hdu 4353 Finding Mine （计算几何 2012 Multi-University Training Contest 6 ）
http://acm.hdu.edu.cn/showproblem.php?pid=4353
题意：
给你n个点，m个雷
找一个多边形，使得多边形的面积除以这个多边形内雷的个数的比值最小
仔细想想，其实就是找一个比值最小的三角形就OK了，因为其他的三角形的比值都比它大，组合成多边形后势必会将比值变大
所以可以直接暴力O(n^3)枚举三角形，再计算三角形内的雷的个数求比值即可
雷得个数的话预处理一个数组吧，画张图就懂了
当然还要取绝对值
1 #include<cstdio>
2 #include<cstring>
3 #include<cmath>
4 #include<iostream>
5 #include<algorithm>
6 #include<set>
7 #include<map>
8 #include<queue>
9 #include<vector>
10 #include<string>
11 #define Min(a,b) a<b?a:b
12 #define Max(a,b) a>b?a:b
13 #define CL(a,num) memset(a,num,sizeof(a));
14 #define maxn 520
15 #define eps 1e-8
16 #define inf 100000000
17 #define mx 1<<60
18 #define ll __int64
19 using namespace std;
20 struct house
21 {
22 double x;
23 double y;
24 }a[maxn],b[maxn];
25 int cmp(house a,house b)
26 {
27 if(a.x == b.x) return a.y < b.y ;
28 else return a.x < b.x ;
29 }
30 double in(house a,house b,house c)
31 {
32 return (b.x-a.x)*(c.y-a.y)-(b.y-a.y)*(c.x-a.x);
33 }
34 double sgn(house a,house b,house c)
35 {
36 return fabs((c.x-a.x)*(b.y-a.y)-(c.y-a.y)*(b.x-a.x))*0.5;
37 }
38 int dp[maxn][maxn] ;
39 int main()
40 {
41 int n,m,i,j,k;
42 int cas = 0;
43 int t;
44 scanf("%d",&t);
45 while(t--)
46 {
47 scanf("%d%d",&n,&m);
48 for(i = 0; i < n;i++)
49 {
50 scanf("%lf%lf",&a[i].x,&a[i].y);
51
52 }
53 sort(a,a + n,cmp);
54 for(j = 0; j < m;j++)
55 {
56 scanf("%lf%lf",&b[j].x,&b[j].y);
57
58 }
59
60 for( i =0 ; i < n;i++)
61 {
62 for(j = i + 1; j< n;j++)
63 {
64 dp[i][j] = 0;
65 for(k = 0; k< m;k++)
66 {
67 if(b[k].x >= a[i].x&&b[k].x < a[j].x)
68 if(in(a[i],a[j],b[k]) > 0) dp[i][j]++;
69 }
70
71
72 }
73
74 }
75 int f = 0 ;
76 double ans = -1;
77 for( i = 0;i< n;i++)
78 {
79 for(j=i+1;j< n;j++)
80 {
81 for(k = j+1;k< n;k++)
82 {
83 double tmp = (double )abs(dp[i][k] - dp[i][j] - dp[j][k]);
84
85 if(tmp == 0)continue ;
86 double s = sgn(a[i],a[j],a[k]) ;
87
88
89 f = 1 ;
90 if(ans == -1 || ans > fabs(s/tmp)) ans = fabs(s/tmp);
91
92 }
93 }
94 }
95
96 if(f == 0)printf("Case #%d: -1\n",++cas);
97 else printf("Case #%d: %.6lf\n",++cas,ans);
98
99 }
100 }
2 #include<cstring>
3 #include<cmath>
4 #include<iostream>
5 #include<algorithm>
6 #include<set>
7 #include<map>
8 #include<queue>
9 #include<vector>
10 #include<string>
11 #define Min(a,b) a<b?a:b
12 #define Max(a,b) a>b?a:b
13 #define CL(a,num) memset(a,num,sizeof(a));
14 #define maxn 520
15 #define eps 1e-8
16 #define inf 100000000
17 #define mx 1<<60
18 #define ll __int64
19 using namespace std;
20 struct house
21 {
22 double x;
23 double y;
24 }a[maxn],b[maxn];
25 int cmp(house a,house b)
26 {
27 if(a.x == b.x) return a.y < b.y ;
28 else return a.x < b.x ;
29 }
30 double in(house a,house b,house c)
31 {
32 return (b.x-a.x)*(c.y-a.y)-(b.y-a.y)*(c.x-a.x);
33 }
34 double sgn(house a,house b,house c)
35 {
36 return fabs((c.x-a.x)*(b.y-a.y)-(c.y-a.y)*(b.x-a.x))*0.5;
37 }
38 int dp[maxn][maxn] ;
39 int main()
40 {
41 int n,m,i,j,k;
42 int cas = 0;
43 int t;
44 scanf("%d",&t);
45 while(t--)
46 {
47 scanf("%d%d",&n,&m);
48 for(i = 0; i < n;i++)
49 {
50 scanf("%lf%lf",&a[i].x,&a[i].y);
51
52 }
53 sort(a,a + n,cmp);
54 for(j = 0; j < m;j++)
55 {
56 scanf("%lf%lf",&b[j].x,&b[j].y);
57
58 }
59
60 for( i =0 ; i < n;i++)
61 {
62 for(j = i + 1; j< n;j++)
63 {
64 dp[i][j] = 0;
65 for(k = 0; k< m;k++)
66 {
67 if(b[k].x >= a[i].x&&b[k].x < a[j].x)
68 if(in(a[i],a[j],b[k]) > 0) dp[i][j]++;
69 }
70
71
72 }
73
74 }
75 int f = 0 ;
76 double ans = -1;
77 for( i = 0;i< n;i++)
78 {
79 for(j=i+1;j< n;j++)
80 {
81 for(k = j+1;k< n;k++)
82 {
83 double tmp = (double )abs(dp[i][k] - dp[i][j] - dp[j][k]);
84
85 if(tmp == 0)continue ;
86 double s = sgn(a[i],a[j],a[k]) ;
87
88
89 f = 1 ;
90 if(ans == -1 || ans > fabs(s/tmp)) ans = fabs(s/tmp);
91
92 }
93 }
94 }
95
96 if(f == 0)printf("Case #%d: -1\n",++cas);
97 else printf("Case #%d: %.6lf\n",++cas,ans);
98
99 }
100 }
