POJ 3384 Feng Shui 凸包直径 + 半平面交
G++一直没有过了 换成 C++果断A掉了。。。It's time to bet RP.
题意：给一个多边形，然后放进去两个圆，让两个圆的覆盖面积尽量最大，输出两个圆心的坐标。
思路：将多边形的边向里平移圆的的半径R，然后求新多边形的距离最长的两个点。
平移多少废了一点脑筋，其他的就都是现成的模板了。
这个是平移的函数，自己想得，不知道还有没有更简便的。左右平移只需要改一下 向量 V
void Panning_Edge(P &a1,P &a2,double dis)
{
//向v的右侧平移
P v = {a2.y-a1.y,a1.x-a2.x};
double t = dis/Cal_Point_Dis(a1,a2);
a1.x = a1.x+v.x * t;
a1.y = a1.y+v.y * t;
a2.x = a2.x+v.x*t;
a2.y = a2.y+v.y*t;
}
PS：好吧，我承认自己没想出，然后翻了别人的题解。。。。这个内推边真的用的好巧哇
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <queue>
#include <cmath>
#include <algorithm>
#include <string>
#define LL long long
#define EPS (1e-9)
#define Right 1;
#define Left -1;
using namespace std;
struct P
{
double x,y;
} p[55],tp[2510],cp[2510];
double X_Mul(P a1,P a2,P b1,P b2)
{
P v1 = {a2.x-a1.x,a2.y-a1.y},v2 = {b2.x-b1.x,b2.y-b1.y};
return v1.x*v2.y - v1.y*v2.x;
}
P Cal_Cross_Position(P a1,P a2,P b1,P b2)
{
double t = fabs(X_Mul(a1,a2,a1,b1))/fabs(X_Mul(a1,a2,b2,b1));
P p = {b1.x + (b2.x-b1.x)*t,b1.y + (b2.y-b1.y)*t};
return p;
}
double Cal_Point_Dis(P a1,P a2)
{
return sqrt((a2.x-a1.x)*(a2.x-a1.x) + (a2.y-a1.y)*(a2.y-a1.y));
}
void Panning_Edge(P &a1,P &a2,double dis)
{
//向v的右侧平移
P v = {a2.y-a1.y,a1.x-a2.x};
double t = dis/Cal_Point_Dis(a1,a2);
a1.x = a1.x+v.x * t;
a1.y = a1.y+v.y * t;
a2.x = a2.x+v.x*t;
a2.y = a2.y+v.y*t;
}
int Cut_Polygon(P a1,P a2,P *tp,int n,P *cp,double rad)
{
Panning_Edge(a1,a2,rad);
double xm1,xm2;
int i ,top = 0;
for(i = 0;i < n; ++i)
{
xm1 = X_Mul(a1,a2,a1,tp[i]),xm2 = X_Mul(a1,a2,a1,tp[i+1]);
if(xm1 < EPS && xm2 < EPS)
{
cp[top++] = tp[i];
}
else if(xm1 < EPS || xm2 < EPS)
{
if(xm1 < EPS)
{
cp[top++] = tp[i];
}
cp[top++] = Cal_Cross_Position(a1,a2,tp[i],tp[i+1]);
}
}
cp[top] = cp[0];
return top;
}
void Cal_Center_Position(P *tp,P *cp,P *p,int n,double rad)
{
int i,j,top;
for(i = 0;i <= n; ++i)
{
tp[i] = p[i];
}
for(top = n,i = 0;i < n; ++i)
{
top = Cut_Polygon(p[i],p[i+1],tp,top,cp,rad);
for(j = 0;j <= top; ++j)
{
tp[j] = cp[j];
}
//点集内有重点
}
//求凸包的直径 鉴于点集不是很大 也懒得写旋转卡壳了
double TempDis,MaxDis = -1;
int s1,s2;
for(i = 0;i <= top; ++i)
{
for(j = 0;j <= top; ++j)
{
TempDis = Cal_Point_Dis(tp[i],tp[j]);
if(MaxDis < TempDis)
{
MaxDis = TempDis,s1 = i,s2 = j;
}
}
}
//最终答案
printf("%.4lf %.4lf %.4lf %.4lf\n",tp[s1].x,tp[s1].y,tp[s2].x,tp[s2].y);
}
int main()
{
int i,n;
double rad;
while(scanf("%d %lf",&n,&rad) != EOF)
{
for(i = 0; i < n; ++i)
{
scanf("%lf %lf",&p[i].x,&p[i].y);
}
p[n] = p[0];
Cal_Center_Position(tp,cp,p,n,rad);
}
return 0;
}