POJ 1696 - Space Ant

Posted 2020-08-14

Technorati Tags: POJ,计算几何,凸包

初学计算几何，引入polygon后的第一个挑战——凸包

此题可用凸包算法做，只要把压入凸包的点从原集合中排除即可，最终形成图形为螺旋线。

关于凸包，具体可见凸包五法：http://blog.csdn.net/bone_ace/article/details/46239187

此处简述我O(nH)的Jarvis法(H: 凸包上点数)

过程较易于理解。

 

 1 //POJ1696
 2 //凸包变形
 3 //AC 2016.10.13
 4 
 5 #include "cstdio"
 6 #include "cstdlib"
 7 #include "iostream"
 8 #include "cmath"
 9 #define MAXN (55)
10 
11 struct point{
12     int num, x, y;
13     bool been;
14     point(){}
15     point(int X, int Y): x(X), y(Y), been(0){}
16     void input(){
17         scanf("%d%d%d", &num, &x, &y);
18         been = 0;
19     }
20     friend point operator >> (const point &p1, const point &p2){
21         return point(p2.x - p1.x, p2.y - p1.y);
22     }
23     friend int operator ^ (const point &p1, const point &p2){
24         return p1.x * p2.y - p1.y * p2.x;
25     }
26 }pt[MAXN];
27 
28 void swap(point &p1, point &p2){
29     point p = p1;
30     p1 = p2;
31     p2 = p;
32 }
33 
34 int main(){
35     int m, n;
36     freopen("fin.c", "r", stdin);
37     scanf("%d", &m);
38     while(m--){
39         scanf("%d", &n);
40         for(int i = 0; i < n; i++){
41             pt[i].input();
42             for (int j = i; j && (pt[j].y < pt[j - 1].y); j--){
43                 swap(pt[j - 1], pt[j]);
44             }
45         }
46         printf("%d %d", n, pt[0].num);
47         pt[0].been = 1;
48         int cur = 0;
49         while (1){
50             int tmp = 0;
51             for (int i = 0; i < n; i++)
52                 if (!pt[i].been){
53                     if (!tmp)
54                         tmp = i;
55                     else if (((pt[cur] >> pt[i]) ^ (pt[cur] >> pt[tmp])) >= 0)
56                         tmp = i;
57                 }
58             if (!tmp) break;
59             printf(" %d", pt[tmp].num);
60             pt[tmp].been = 1;
61             cur = tmp;
62         }
63         puts("");
64     }
65 }