POJ 1696 - Space Ant 凸包的变形

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。

 //POJ1696
 //凸包变形
 //AC 2016.10.13

 #include "cstdio"
 #include "cstdlib"
 #include "iostream"
 #include "cmath"
 #define MAXN (55)

 struct point{
     int num, x, y;
     bool been;
     point(){}
     point(int X, int Y): x(X), y(Y), been(){}
     void input(){
         scanf("%d%d%d", &num, &x, &y);
         been = ;
     }
     friend point operator >> (const point &p1, const point &p2){
         return point(p2.x - p1.x, p2.y - p1.y);
     }
     friend int operator ^ (const point &p1, const point &p2){
         return p1.x * p2.y - p1.y * p2.x;
     }
 }pt[MAXN];

 void swap(point &p1, point &p2){
     point p = p1;
     p1 = p2;
     p2 = p;
 }

 int main(){
     int m, n;
     freopen("fin.c", "r", stdin);
     scanf("%d", &m);
     while(m--){
         scanf("%d", &n);
         for(int i = ; i < n; i++){
             pt[i].input();
             for (int j = i; j && (pt[j].y < pt[j - ].y); j--){
                 swap(pt[j - ], pt[j]);
             }
         }
         printf("%d %d", n, pt[].num);
         pt[].been = ;
         int cur = ;
         while (){
             int tmp = ;
             for (int i = ; i < n; i++)
                 if (!pt[i].been){
                     if (!tmp)
                         tmp = i;
                     else if (((pt[cur] >> pt[i]) ^ (pt[cur] >> pt[tmp])) >= )
                         tmp = i;
                 }
             if (!tmp) break;
             printf(" %d", pt[tmp].num);
             pt[tmp].been = ;
             cur = tmp;
         }
         puts("");
     }
 }