poj 1113 Wall

题目链接：http://poj.org/problem?id=1113

题目大意：给出点集和一个长度L，要求用最短长度的围墙把所有点集围住，并且围墙每一处距离所有点的距离最少为L，求围墙的长度。

解法：凸包+以L为半径的圆的周长。以题目中的图为例，两点之间的围墙长度之和正好就是凸包的长度，再加上每个点的拐角处（注意此处为弧，才能保证城墙距离点的距离最短）的长度。

 1 #include<iostream>

 2 #include<cstdio>

 3 #include<cstdlib>

 4 #include<cstring>

 5 #include<cmath>

 6 #include<algorithm>

 7 #define inf 0x7fffffff

 8 #define exp 1e-10

 9 #define PI 3.141592654

10 using namespace std;

11 int n,L;

12 struct Point

13 {

14     double x,y;

15     Point (double x=0,double y=0):x(x),y(y){}

16     friend bool operator < (Point a,Point b)

17     {

18         if (a.x!=b.x) return a.x<b.x;

19         return a.y<b.y;

20     }

21 }an[1000+10],bn[1000+10];

22 typedef Point Vector;

23 Vector operator + (Vector A,Vector B) {return Vector(A.x+B.x , A.y+B.y); }

24 Vector operator - (Vector A,Vector B) {return Vector(A.x-B.x , A.y-B.y); }

25 Vector operator * (Vector A,double p) {return Vector(A.x*p , A.y*p); }

26 int dcmp(double x)

27 {

28     if (fabs(x)<exp) return 0;

29     else return x<0 ? -1 : 1;

30 }

31 double cross(Vector A,Vector B)

32 {

33     return A.x*B.y-B.x*A.y;

34 }

35 int ConvexHull(Point *p,int n,Point *ch)

36 {

37     sort(p,p+n);

38     int m=0;

39     for (int i=0 ;i<n ;i++)

40     {

41         while (m>1 && dcmp(cross(ch[m-1]-ch[m-2],p[i]-ch[m-1]))<=0) m--;

42         ch[m++]=p[i];

43     }

44     int k=m;

45     for (int i=n-2 ;i>=0 ;i--)

46     {

47         while (k>m && dcmp(cross(ch[k-1]-ch[k-2],p[i]-ch[k-1]))<=0) k--;

48         ch[k++]=p[i];

49     }

50     ch[k++]=ch[0];

51     if (n>1) k--;

52     return k;

53 }

54 int main()

55 {

56     while (cin>>n>>L)

57     {

58         for (int i=0 ;i<n ;i++)

59         scanf("%lf%lf",&an[i].x,&an[i].y);

60 

61         int k=ConvexHull(an,n,bn);

62         double sum=0;

63         sum += 2*PI*L;

64         for (int i=0 ;i<k ;i++)

65         {

66             sum += sqrt((bn[i].x-bn[i+1].x)*(bn[i].x-bn[i+1].x)+(bn[i].y-bn[i+1].y)*(bn[i].y-bn[i+1].y));

67         }

68         printf("%.0f\n",sum);

69     }

70     return 0;

71 }