swust oj--凸包面积

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<algorithm>
 4 #include<stack>
 5 #include<cmath>
 6 using namespace std;
 7 struct node{
 8     double x, y;
 9 }point[110], pos, tmp;
10 double dis(node a, node b){
11     return pow((a.x - b.y), 2) + pow((a.y - b.y), 2);
12 }
13 //按点集分布排序,利用向量平行关系判断
14 bool cmp(node a, node b){
15     double povit = (a.x - pos.x)*(b.y - pos.y) - (b.x - pos.x)*(a.y - pos.y);
16     if (povit > 0 || !povit && (dis(a, pos) < dis(b, pos)))
17         return true;
18     return false;
19 }
20 //当前点是否在点集左侧,利用叉乘比较3个点两条线的斜率关系
21 bool turn_left(node p1, node p2, node p3){
22     return (p2.x*p1.y + p3.x*p2.y + p1.x*p3.y - p3.x*p1.y - p1.x*p2.y - p2.x*p3.y) > 0 ? true : false;
23 }
24 int main(){
25     int i, sign, n, t;
26     double area;
27     cin >> t;
28     while (t--){
29         cin >> n;
30         for (i = 0; i < n; i++)
31             cin >> point[i].x >> point[i].y;
32         if (n <= 2){
33             cout << "0.0\n";
34             continue;
35         }
36         stack<node> Q;
37         sign = 0;
38         pos = point[0];
39         for (i = 1; i < n; i++){
40             if (pos.y == point[i].y&&pos.x>point[i].x || point[i].y < pos.y){
41                 pos = point[i];
42                 sign = i;
43             }
44         }
45         swap(point[0], point[sign]);
46         sort(point + 1, point + n, cmp);
47         Q.push(point[0]), Q.push(point[1]), Q.push(point[2]);
48         for (i = 3; i < n; i++){
49             while (!Q.empty()){
50                 tmp = Q.top();
51                 Q.pop();
52                 if (turn_left(tmp, Q.top(), point[i])){
53                     Q.push(tmp);
54                     break;
55                 }
56             }
57             Q.push(point[i]);
58         }
59         area = 0;
60         tmp = Q.top(), Q.pop();
61         area += (pos.x*tmp.y - pos.y*tmp.x) / 2.0;
62         while (!Q.empty()){
63             area += (tmp.x*Q.top().y - tmp.y*Q.top().x) / 2.0;
64             tmp = Q.top();
65             Q.pop();
66         }
67         printf("%.1lf\n", fabs(area));
68     }
69     return 0;
70 }