poj2079Triangle(N点中三点组成三角形面积最大）

链接

根据旋转卡壳的思想，找到当前边的最远点。

确定i,j找到最远的k使 cross(i,j,k)最大，那么i,j+1时只需从k+1开始找即可 。

  1 #include <iostream>
  2 #include<cstdio>
  3 #include<cstring>
  4 #include<algorithm>
  5 #include<stdlib.h>
  6 #include<vector>
  7 #include<cmath>
  8 #include<queue>
  9 #include<set>
 10 using namespace std;
 11 #define N 50010
 12 #define LL long long
 13 #define INF 0xfffffff
 14 const double eps = 1e-8;
 15 const double pi = acos(-1.0);
 16 const double inf = ~0u>>2;
 17 struct point
 18 {
 19     int x,y;
 20     point(int x=0,int y=0):x(x),y(y) {}
 21 } p[N],ch[N];
 22 typedef point pointt;
 23 pointt operator - (point a,point b)
 24 {
 25     return point(a.x-b.x,a.y-b.y);
 26 }
 27 int dcmp(double x)
 28 {
 29     if(fabs(x)<eps) return 0;
 30     return x<0?-1:1;
 31 }
 32 double cross(point a,point b)
 33 {
 34     return 1.0*a.x*b.y-1.0*a.y*b.x;
 35 }
 36 double getarea(point a,point b,point c)
 37 {
 38     return fabs(cross(b-a,c-a))/2;
 39 }
 40 double mul(point p0,point p1,point p2)
 41 {
 42     return cross(p1-p0,p2-p0);
 43 }
 44 double dis(point a)
 45 {
 46     return sqrt(1.0*a.x*a.x+a.y*a.y);
 47 }
 48 bool cmp(point a,point b)
 49 {
 50     if(dcmp(mul(p[0],a,b))==0) return dis(a-p[0])<dis(b-p[0]);
 51     return dcmp(mul(p[0],a,b))>0;
 52 }
 53 int graham(int n)
 54 {
 55     int i,k=0,top;
 56     point tmp;
 57     for(i = 0;  i< n; i++)
 58     {
 59         if(p[i].y<p[k].y||(p[i].y==p[k].y&&p[i].x<p[k].x))
 60             k = i;
 61     }
 62     if(k!=0)
 63         swap(p[0],p[k]);
 64     sort(p+1,p+n,cmp);
 65     ch[0] = p[0];
 66     ch[1] = p[1];
 67     top = 1;
 68     for(i = 2; i < n; i++)
 69     {
 70         while(top>0&&dcmp(mul(ch[top-1],ch[top],p[i]))<=0)
 71             top--;
 72         ch[++top] = p[i];
 73     }
 74     return top;
 75 }
 76 int main()
 77 {
 78     int n,i,j,k,kk;
 79     while(scanf("%d",&n)!=EOF)
 80     {
 81         if(n==-1) break;
 82         for(i = 0; i < n; i++)
 83             scanf("%d%d",&p[i].x,&p[i].y);
 84         int top = graham(n);
 85         double maxz=0,area;
 86     ++top;
 87     ch[top] = ch[0];
 88     for(i=0; i<top; ++i)
 89     {
 90         j=(i+1)%top;
 91         k=(j+1)%top;
 92         while(k!=i && getarea(ch[i],ch[j],ch[k])<getarea(ch[i],ch[j],ch[k+1]))
 93             k=(k+1)%top;
 94         maxz = max(maxz,getarea(ch[i],ch[j],ch[k]));
 95         if(k == i)
 96             continue;
 97         kk=(k+1)%top;
 98         while(j!=kk && k!=i)
 99         {
100             area=getarea(ch[i],ch[j],ch[k]);
101             if(area>maxz)
102                 area=maxz;
103             while(k!=i && getarea(ch[i],ch[j],ch[k])<getarea(ch[i],ch[j],ch[k+1]))
104                 k=(k+1)%top;
105             maxz = max(maxz,getarea(ch[i],ch[j],ch[k]));
106             j=(j+1)%top;
107         }
108     }
109     printf("%.2f\n",maxz);
110
111     }return 0;
112 }

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