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blowing_candles.cpp
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blowing_candles.cpp
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/*
* _ _ _ _ _
* | |__ | | _____ _(_)_ __ __ _ ___ __ _ _ __ __| | | ___ ___
* | '_ \| |/ _ \ \ /\ / / | '_ \ / _` | / __/ _` | '_ \ / _` | |/ _ \/ __|
* | |_) | | (_) \ V V /| | | | | (_| | | (_| (_| | | | | (_| | | __/\__ \
* |_.__/|_|\___/ \_/\_/ |_|_| |_|\__, | \___\__,_|_| |_|\__,_|_|\___||___/
* |___/
*
*/
#include <bits/stdc++.h>
typedef long long LL;
namespace geo {
struct point {
LL x,y;
point() : x{0LL}, y{0LL} { }
point(LL x, LL y) : x{x}, y{y} { }
bool operator<(const geo::point &other) const {
return x == other.x ? y < other.y : x < other.x;
}
friend std::ostream &operator<<(std::ostream &os, const geo::point &p) {
return os << '(' << p.x << ',' << p.y << ')';
}
static double dist(const geo::point &p1, const geo::point &p2) {
return std::hypot(p1.x-p2.x, p1.y-p2.y);
}
};
struct line {
double a,b,c; // ax + bx = c
line() : a{0.0}, b{0.0}, c{0.0} { }
line(double a, double b, double c) : a{a}, b{b}, c{c} { }
line(const geo::point &p1, const geo::point &p2) {
if (p1.x == p2.x) {
a = 1.0; b = 0.0, c = static_cast<double>(-p1.x);
} else {
a = -static_cast<double>(p1.y - p2.y) / (p1.x - p2.x);
b = 1.0;
c = -static_cast<double>(a * p1.x) - p1.y;
}
}
friend std::ostream &operator<<(std::ostream &os, const geo::line &l) {
return os << '(' << l.a << "x + " << l.b << "y = " << l.c << ')';
}
};
struct vector {
LL x,y,z;
vector() : x{0LL}, y{0LL}, z{0LL} { }
vector(LL x, LL y) : x{x}, y{y}, z{0LL} { }
vector(LL x, LL y, LL z) : x{x}, y{y}, z{z} { }
vector(const geo::point &p1, const geo::point &p2) : x{p2.x-p1.x}, y{p2.y-p1.y}, z{0LL} { }
double magnitude() const {
return std::hypot(x,y,z);
}
// a * b
static LL dot(const geo::vector &a, const geo::vector &b) {
return a.x * b.x + a.y * b.y + a.z * b.z;
}
// a x b
static geo::vector cross(const geo::vector &a, const geo::vector &b) {
return geo::vector(a.y*b.z - a.z*b.y, a.z*b.x - a.x*b.z, a.x*b.y - a.y*b.x);
}
friend std::ostream &operator<<(std::ostream &os, const geo::vector &v) {
return os << '<' << v.x << ',' << v.y << ',' << v.z << '>';
}
};
inline double distToLine(const geo::point &p, const geo::point &a, const geo::point &b) {
geo::vector ap(a,p), ab(a,b);
double u = static_cast<double>(geo::vector::dot(ap, ab)) / (ab.x*ab.x + ab.y*ab.y + ab.z*ab.z);
double cx = a.x + ab.x*u;
double cy = a.y + ab.y*u;
return std::hypot(cx - p.x, cy - p.y);
}
};
int main() {
LL N,R; scanf("%lld %lld", &N, &R);
std::vector<geo::point> pts(N);
for (int i = 0; i < N; ++i) {
scanf("%lld %lld", &pts[i].x, &pts[i].y);
}
std::sort(std::begin(pts), std::end(pts));
std::vector<geo::point> lower_hull;
for (const geo::point &p : pts) {
while (static_cast<int>(lower_hull.size()) >= 2) {
geo::point &a = lower_hull[static_cast<int>(lower_hull.size()) - 2];
geo::point &b = lower_hull[static_cast<int>(lower_hull.size()) - 1];
geo::point c = p;
geo::vector v1(a,b);
geo::vector v2(b,c);
if (geo::vector::cross(v1,v2).z > 0) { break; }
lower_hull.pop_back();
}
lower_hull.push_back(p);
}
std::vector<geo::point> upper_hull;
for (const geo::point &p : pts) {
while (static_cast<int>(upper_hull.size()) >= 2) {
geo::point &a = upper_hull[static_cast<int>(upper_hull.size()) - 2];
geo::point &b = upper_hull[static_cast<int>(upper_hull.size()) - 1];
geo::point c = p;
geo::vector v1(a,b);
geo::vector v2(b,c);
if (geo::vector::cross(v1,v2).z < 0) { break; }
upper_hull.pop_back();
}
upper_hull.push_back(p);
}
std::vector<geo::point> convex_hull(static_cast<int>(lower_hull.size()) + static_cast<int>(upper_hull.size()) - 2);
int j = 0;
for (int i = 0; i < static_cast<int>(lower_hull.size()); ++i) { convex_hull[j++] = lower_hull[i]; }
for (int i = static_cast<int>(upper_hull.size())-2; i > 0; --i) { convex_hull[j++] = upper_hull[i]; }
if (static_cast<int>(convex_hull.size()) <= 2) {
printf("0\n");
return 0;
}
j = 1;
double min_width = std::numeric_limits<double>::max();
for (int i = 0; i < static_cast<int>(convex_hull.size()); ++i) {
geo::point &a = convex_hull[i];
geo::point &b = convex_hull[(i+1)%static_cast<int>(convex_hull.size())];
geo::vector v(b,a);
while (true) {
geo::point &c = convex_hull[j%static_cast<int>(convex_hull.size())];
geo::point &d = convex_hull[(j+1)%static_cast<int>(convex_hull.size())];
geo::vector _v(c,d);
if (geo::vector::cross(_v, v).z < 0) {
break;
}
++j;
}
min_width = std::min(min_width, geo::distToLine(convex_hull[j%static_cast<int>(convex_hull.size())], a, b));
}
printf("%.9lf\n", min_width);
return 0;
}