LA 3890 Most Distant Point from the Sea(半平面交)
Most Distant Point from the Sea
【题目链接】Most Distant Point from the Sea
【题目类型】半平面交
&题解:
蓝书279 二分答案,判断平移后的直线的半平面交是否为空.
模板是照着敲的,还有一些地方不是很懂, 应该还要慢慢体会吧
&代码:
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <vector>
using namespace std;
struct Point {
double x, y;
Point(double x = 0, double y = 0): x(x), y(y) {}
};
typedef Point Vector;
Vector operator + (const Vector& A, const Vector& B) {return Vector(A.x + B.x, A.y + B.y);}
Vector operator - (const Vector& A, const Vector& B) {return Vector(A.x - B.x, A.y - B.y);}
Vector operator * (const Vector& A, double p) {return Vector(A.x * p, A.y * p);}
double Dot(const Vector& A, const Vector& B) {return A.x * B.x + A.y * B.y;}
double Cross(const Vector& A, const Vector& B) {return A.x * B.y - A.y * B.x;}
double Length(const Vector& A) {return sqrt(Dot(A, A));}
Vector Normal(const Vector& A) {double l = Length(A); return Vector(-A.y / l, A.x / l);}
double PolygonArea(vector<Point> p) {
int n = p.size();
double s = 0;
for(int i = 1; i < n - 1; i++) {
s += Cross(p[i] - p[0], p[i + 1] - p[0]);
}
return s / 2;
}
struct Line {
Point p, v;
double ang;
Line() {}
Line(Point p, Vector v): p(p), v(v) {ang = atan2(v.y, v.x);}
bool operator < (const Line& l) const {
return ang < l.ang;
}
};
bool OnLeft(const Line& L, const Point& p) {
return Cross(L.v, p - L.p) > 0;
}
Point GetLineIntersection(const Line& a, const Line& b) {
Vector u = a.p - b.p;
double t = Cross(b.v, u) / Cross(a.v, b.v);
return a.p + a.v * t;
}
const double eps = 1e-6;
vector<Point> HalfplaneIntersection(vector<Line> L) {
int n = L.size();
sort(L.begin(), L.end());
int first, last;
vector<Point> p(n), ans;
vector<Line> que(n);
que[first = last = 0] = L[0];
for(int i = 1; i < n; i++) {
while(first < last && !OnLeft(L[i], p[last - 1])) last--;
while(first < last && !OnLeft(L[i], p[first])) first++;
que[++last] = L[i];
if(fabs(Cross(que[last].v, que[last - 1].v)) < eps) {
last--;
if(OnLeft(que[last], L[i].p)) que[last] = L[i];
}
if(first < last) p[last - 1] = GetLineIntersection(que[last - 1], que[last]);
}
while(first < last && !OnLeft(que[first], p[last - 1])) last--;
if(last - first <= 1) return ans;
p[last] = GetLineIntersection(que[last], que[first]);
for(int i = first; i <= last; i++)
ans.push_back(p[i]);
return ans;
}
int main() {
//("E:1.in", "r", stdin);
int n;
while(scanf("%d", &n) == 1 && n) {
vector<Vector> p, v, nor;
int m, x, y;
for(int i = 0; i < n; i++) {
scanf("%d%d", &x, &y);
p.push_back(Point(x, y));
}
if(PolygonArea(p) < 0) reverse(p.begin(), p.end());
for(int i = 0; i < n; i++) {
v.push_back(p[(i + 1) % n] - p[i]);
nor.push_back(Normal(v[i]));
}
double left = 0, right = 20000;
while(right - left > 1e-6) {
vector<Line> L;
double mid = left + (right - left) / 2;
for(int i = 0; i < n; i++)
L.push_back(Line(p[i] + nor[i]*mid, v[i]));
vector<Point> poly = HalfplaneIntersection(L);
if(poly.empty()) right = mid;
else left = mid;
}
printf("%f\n", left);
}
return 0;
}
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