QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#525432 | #7521. Find the Gap | mhw# | WA | 1ms | 3860kb | C++23 | 5.2kb | 2024-08-20 16:33:32 | 2024-08-20 16:33:33 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
int sgn(double x) {
if (fabs(x) < eps) return 0;
if (x < 0) return -1;
else return 1;
}
struct Point3 {
double x, y, z;
Point3(double _x = 0, double _y = 0, double _z = 0)
{
x = _x;
y = _y;
z = _z;
}
void input() { cin >> x >> y >> z; }
void output() { cout << fixed << setprecision(8) << x << " " << y << " " << z << '\n'; }
bool operator==(const Point3 &b) const { return sgn(x - b.x) == 0 && sgn(y - b.y) == 0 && sgn(z - b.z) == 0; }
bool operator<(const Point3 &b) const { return sgn(x - b.x) == 0 ? (sgn(y - b.y) == 0 ? sgn(z - b.z) < 0 : y < b.y) : x < b.x; }
double len() { return sqrt(x * x + y * y + z * z); }
double len2() { return x * x + y * y + z * z; }
double distance(const Point3 &b) const { return sqrt((x - b.x) * (x - b.x) + (y - b.y) * (y - b.y) + (z - b.z) * (z - b.z)); }
Point3 operator-(const Point3 &b) const { return Point3(x - b.x, y - b.y, z - b.z); }
Point3 operator+(const Point3 &b) const { return Point3(x + b.x, y + b.y, z + b.z); }
Point3 operator*(const double &k) const { return Point3(x * k, y * k, z * k); }
Point3 operator/(const double &k) const { return Point3(x / k, y / k, z / k); }
// 点乘
double operator*(const Point3 &b) const { return x * b.x + y * b.y + z * b.z; }
// 叉乘
Point3 operator^(const Point3 &b) const { return Point3(y * b.z - z * b.y, z * b.x - x * b.z, x * b.y - y * b.x); }
double rad(Point3 a, Point3 b)
{
Point3 p = (*this);
return acos(((a - p) * (b - p)) / (a.distance(p) * b.distance(p)));
}
// 变换长度
Point3 trunc(double r)
{
double l = len();
if (!sgn(l)) return *this;
r /= l;
return Point3(x * r, y * r, z * r);
}
};
struct Line3
{
Point3 s, e;
Line3() {}
Line3(Point3 _s, Point3 _e)
{
s = _s;
e = _e;
}
bool operator==(const Line3 v) { return (s == v.s) && (e == v.e); }
void input()
{
s.input();
e.input();
}
double length() { return s.distance(e); }
// 点到直线距离
double dispointtoline(Point3 p) { return ((e - s) ^ (p - s)).len() / s.distance(e); }
// 点到线段距离
double dispointtoseg(Point3 p)
{
if (sgn((p - s) * (e - s)) < 0 || sgn((p - e) * (s - e)) < 0)
return min(p.distance(s), e.distance(p));
return dispointtoline(p);
}
// 返回点p在直线上的投影
Point3 lineprog(Point3 p)
{
return s + (((e - s) * ((e - s) * (p - s))) / ((e - s).len2()));
}
// p绕此向量逆时针arg角度
Point3 rotate(Point3 p, double ang)
{
if (sgn(((s - p) ^ (e - p)).len()) == 0) return p;
Point3 f1 = (e - s) ^ (p - s);
Point3 f2 = (e - s) ^ (f1);
double len = ((s - p) ^ (e - p)).len() / s.distance(e);
f1 = f1.trunc(len);
f2 = f2.trunc(len);
Point3 h = p + f2;
Point3 pp = h + f1;
return h + ((p - h) * cos(ang)) + ((pp - h) * sin(ang));
}
// 点在直线上
bool pointonseg(Point3 p)
{
return sgn(((s - p) ^ (e - p)).len()) == 0 && sgn((s - p) * (e - p)) == 0;
}
};
struct Plane
{
Point3 a, b, c, o; // 平面上的三个点,以及法向量
Plane() {}
Plane(Point3 _a, Point3 _b, Point3 _c)
{
a = _a;
b = _b;
c = _c;
o = pvec();
}
Point3 pvec() { return (b - a) ^ (c - a); }
// ax + by + cz + d = 0
Plane(double _a, double _b, double _c, double _d)
{
o = Point3(_a, _b, _c);
if (sgn(_a) != 0) a = Point3((-_d - _c - _b) / _a, 1, 1);
else if (sgn(_b) != 0) a = Point3(1, (-_d - _c - _a) / _b, 1);
else if (sgn(_c) != 0) a = Point3(1, 1, (-_d - _a - _b) / _c);
}
// 点在平面上的判断
int pointonplane(Point3 p) { return sgn((p - a) * o); }
// 两平面夹角
double angleplane(Plane f) { return acos(o * f.o) / (o.len() * f.o.len()); }
// 平面和直线的交点,返回值是交点个数
int crossline(Line3 u, Point3 &p)
{
double x = o * (u.e - a);
double y = o * (u.s - a);
double d = x - y;
if (sgn(d) == 0) return 0;
p = ((u.s * x) - (u.e * y)) / d;
return 1;
}
// 点到平面最近点(也就是投影)
Point3 pointtoplane(Point3 p)
{
Line3 u = Line3(p, p + o);
crossline(u, p);
return p;
}
// 平面和平面的交线
int crossplane(Plane f, Line3 &u)
{
Point3 oo = o ^ f.o;
Point3 v = o ^ oo;
double d = fabs(f.o * v);
if (sgn(d) == 0) return 0;
Point3 q = a + (v * (f.o * (f.a - a)) / d);
u = Line3(q, q + oo);
return 1;
}
};
Point3 a[60];
int main()
{
int n;cin>>n;
double ans=1e18;
for(int i=1;i<=n;i++) a[i].input();
for(int i=1;i<=n;i++)
{
for(int j=i+1;j<=n;j++)
{
for(int k=j+1;k<=n;k++)
{
Line3 l={a[i],a[j]};
if(sgn(l.dispointtoline(a[k]))==0) continue;
Plane p=Plane(a[i],a[j],a[k]);
double minn=1e18;
int f;
for(int o=1;o<=n;o++)
{
if(o==i||o==j||o==k) continue;
int temp=p.pointonplane(a[o]);
if(o==1) f=temp;
else if(temp!=0&&f!=temp)
{
f=0;
break;
}
if(temp==0) continue;
double dis=a[o].distance(p.pointtoplane(a[o]));
// cout<<temp<<" "<<i<<" "<<j<<" "<<k<<" "<<o<<" "<<dis<<endl;
minn=min(minn,dis);
}
if(f!=0) ans=min(ans,minn);
}
}
}
cout<<fixed<<setprecision(12)<<ans<<'\n';
}
Details
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Test #1:
score: 100
Accepted
time: 0ms
memory: 3852kb
input:
8 1 1 1 1 1 2 1 2 1 1 2 2 2 1 1 2 1 2 2 2 1 2 2 2
output:
1.000000000000
result:
ok found '1.000000000', expected '1.000000000', error '0.000000000'
Test #2:
score: 0
Accepted
time: 0ms
memory: 3860kb
input:
5 1 1 1 1 2 1 1 1 2 1 2 2 2 1 1
output:
0.707106781187
result:
ok found '0.707106781', expected '0.707106781', error '0.000000000'
Test #3:
score: -100
Wrong Answer
time: 1ms
memory: 3856kb
input:
50 973 1799 4431 1036 1888 4509 1099 1977 4587 1162 2066 4665 1225 2155 4743 1288 2244 4821 1351 2333 4899 1414 2422 4977 1540 2600 5133 1603 2689 5211 1666 2778 5289 1729 2867 5367 1792 2956 5445 1855 3045 5523 1918 3134 5601 1981 3223 5679 2044 3312 5757 2107 3401 5835 2170 3490 5913 2296 3668 606...
output:
1000000000000000000.000000000000
result:
wrong answer 1st numbers differ - expected: '0.0000000', found: '1000000000000000000.0000000', error = '1000000000000000000.0000000'