poj A Round Peg in a Ground Hole

http://poj.org/problem?id=1584

  1 #include<cstdio>

  2 #include<cstring>

  3 #include<cmath>

  4 #include<algorithm>

  5 using namespace std;

  6 

  7 const int maxn=50000;

  8 const double pi=acos(-1.0);

  9 const double eps=10e-8;

 10 

 11 int cmp(double x)

 12 {

 13    if(fabs(x)<eps) return 0;

 14    if(x>0) return 1;

 15    return -1;

 16 }

 17 

 18 double sqr(double x)

 19 {

 20     return x*x;

 21 }

 22 

 23 struct point

 24 {

 25     double x,y;

 26     point(){}

 27     point(double a,double b):x(a),y(b){}

 28     bool operator <(const point &a)const

 29     {

 30         return (x<a.x)||(x==a.x&&y<a.y);

 31     }

 32     friend point operator -(const point &a,const point &b){

 33         return point(a.x-b.x,a.y-b.y);

 34     }

 35     double norm(){

 36         return sqrt(sqr(x)+sqr(y));

 37     }

 38 }p[maxn],ch[maxn];

 39 

 40 struct line

 41 {

 42    point a,b;

 43    line(){}

 44    line(point x,point y):a(x),b(y){}

 45 };

 46 

 47 double det(point a,point b,point c)

 48 {

 49     return ((b.x-a.x)*(c.y-a.y)-(c.x-a.x)*(b.y-a.y));

 50 }

 51 

 52 double cross(point a,point b,point c)

 53 {

 54     return ((b.x-a.x)*(c.y-b.y)-(c.x-b.x)*(b.y-a.y));

 55 }

 56 double det1(const point &a,const point &b)

 57 {

 58     return a.x*b.y-a.y*b.x;

 59 }

 60 

 61 double dot(const point &a,const point &b)

 62 {

 63     return a.x*b.x+a.y*b.y;

 64 }

 65 

 66 double dis(point a,point b)

 67 {

 68     return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y));

 69 }

 70 

 71 double dis_point_segment(const point p,const point s,const point t)

 72 {

 73     if(cmp(dot(p-s,t-s))<0) return (p-s).norm();

 74     if(cmp(dot(p-t,s-t))<0) return (p-t).norm();

 75     return fabs(det1(s-p,t-p)/dis(s,t));

 76 }

 77 

 78 bool pointonsegment(point p,point s,point t)

 79 {

 80     return cmp(det1(p-s,t-s))==0&&cmp(dot(p-s,p-t))<=0;

 81 }

 82 

 83 int convex_hull(point *p,int n,point *ch)

 84 {

 85     sort(p,p+n);

 86     int m=0;

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

 88     {

 89         while(m>1&&det(ch[m-2],ch[m-1],p[i])<=0) m--;

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

 91     }

 92     int k=m;

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

 94     {

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

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

 97     }

 98     if(n>1) m--;

 99     return m;

100 }

101 

102 

103 bool convex_hull1(point *p,int n)

104 {

105     int flag=0;

106     p[n]=p[0];

107     for(int i=2; i<=n; i++)

108     {

109         //printf("%lf%lf %lf%lf %lf%lf\n",p[i-2].x,p[i-2].y,p[i-1].x,p[i-1].y,p[i].x,p[i].y);

110         int t=cmp(cross(p[i-2],p[i-1],p[i]));

111         //printf("%d\n",t);

112         if(!flag) flag=t;

113         if(flag*t<0) return false;

114     }

115     return true;

116 }

117 int point_in(point t,point *ch,int n)

118 {

119     int num=0,d1,d2,k;

120     ch[n]=ch[0];

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

122     {

123         if(pointonsegment(t,ch[i],ch[i+1])) return 2;

124         k=cmp(det1(ch[i+1]-ch[i],t-ch[i]));

125         d1=cmp(ch[i].y-t.y);

126         d2=cmp(ch[i+1].y-t.y);

127         if(k>0&&d1<=0&&d2>0) num++;

128         if(k<0&&d2<=0&&d1>0) num--;

129     }

130     return num!=0;

131 }

132 int main()

133 {

134     int n;

135     double r,x,y;

136     //freopen("sb.txt","w",stdout);

137     while(scanf("%d",&n)!=EOF)

138     {

139         if(n<3) break;

140         scanf("%lf%lf%lf",&r,&x,&y);

141         point t(x,y);

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

143         {

144             scanf("%lf%lf",&p[i].x,&p[i].y);

145         }

146 

147         if(!convex_hull1(p,n))

148         {

149             printf("HOLE IS ILL-FORMED\n");

150             continue;

151         }

152         int cn=convex_hull(p,n,ch);

153         if(point_in(t,ch,cn))

154         {

155             double max1=dis_point_segment(t,ch[0],ch[1]);

156             for(int i=1; i<cn+1; i++)

157             {

158                 max1=min(max1,dis_point_segment(t,ch[i-1],ch[i]));

159             }

160             if(max1-r>=0) printf("PEG WILL FIT\n");

161             else printf("PEG WILL NOT FIT\n");

162         }

163         else printf("PEG WILL NOT FIT\n");

164     }

165     return 0;

166 }

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