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QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#317623 | #5067. Two Walls | lmf_up | WA | 115ms | 3912kb | C++20 | 18.2kb | 2024-01-29 10:21:50 | 2024-01-29 10:21:51 |
Judging History
answer
#include<bits/stdc++.h>
#define cp const point &
#define cl const line &
#define cc const circle &
#define LD long long
std::mt19937 rnd(time(0));
const LD eps = 1e-12;
const LD pi = std::numbers::pi;
const LD INF = 1e9;
int sgn(LD x)
{
return x > eps ? 1 : (x < -eps ? -1 : 0);
}
LD sqr(LD x)
{ return x * x; }
struct point
{
LD x, y;
point operator+(cp a) const
{ return {x + a.x, y + a.y}; }
point operator-(cp a) const
{ return {x - a.x, y - a.y}; }
point operator*(LD t) const
{ return {x * t, y * t}; }
point operator/(LD t) const
{ return {x / t, y / t}; }
point rot(LD t) const
{ return {(long long)(x * cos(t) - y * sin(t)), (long long)(x * sin(t) + y * cos(t))}; }
point rot90() const
{ return {-y, x}; }
LD len2() const
{ return x * x + y * y; }
LD len() const
{ return sqrtl(x * x + y * y); }
point unit() const
{
double d = len();
return {(long long)(x / d), (long long)(y / d)};
}
int on_up()//b不判(0,0)
{
return sgn(y)==1||(sgn(y)==0&&sgn(x)>0);
}
void print()
{
std::cout<<x<<' '<<y<<std::endl;
}
void read()
{
std::cin>>x>>y;
}
friend bool operator<(cp a, cp b)
{
return a.x == b.x ? a.y < b.y : a.x < b.x;
}
friend bool operator>(cp a, cp b)
{
return a.x == b.x ? a.y > b.y : a.x > b.x;
}
};
LD dot(cp a, cp b);
bool operator==(cp a, cp b)
{
return !sgn(dot(a - b, a - b));
}
LD dis(cp a, cp b)//两点距离
{
return sqrtl(sqr(a.x - b.x) + sqr(a.y - b.y));
}
LD dot(cp a, cp b)//点乘
{
return a.x * b.x + a.y * b.y;
}
LD det(cp a, cp b)//叉乘
{
return a.x * b.y - b.x * a.y;
}
bool turn_left(cp a, cp b, cp c)//判断ba是否逆时针转少于180°到ca
{
return sgn(det(b - a, c - a)) > 0;//大于是严格凸包
}
struct line
{
point s, t;
line() {}
line(point a, point b) : s(a), t(b)
{}
void read()
{
s.read(),t.read();
}
void print()
{
s.print(),std::cout<<' ',t.print();
}
};
struct circle
{
point c;
LD r;
circle()
{}
circle(point C, LD R)
{ c = C, r = R; }
};
bool in_circle(cp a, cc b)
{
return sgn((b.c - a).len() - b.r) <= 0;
}
circle make_circle(point u, point v)
{
point p = (u + v) / 2;
return circle(p, (u - p).len());
}
circle make_circle(cp a, cp b, cp c)
{
point p = b - a, q = c - a;
point s(dot(p, p) / 2, dot(q, q) / 2);
LD d = det(p, q);
p = point(det(s, point(p.y, q.y)), det(point(p.x, q.x), s)) / d;
return circle(a + p, p.len());
}
circle min_circle(std::vector<point> p)
{
circle ret(p[0], 0);
std::shuffle(p.begin(), p.end(), rnd);
int len = p.size();
for (int i = 0; i < len; i++)
if (!in_circle(p[i], ret))
{
ret = circle(p[i], 0);
for (int j = 0; j < i; j++)
if (!in_circle(p[j], ret))
{
ret = make_circle(p[j], p[i]);
for (int k = 0; k < j; ++k)
if (!in_circle(p[k], ret))
ret = make_circle(p[i], p[j], p[k]);
}
}
return ret;
}
bool same_dir(cl a, cl b)//判断方向是否一致
{
return sgn(det(b.t - b.s, a.t - a.s)) == 0 && sgn(dot(b.t - b.s, a.t - a.s)) > 0;
}
bool point_on_line(cp a, cl l)//判断点是否在直线上
{
return sgn(det(a-l.s, l.t - l.s)) == 0;
}
bool point_on_segment(cp a, cl l)//判断点是否在线段上
{
return point_on_line(a, l) && sgn(dot(l.s - a, l.t-a )) <= 0;//(<=代表可以端点
}
bool two_side(cp a, cp b, cl c)//判断两个点是否在线段的两边
{
return sgn(det(a - c.s, c.t - c.s)) * sgn(det(b - c.s, c.t - c.s)) < 0;
}
bool intersect_judge_strict(cl a, cl b)
{
return two_side(a.s,a.t,b)&& two_side(b.s,b.t,a);
}
bool intersect_judge(cl a, cl b)
{//判断两个线段是否相交
if (point_on_segment(a.s, b) || point_on_segment(a.t, b) || point_on_segment(b.s, a) ||
point_on_segment(b.t, a))
return true;
return intersect_judge_strict(a,b);
}
point line_intersect(cl a, cl b)
{//得到两线段的交点
double s1 = det(a.t - a.s, b.s - a.s);
double s2 = det(a.t - a.s, b.t - a.s);
return (b.s * s2 - b.t * s1) / (s2 - s1);
}
bool point_on_ray(cp a, cl b)
{//判断点是否在射线上
return sgn(det(a - b.s, b.t - b.s)) == 0 && sgn(dot(a - b.s, b.t - b.s)) >= 0;
}
bool ray_intersect_judge(line a, line b)//判断两射线是否相交
{
double s1, s2;
s1 = det(a.t - a.s, b.s - a.s);
s2 = det(a.t - a.s, b.t - a.s);
if (sgn(s1) == 0 && sgn(s2) == 0)
return sgn(dot(a.t - a.s, b.s - a.s)) >= 0 || sgn(dot(b.t - b.s, a.s - b.s));
if (!sgn(s1 - s2) || sgn(s1) == sgn(s2 - s1))return 0;
std::swap(a, b);
s1 = det(a.t - a.s, b.s - a.s);
s2 = det(a.t - a.s, b.t - a.s);
return sgn(s1) != sgn(s2 - s1);
}
LD point_to_line(cp a, cl b)
{//点到直线的距离
return abs(det(b.t - b.s, a - b.s)) / dis(b.s, b.t);
}
point project_to_line(cp a, cl b)
{//得到点在线上的投影
return b.s + (b.t - b.s) * (dot(a - b.s, b.t - b.s) / (b.t - b.s).len2());
}
LD point_to_segment(cp a, cl b)
{//点到线段的距离
if (b.s == b.t)
return dis(a, b.s);
if (sgn(dot(b.s - a, b.t - b.s)) * sgn(dot(b.t - a, b.t - b.s)) <= 0)
return abs(det(b.t - b.s, a - b.s)) / dis(b.s, b.t);
return std::min(dis(a, b.s), dis(a, b.t));
}
std::vector<point>line_circle_intersect(cl a,cc b)
{//返回线与圆的交点
if(sgn(point_to_segment(b.c,a)-b.r)>0)
return std::vector<point>();
LD x=sqrtl(sqr(b.r)- sqr(point_to_line(b.c,a)));
return std::vector<point>({project_to_line(b.c,a)+(a.s-a.t).unit()*x, project_to_line(b.c,a)-(a.s-a.t).unit()*x});
}
LD circle_intersect_area(cc a,cc b){
LD d=dis(a.c,b.c);
if(sgn(d-(a.r+b.r))>=0)return 0;
if(sgn(d- abs(a.r-b.r))<=0){
LD r=std::min(a.r,b.r);
return r*r*pi;
}
LD x=(d*d+a.r*a.r-b.r*b.r)/(2*d),
t1=acosl(std::min((LD)1,std::max((LD)-1,x/a.r))),
t2=acosl(std::min((LD)1,std::max((LD)-1,(d-x)/b.r)));
return sqr(a.r)*t1+ sqr(b.r)*t2-d*a.r*sinl(t1);
}
std::vector<point> circle_intersect(cc a,cc b)
{
if(a.c==b.c||sgn(dis(a.c,b.c)-a.r-b.r)>0||sgn(dis(a.c,b.c)-abs(a.r-b.r))<0)
return {};
point r=(b.c-a.c).unit();
LD d=dis(a.c,b.c);
LD x=((sqr(a.r)-sqr(b.r))/d+d)/2;
LD h=sqrtl(sqr(a.r)-sqr(x));
if(sgn(h)==0)return {a.c+r*x};
return {a.c+r*x+r.rot90()*h,a.c+r*x-r.rot90()*h};
}
std::vector<point>tangent(cp a,cc b)
{
circle p= make_circle(a,b.c);
return circle_intersect(p,b);
}
std::vector<line>extangent(cc a,cc b)
{
std::vector<line>ret;
if(sgn(dis(a.c,b.c)-abs(a.r-b.r))<=0)return ret;
if(sgn(a.r-b.r)==0)
{
point dir=b.c-a.c;
dir=(dir*a.r/dir.len()).rot90();
ret.push_back(line(a.c+dir,b.c+dir));
ret.push_back(line(a.c-dir,b.c-dir));
}
else{
point p=(b.c*a.r-a.c*b.r)/(a.r-b.r);
std::vector pp= tangent(p,a),qq= tangent(p,b);
if(pp.size()==2&&qq.size()==2)
{
if(sgn(a.r-b.r)<0)
std::swap(pp[0],pp[1]),std::swap(qq[0],qq[1]);
ret.push_back(line(pp[0],qq[0]));
ret.push_back(line(pp[1],qq[1]));
}
}
return ret;
}
std::vector<line>intangeent(cc a,cc b)
{
std::vector<line> ret;
point p=(b.c*a.r+a.c*b.r)/(a.r+b.r);
std::vector pp= tangent(p,a),qq= tangent(p,b);
if(pp.size()==2&&qq.size()==2){
ret.push_back(line(pp[0],qq[0]));
ret.push_back(line(pp[1],qq[1]));
}
return ret;
}
std::vector<point>cut(const std::vector<point>&c,line p){
std::vector<point>ret;
if(c.empty())return ret;
int len=c.size();
for(int i=0;i<len;i++)
{
int j=(i+1)%len;
if(turn_left(p.s,p.t,c[i]))ret.push_back(c[i]);
if(two_side(c[i],c[j],p))
ret.push_back(line_intersect(p,line(c[i],c[j])));
}
return ret;
}
std::vector<point> convex_hull(std::vector<point> a)
{//凸包,字典序
int n = (int) a.size(), cnt = 0;
if (n < 2) return a;
std::sort(a.begin(), a.end()); // less<pair>
std::vector<point> ret;
for (int i = 0; i < n; ++i)
{
while (cnt > 1
&& !turn_left(ret[cnt - 1], a[i], ret[cnt - 2]))
--cnt, ret.pop_back();
++cnt, ret.push_back(a[i]);
}
int fixed = cnt;
for (int i = n - 2; i >= 0; --i)
{
while (cnt > fixed
&& !turn_left(ret[cnt - 1], a[i], ret[cnt - 2]))
--cnt, ret.pop_back();
++cnt, ret.push_back(a[i]);
}
ret.pop_back();
return ret;
}
std::vector<point> minkovski(std::vector<std::vector<point>> a)
{
if (a[0].size() == 1)
return a[1];
if (a[1].size() == 1)
return a[0];
for (int i = 0; i < 2; i++)a[i].push_back(a[i].front());
int i[2] = {0, 0}, len[2] = {(int) a[0].size() - 1, (int) a[1].size() - 1};
std::vector<point> ret;
ret.push_back(a[0][0] + a[1][0]);
do
{
int d = sgn(det(a[1][i[1] + 1] - a[1][i[1]], a[0][i[0] + 1] - a[0][i[0]])) >= 0;
ret.push_back(a[d][i[d] + 1] - a[d][i[d]] + ret.back());
i[d] = (i[d] + 1) % len[d];
}
while (i[0] || i[1]);
return ret;
}
struct Convex
{
int n;
std::vector<point> a, upper, lower;
Convex(std::vector<point> _a) : a(_a)
{
n = a.size();
int k = 0;
for (int i = 1; i < n; i++)if (a[k] < a[i])k = i;
for (int i = 0; i <= k; i++) lower.push_back(a[i]);
for (int i = k; i < n; i++) upper.push_back(a[i]);
upper.push_back(a[0]);
}
std::pair<LD, int> get_tan(std::vector<point> &con, point vec)
{
int l = 0, r = (int) con.size() - 2;
for (; l + 1 < r;)
{
int mid = (l + r) / 2;
if (sgn(det(con[mid + 1] - con[mid], vec)) > 0)r = mid;
else l = mid;
}
return std::max(std::make_pair(det(vec, con[r]), r), std::make_pair(det(vec, con[0]), 0));
}
void upd_tan(cp p, int id, int &i0, int &i1)
{
if (sgn(det(a[i0] - p, a[id] - p)) > 0) i0 = id;
if (sgn(det(a[i1] - p, a[id] - p)) < 0) i1 = id;
}
void search(int l, int r, point p, int &i0, int &i1)
{
if (l == r)return;
upd_tan(p, l % n, i0, i1);
int sl = sgn(det(a[l % n] - p, a[(l + 1) % n] - p));
for (; l + 1 < r;)
{
int mid = (l + r) / 2;
int smid = sgn(det(a[mid % n] - p, a[(mid + 1) % n] - p));
if (smid == sl)l = mid;
else r = mid;
}
upd_tan(p, r % n, i0, i1);
}
int search(point u, point v, int l, int r)
{
int sl = sgn(det(v - u, a[l % n] - u));
for (; l + 1 < r;)
{
int mid = (l + r) / 2;
int smid = sgn(det(v - u, a[mid % n] - u));
if (smid == sl) l = mid;
else r = mid;
}
return l % n;
}
//判定点是否在凸包内,在边界返回true
bool contain(point p)
{
if (p.x < lower[0].x || p.x > lower.back().x)return false;
int id = std::lower_bound(lower.begin(), lower.end(), point(p.x, -INF)) - lower.begin();
if (lower[id].x == p.x)
{
if (lower[id].y > p.y)return false;
}
else if (det(lower[id - 1] - p, lower[id] - p) < 0)
return false;
id = std::lower_bound(upper.begin(), upper.end(), point(p.x, INF), std::greater<point>()) - upper.begin();
if (upper[id].x == p.x)
{
if (upper[id].y < p.y)return false;
}
else if (det(upper[id - 1] - p, upper[id] - p) < 0)
return false;
return true;
}
bool get_tan(point p,int &i0,int &i1){// 求点 p 关于凸包的两个切点, 如果在凸包外则有序返回编号, 共线的多个切点返回任意一个, 否则返回 false
i0=i1=0;
int id=int(std::lower_bound(lower.begin(),lower.end(),p)-lower.begin());
search(0,id,p,i0,i1);
search(id,(int)lower.size(),p,i0,i1);
id=int(std::lower_bound(upper.begin(),upper.end(),p,std::greater<point>())-upper.begin());
search((int)lower.size()-1,(int)lower.size()-1+id,p,i0,i1);
search((int)lower.size()-1+id,(int)lower.size()-1+(int)upper.size(),p,i0,i1);
return true;
}
// 求凸包上和向量 vec 叉积最大的点, 返回编号, 共线的多个切点返回任意一个
int get_tan(point vec)
{
std::pair<LD,int>ret= get_tan(upper,vec);
ret.second=(ret.second+(int)lower.size()-1)%n;
ret=std::max(ret, get_tan(lower,vec));
return ret.second;
}
// 求凸包和直线 u,v 的交点, 如果无严格相交返回 false. 如果有则是和 (i,next(i)) 的交点, 两个点无序, 交在点上不确定返回前后两条线段其中之一
bool get_inter(point u,point v,int &i0,int &i1){
int p0= get_tan(u-v),p1= get_tan(v-u);
if(sgn(det(v-u,a[p0]-u))*sgn(det(v-u,a[p1]-u))<0)
{
if(p0>p1)std::swap(p0,p1);
i0= search(u,v,p0,p1);
i1= search(u,v,p1,p0+n);
return true;
}
else return false;
}
};
bool in_polygon(cp p,const std::vector<point>&po)
{
int n=(int)po.size();int cnt=0;
for(int i=0;i<n;i++)
{
point a=po[i],b=po[(i+1)%n];
if(point_on_segment(p,line(a,b)))return true;
int x=sgn(det(p-a,b-a)),y=sgn(a.y-p.y),z=sgn(b.y-p.y);
if(x>0&&y<=0&&z>0)++cnt;
if(x<0&&z<=0&&y>0)--cnt;
}
return cnt!=0;
}
bool In_Polygon(cp P,std::vector<point>&polygon)
{
bool flag = false; //相当于计数
point P1,P2; //多边形一条边的两个顶点
int n=polygon.size();
for(int i=0,j=n-1;i<n;j=i++)
{
//polygon[]是给出多边形的顶点
P1 = polygon[i];
P2 = polygon[j];
if(point_on_segment(P,line(P1,P2)))return true;
//前一个判断min(P1.y,P2.y)<P.y<=max(P1.y,P2.y)
//这个判断代码我觉得写的很精妙 我网上看的 应该是大神模版
//后一个判断被测点 在 射线与边交点 的左边
if( (sgn(P1.y-P.y)>0 != sgn(P2.y-P.y)>0) && sgn(P.x - (P.y-P1.y)*(P1.x-P2.x)/(P1.y-P2.y)-P1.x)<0)
flag = !flag;
}
return flag;
}
std::vector<point> Minkovski(std::vector<std::vector<point>> a)
{ //闵可夫斯基和
std::vector<point> S;
int n = a[0].size(), m = a[1].size();
std::vector<point> A(n ), B(m );
for (int i = 0; i < n - 1; i++) A[i] = a[0][i + 1] - a[0][i];
A[n - 1] = a[0][0] - a[0][n - 1];
for (int i = 0; i < m - 1; i++) B[i] = a[1][i + 1] - a[1][i];
B[m - 1] = a[1][0] - a[1][m - 1]; //将两个凸包上的边向量都存入a,b中
S.push_back(a[0][0] + a[1][0]);
int p1 = 0, p2 = 0;
while (p1 < n && p2 < m)
{
LD d = det(A[p1], B[p2]);
if (d > 0)
S.push_back(S.back()+A[p1++]);
else if (d < 0)
S.push_back(S.back()+B[p2++]);
else
{
if(dot(A[p1],B[p1])>=0)
S.push_back(S.back()+A[p1++]);
else
{
auto [x,y]=A[p1];
if(x>0)
S.push_back(S.back()+A[p1++]);
else if(x<0)
S.push_back(S.back()+B[p2++]);
else
{
if(y>0)
S.push_back(S.back()+A[p1++]);
else S.push_back(S.back()+B[p2++]);
}
}
}
}
while (p1 < n)
S.push_back(S.back() + A[p1++]);
while (p2 < m)
S.push_back(S.back() + B[p2++]);
return S;
}
void print(std::vector<point> res)
{
std::cout << "print:\n";
int cnt=0;
for (auto [x, y]: res)
std::cout <<++cnt<<' '<< x << ' ' << y << std::endl;
std::cout << "end\n";
}
void solve()
{
point p,q;
p.read(),q.read();
line li1 , li2;
line li(p,q);
li1.read(),li2.read();
if(!intersect_judge(li,li1)&&!intersect_judge(li,li2))
{
std::cout<<0<<std::endl;
return ;
}
if(!intersect_judge_strict(li1,li2))
{
std::cout<<1<<std::endl;
return ;
}
point base= line_intersect(li1,li2);
std::vector<point>pu;
pu.push_back(p);
pu.push_back(q);
pu.push_back(li1.s),pu.push_back(li1.t);
pu.push_back(li2.s),pu.push_back(li2.t);
// base.print();
std::sort(pu.begin(),pu.end(),[&](auto x,auto y){
point u=x-base,v=y-base;
if(u.on_up()!=v.on_up())return u.on_up()<v.on_up();
return det(u,v)>0;
});
int flag=0;
for(int i=0;i<6;i++)
{
// pu[i].print();
if((p==pu[i]||q==pu[i])&&(p==pu[(i+2)%6]||q==pu[(i+2)%6]))
{
flag=1;
break;
}
}
if(flag)
{
std::cout<<1<<std::endl;
return ;
}
std::vector<line> lu;
for(int i=0;i<6;i++)
{
if(p==pu[i])
{
lu.push_back(line(p,pu[(i+1)%6]));
lu.push_back(line(p,pu[(i+5)%6]));
}
if(q==pu[i])
{
lu.push_back(line(q,pu[(i+1)%6]));
lu.push_back(line(q,pu[(i+5)%6]));
}
}
// for(auto x:lu)
// x.print();
for(int i=0;i<2;i++)
for(int j=2;j<4;j++)
if(ray_intersect_judge(lu[i],lu[j]))
{
std::cout<<1<<std::endl;
return ;
}
std::cout<<2<<std::endl;
}
int main()
{
std::ios::sync_with_stdio(false);
std::cin.tie(0),std::cout.tie(0);
int T;
T=1;
std::cin>>T;
while(T--)
solve();
}
详细
Test #1:
score: 100
Accepted
time: 0ms
memory: 3820kb
input:
3 0 0 1 1 2 2 3 3 4 4 5 5 0 0 1 1 2 2 3 3 2 2 3 3 0 0 10 10 10 0 0 10 1 1 2 2
output:
0 0 1
result:
ok 3 number(s): "0 0 1"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3748kb
input:
2 -999999999 999999998 999999999 999999998 -1000000000 -1000000000 1000000000 1000000000 1000000000 -1000000000 -1000000000 1000000000 -999999999 999999998 999999999 999999998 -999999998 -999999998 1000000000 1000000000 999999998 -999999998 -1000000000 1000000000
output:
2 1
result:
ok 2 number(s): "2 1"
Test #3:
score: 0
Accepted
time: 0ms
memory: 3756kb
input:
1 0 0 1 1 2 2 3 3 4 4 5 5
output:
0
result:
ok 1 number(s): "0"
Test #4:
score: -100
Wrong Answer
time: 115ms
memory: 3912kb
input:
100000 -851839419 34688642 -667081997 395784949 -624068418 -155389155 119194510 -758711821 -992436155 -812775173 851861070 -592596572 974613003 -179673992 -485749861 520596304 -115838823 -265233646 -573799007 -222234500 608830643 -887109945 483106217 -906910755 -597593284 384264657 940783 476657007 ...
output:
0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 2 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 ...
result:
wrong answer 21st numbers differ - expected: '1', found: '2'