BZOJ1069 [SCOI2007]最大土地面积

 1 /**************************************************************
 2     Problem: 1069
 3     User: rausen
 4     Language: C++
 5     Result: Accepted
 6     Time:148 ms
 7     Memory:872 kb
 8 ****************************************************************/
 9  
10 #include <cstdio>
11 #include <algorithm>
12  
13 #define points P
14 using namespace std;
15 typedef double lf;
16 const int N = 2005;
17 struct points{
18     lf x, y;
19 }p[N], s[N];
20 int n, top;
21  
22  
23 inline lf operator * (const P a, const P b){
24     return a.x * b.y - a.y * b.x;
25 }
26  
27 inline P operator - (const P a, const P b){
28     P tmp;
29     tmp.x = a.x - b.x, tmp.y = a.y - b.y;
30     return tmp;
31 }
32  
33 inline lf Sqr(const lf x){
34     return x * x;
35 }
36  
37 inline lf dis(const P a, const P b){
38     return Sqr(a.x - b.x) + Sqr(a.y - b.y);
39 }
40  
41 inline bool operator < (const P a, const P b){
42     lf tmp = (a - p[1]) * (b - p[1]);
43     return tmp == 0 ? dis(p[1], a) < dis(p[1], b) : tmp > 0;
44 }
45  
46 inline lf Area(const int x, const int y, const int z){
47     return (s[z] - s[x]) * (s[y] - s[x]);
48 }
49  
50 int work(){
51     int k = 1;
52     for (int i = 2; i <= n; ++i)
53         if (p[i].y == p[k].y ? p[i].x < p[k].x : p[i].y < p[k].y) k = i;
54     swap(p[1], p[k]);
55     sort(p + 2, p + n + 1);
56     top = 2, s[1] = p[1], s[2] = p[2];
57     for (int i = 3; i <= n; ++i){
58         while ((s[top] - s[top - 1]) * (p[i] - s[top]) <= 0) --top;
59         s[++top] = p[i];
60     }
61 }
62  
63 double Calc(){
64     s[top + 1] = p[1];
65     lf res = 0;
66     int a, b, x, y;
67     for (x = 1; x <= top; ++x){
68         a = x % top + 1, b = (x + 2) % top + 1;
69         for (y = x + 2; y <= top; ++y){
70             while (a % top + 1 != y && Area(x, y, a + 1) > Area(x, y, a))
71                 a = a % top + 1;
72             while (b % top + 1 != x && Area(x, b + 1, y) > Area(x, b, y))
73                 b = b % top + 1;
74             res = max(Area(x, y, a) + Area(x, b, y), res);
75         }
76     }
77     return res;
78 }
79  
80 int main(){
81     scanf("%d\n", &n);
82     for (int i = 1; i <= n; ++i)
83         scanf("%lf%lf", &p[i].x, &p[i].y);
84     work();
85     printf("%.3lf\n", Calc() / 2);
86     return 0;
87 }