll>;template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}template<typename T>void debug(vector<vector<T>>&v,ll h,ll w){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout spa v[i][j];cout<<endl;}};void debug(vector<string>&v,ll h,ll w){for(ll i=0;i<h;i++){for(ll j=0;j<w;j++)cout<<v[i][j];cout<<endl;}};template<typename T>void debug(vector<T>&v,ll n){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout spa v[i];cout<<endl;};template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;}vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << p.first << " " << p.second;}template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;}//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());using Real = double;using Point = complex< Real >;const Real EPS = 1e-8, PI = acos(-1);inline bool eq(Real a, Real b) { return fabs(b - a) < EPS; }Point operator*(const Point &p, const Real &d) {return Point(real(p) * d, imag(p) * d);}istream &operator>>(istream &is, Point &p) {Real a, b;is >> a >> b;p = Point(a, b);return is;}ostream &operator<<(ostream &os, Point &p) {return os << fixed << setprecision(10) << p.real() << " " << p.imag();}// 点 p を反時計回りに theta 回転Point rotate(Real theta, const Point &p) {return Point(cos(theta) * p.real() - sin(theta) * p.imag(), sin(theta) * p.real() + cos(theta) * p.imag());}Real radian_to_degree(Real r) {return (r * 180.0 / PI);}Real degree_to_radian(Real d) {return (d * PI / 180.0);}// a-b-c の角度のうち小さい方を返すReal get_angle(const Point &a, const Point &b, const Point &c) {const Point v(b - a), w(c - b);Real alpha = atan2(v.imag(), v.real()), beta = atan2(w.imag(), w.real());if(alpha > beta) swap(alpha, beta);Real theta = (beta - alpha);return min(theta, 2 * acos(-1) - theta);}namespace std {bool operator<(const Point &a, const Point &b) {return a.real() != b.real() ? a.real() < b.real() : a.imag() < b.imag();}}struct Line {Point a, b;Line() = default;Line(Point a, Point b) : a(a), b(b) {}Line(Real A, Real B, Real C) // Ax + By = C{if(eq(A, 0)) a = Point(0, C / B), b = Point(1, C / B);else if(eq(B, 0)) b = Point(C / A, 0), b = Point(C / A, 1);else a = Point(0, C / B), b = Point(C / A, 0);}friend ostream &operator<<(ostream &os, Line &p) {return os << p.a << " to " << p.b;}friend istream &operator>>(istream &is, Line &a) {return is >> a.a >> a.b;}};struct Segment : Line {Segment() = default;Segment(Point a, Point b) : Line(a, b) {}};struct Circle {Point p;Real r;Circle() = default;Circle(Point p, Real r) : p(p), r(r) {}};using Points = vector< Point >;using Polygon = vector< Point >;using Segments = vector< Segment >;using Lines = vector< Line >;using Circles = vector< Circle >;Real cross(const Point &a, const Point &b) {return real(a) * imag(b) - imag(a) * real(b);}Real dot(const Point &a, const Point &b) {return real(a) * real(b) + imag(a) * imag(b);}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C// 点の回転方向int ccw(const Point &a, Point b, Point c) {b = b - a, c = c - a;if(cross(b, c) > EPS) return +1; // "COUNTER_CLOCKWISE"if(cross(b, c) < -EPS) return -1; // "CLOCKWISE"if(dot(b, c) < 0) return +2; // "ONLINE_BACK"if(norm(b) < norm(c)) return -2; // "ONLINE_FRONT"return 0; // "ON_SEGMENT"}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A// 平行判定bool parallel(const Line &a, const Line &b) {return eq(cross(a.b - a.a, b.b - b.a), 0.0);}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A// 垂直判定bool orthogonal(const Line &a, const Line &b) {return eq(dot(a.a - a.b, b.a - b.b), 0.0);}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_A// 射影// 直線 l に p から垂線を引いた交点を求めるPoint projection(const Line &l, const Point &p) {double t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);return l.a + (l.a - l.b) * t;}Point projection(const Segment &l, const Point &p) {double t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);return l.a + (l.a - l.b) * t;}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_B// 反射// 直線 l を対称軸として点 p と線対称にある点を求めるPoint reflection(const Line &l, const Point &p) {return p + (projection(l, p) - p) * 2.0;}bool intersect(const Line &l, const Point &p) {return abs(ccw(l.a, l.b, p)) != 1;}bool intersect(const Line &l, const Line &m) {return abs(cross(l.b - l.a, m.b - m.a)) > EPS || abs(cross(l.b - l.a, m.b - l.a)) < EPS;}bool intersect(const Segment &s, const Point &p) {return ccw(s.a, s.b, p) == 0;}bool intersect(const Line &l, const Segment &s) {return cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < EPS;}Real distance(const Line &l, const Point &p);bool intersect(const Circle &c, const Line &l) {return distance(l, c.p) <= c.r + EPS;}bool intersect(const Circle &c, const Point &p) {return abs(abs(p - c.p) - c.r) < EPS;}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_Bbool intersect(const Segment &s, const Segment &t) {return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 && ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;}int intersect(const Circle &c, const Segment &l) {if(norm(projection(l, c.p) - c.p) - c.r * c.r > EPS) return 0;auto d1 = abs(c.p - l.a), d2 = abs(c.p - l.b);if(d1 < c.r + EPS && d2 < c.r + EPS) return 0;if(d1 < c.r - EPS && d2 > c.r + EPS || d1 > c.r + EPS && d2 < c.r - EPS) return 1;const Point h = projection(l, c.p);if(dot(l.a - h, l.b - h) < 0) return 2;return 0;}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_A&lang=jpint intersect(Circle c1, Circle c2) {if(c1.r < c2.r) swap(c1, c2);Real d = abs(c1.p - c2.p);if(c1.r + c2.r < d) return 4;if(eq(c1.r + c2.r, d)) return 3;if(c1.r - c2.r < d) return 2;if(eq(c1.r - c2.r, d)) return 1;return 0;}Real distance(const Point &a, const Point &b) {return abs(a - b);}Real distance(const Line &l, const Point &p) {return abs(p - projection(l, p));}Real distance(const Line &l, const Line &m) {return intersect(l, m) ? 0 : distance(l, m.a);}Real distance(const Segment &s, const Point &p) {Point r = projection(s, p);if(intersect(s, r)) return abs(r - p);return min(abs(s.a - p), abs(s.b - p));}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_DReal distance(const Segment &a, const Segment &b) {if(intersect(a, b)) return 0;return min({distance(a, b.a), distance(a, b.b), distance(b, a.a), distance(b, a.b)});}Real distance(const Line &l, const Segment &s) {if(intersect(l, s)) return 0;return min(distance(l, s.a), distance(l, s.b));}Point crosspoint(const Line &l, const Line &m) {Real A = cross(l.b - l.a, m.b - m.a);Real B = cross(l.b - l.a, l.b - m.a);if(eq(abs(A), 0.0) && eq(abs(B), 0.0)) return m.a;return m.a + (m.b - m.a) * B / A;}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_CPoint crosspoint(const Segment &l, const Segment &m) {return crosspoint(Line(l), Line(m));}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_Dpair< Point, Point > crosspoint(const Circle &c, const Line l) {Point pr = projection(l, c.p);Point e = (l.b - l.a) / abs(l.b - l.a);if(eq(distance(l, c.p), c.r)) return {pr, pr};double base = sqrt(c.r * c.r - norm(pr - c.p));return {pr - e * base, pr + e * base};}pair< Point, Point > crosspoint(const Circle &c, const Segment &l) {Line aa = Line(l.a, l.b);if(intersect(c, l) == 2) return crosspoint(c, aa);auto ret = crosspoint(c, aa);if(dot(l.a - ret.first, l.b - ret.first) < 0) ret.second = ret.first;else ret.first = ret.second;return ret;}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_Epair< Point, Point > crosspoint(const Circle &c1, const Circle &c2) {Real d = abs(c1.p - c2.p);Real a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));Real t = atan2(c2.p.imag() - c1.p.imag(), c2.p.real() - c1.p.real());Point p1 = c1.p + Point(cos(t + a) * c1.r, sin(t + a) * c1.r);Point p2 = c1.p + Point(cos(t - a) * c1.r, sin(t - a) * c1.r);return {p1, p2};}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_F// 点 p を通る円 c の接線pair< Point, Point > tangent(const Circle &c1, const Point &p2) {return crosspoint(c1, Circle(p2, sqrt(norm(c1.p - p2) - c1.r * c1.r)));}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_G// 円 c1, c2 の共通接線Lines tangent(Circle c1, Circle c2) {Lines ret;if(c1.r < c2.r) swap(c1, c2);Real g = norm(c1.p - c2.p);if(eq(g, 0)) return ret;Point u = (c2.p - c1.p) / sqrt(g);Point v = rotate(PI * 0.5, u);for(int s : {-1, 1}) {Real h = (c1.r + s * c2.r) / sqrt(g);if(eq(1 - h * h, 0)) {ret.emplace_back(c1.p + u * c1.r, c1.p + (u + v) * c1.r);} else if(1 - h * h > 0) {Point uu = u * h, vv = v * sqrt(1 - h * h);ret.emplace_back(c1.p + (uu + vv) * c1.r, c2.p - (uu + vv) * c2.r * s);ret.emplace_back(c1.p + (uu - vv) * c1.r, c2.p - (uu - vv) * c2.r * s);}}return ret;}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_B// 凸性判定bool is_convex(const Polygon &p) {int n = (int) p.size();for(int i = 0; i < n; i++) {if(ccw(p[(i + n - 1) % n], p[i], p[(i + 1) % n]) == -1) return false;}return true;}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_A// 凸包Polygon convex_hull(Polygon &p) {int n = (int) p.size(), k = 0;if(n <= 2) return p;sort(p.begin(), p.end());vector< Point > ch(2 * n);for(int i = 0; i < n; ch[k++] = p[i++]) {while(k >= 2 && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < EPS) --k;}for(int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) {while(k >= t && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < EPS) --k;}ch.resize(k - 1);return ch;}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C// 多角形と点の包含判定enum {OUT, ON, IN};int contains(const Polygon &Q, const Point &p) {bool in = false;for(int i = 0; i < Q.size(); i++) {Point a = Q[i] - p, b = Q[(i + 1) % Q.size()] - p;if(a.imag() > b.imag()) swap(a, b);if(a.imag() <= 0 && 0 < b.imag() && cross(a, b) < 0) in = !in;if(cross(a, b) == 0 && dot(a, b) <= 0) return ON;}return in ? IN : OUT;}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1033// 線分の重複除去void merge_segments(vector< Segment > &segs) {auto merge_if_able = [](Segment &s1, const Segment &s2) {if(abs(cross(s1.b - s1.a, s2.b - s2.a)) > EPS) return false;if(ccw(s1.a, s2.a, s1.b) == 1 || ccw(s1.a, s2.a, s1.b) == -1) return false;if(ccw(s1.a, s1.b, s2.a) == -2 || ccw(s2.a, s2.b, s1.a) == -2) return false;s1 = Segment(min(s1.a, s2.a), max(s1.b, s2.b));return true;};for(int i = 0; i < segs.size(); i++) {if(segs[i].b < segs[i].a) swap(segs[i].a, segs[i].b);}for(int i = 0; i < segs.size(); i++) {for(int j = i + 1; j < segs.size(); j++) {if(merge_if_able(segs[i], segs[j])) {segs[j--] = segs.back(), segs.pop_back();}}}}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1033// 線分アレンジメント// 任意の2線分の交点を頂点としたグラフを構築するvector< vector< int > > segment_arrangement(vector< Segment > &segs, vector< Point > &ps) {vector< vector< int > > g;int N = (int) segs.size();for(int i = 0; i < N; i++) {ps.emplace_back(segs[i].a);ps.emplace_back(segs[i].b);for(int j = i + 1; j < N; j++) {const Point p1 = segs[i].b - segs[i].a;const Point p2 = segs[j].b - segs[j].a;if(cross(p1, p2) == 0) continue;if(intersect(segs[i], segs[j])) {ps.emplace_back(crosspoint(segs[i], segs[j]));}}}sort(begin(ps), end(ps));ps.erase(unique(begin(ps), end(ps)), end(ps));int M = (int) ps.size();g.resize(M);for(int i = 0; i < N; i++) {vector< int > vec;for(int j = 0; j < M; j++) {if(intersect(segs[i], ps[j])) {vec.emplace_back(j);}}for(int j = 1; j < vec.size(); j++) {g[vec[j - 1]].push_back(vec[j]);g[vec[j]].push_back(vec[j - 1]);}}return (g);}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_C// 凸多角形の切断// 直線 l.a-l.b で切断しその左側にできる凸多角形を返すPolygon convex_cut(const Polygon &U, Line l) {Polygon ret;for(int i = 0; i < U.size(); i++) {Point now = U[i], nxt = U[(i + 1) % U.size()];if(ccw(l.a, l.b, now) != -1) ret.push_back(now);if(ccw(l.a, l.b, now) * ccw(l.a, l.b, nxt) < 0) {ret.push_back(crosspoint(Line(now, nxt), l));}}return (ret);}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_A// 多角形の面積Real area(const Polygon &p) {Real A = 0;for(int i = 0; i < p.size(); ++i) {A += cross(p[i], p[(i + 1) % p.size()]);}return A * 0.5;}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_H// 円と多角形の共通部分の面積Real area(const Polygon &p, const Circle &c) {if(p.size() < 3) return 0.0;function< Real(Circle, Point, Point) > cross_area = [&](const Circle &c, const Point &a, const Point &b) {Point va = c.p - a, vb = c.p - b;Real f = cross(va, vb), ret = 0.0;if(eq(f, 0.0)) return ret;if(max(abs(va), abs(vb)) < c.r + EPS) return f;if(distance(Segment(a, b), c.p) > c.r - EPS) return c.r * c.r * arg(vb * conj(va));auto u = crosspoint(c, Segment(a, b));vector< Point > tot{a, u.first, u.second, b};for(int i = 0; i + 1 < tot.size(); i++) {ret += cross_area(c, tot[i], tot[i + 1]);}return ret;};Real A = 0;for(int i = 0; i < p.size(); i++) {A += cross_area(c, p[i], p[(i + 1) % p.size()]);}return A;}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_B// 凸多角形の直径(最遠頂点対間距離)Real convex_diameter(const Polygon &p) {int N = (int) p.size();int is = 0, js = 0;for(int i = 1; i < N; i++) {if(p[i].imag() > p[is].imag()) is = i;if(p[i].imag() < p[js].imag()) js = i;}Real maxdis = norm(p[is] - p[js]);int maxi, maxj, i, j;i = maxi = is;j = maxj = js;do {if(cross(p[(i + 1) % N] - p[i], p[(j + 1) % N] - p[j]) >= 0) {j = (j + 1) % N;} else {i = (i + 1) % N;}if(norm(p[i] - p[j]) > maxdis) {maxdis = norm(p[i] - p[j]);maxi = i;maxj = j;}} while(i != is || j != js);return sqrt(maxdis);}// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_5_A// 最近点対Real closest_pair(Points ps) {if(ps.size() <= 1) throw (0);sort(begin(ps), end(ps));auto compare_y = [&](const Point &a, const Point &b) {return imag(a) < imag(b);};vector< Point > beet(ps.size());const Real INF = 1e18;function< Real(int, int) > rec = [&](int left, int right) {if(right - left <= 1) return INF;int mid = (left + right) >> 1;auto x = real(ps[mid]);auto ret = min(rec(left, mid), rec(mid, right));inplace_merge(begin(ps) + left, begin(ps) + mid, begin(ps) + right, compare_y);int ptr = 0;for(int i = left; i < right; i++) {if(abs(real(ps[i]) - x) >= ret) continue;for(int j = 0; j < ptr; j++) {auto luz = ps[i] - beet[ptr - j - 1];if(imag(luz) >= ret) break;ret = min(ret, abs(luz));}beet[ptr++] = ps[i];}return ret;};return rec(0, (int) ps.size());}int main(){cin.tie(nullptr);ios_base::sync_with_stdio(false);ll res=0,buf=0;bool judge = true;ll a,b,c,d,e,f;cin>>a>>b>>c>>d>>e>>f;Line l(a,b,c);Line r(d,e,f);auto p=crosspoint(l,r);lfs<<p<<endl;return 0;}