Surround the Trees

  1 /*
  2 2015.5
  3 Surround the Trees
  4 
  5 */
  6 
  7 #include<iostream>
  8 #include<math.h>
  9 #include<stdlib.h>
 10 #define MAXD 110
 11 using namespace std;
 12 
 13 typedef struct
 14 {
 15     double x, y;
 16 }point; 
 17 point Tree[MAXD], Result[MAXD];
 18 int N, P;
 19 
 20 /*
 21 叉乘
 22 P1 x P2
 23     >0 : P1 is clockwise from P2 with respect to (0,0)
 24     <0 : counterclockwise (即P1在P2左边)
 25     =0 : collinear
 26 */
 27 double cross(double x1, double y1, double x2, double y2)
 28 {
 29     return x1 * y2 - x2 * y1;
 30 }
 31 
 32 // 按 y坐标从低到高排序，若 y相等则按 x坐标排序
 33 int cmp(const void *_p, const void *_q)
 34 {
 35     point *p = (point *)_p, *q = (point *)_q;
 36     if (p->y == q->y)
 37         return p->x < q->x ? -1 : 1;
 38 
 39     return p->y < q->y ? -1 : 1;
 40 }
 41 
 42 double Distance(double x, double y, double x1, double y1)
 43 {
 44     double temp1 = (x - x1)*(x - x1);
 45     double temp2 = (y - y1)*(y - y1);
 46     return sqrt(temp1+temp2);
 47 }
 48 
 49 double sqr(double x)
 50 {
 51     return x * x;
 52 }
 53 
 54 // 是否删除
 55 int del(int top, int i)
 56 {
 57     if (cross(Result[top].x - Result[top - 1].x, Result[top].y - Result[top - 1].y,
 58         Tree[i].x - Result[top].x, Tree[i].y - Result[top].y) < 0)
 59         return 1;
 60     return 0;
 61 }
 62 
 63 int graham()
 64 {
 65     int i, mint, top = 1;
 66     Result[0] = Tree[0];
 67     Result[1] = Tree[1];
 68     for (i = 2; i < N; i++)
 69     {
 70         while (top && del(top, i))
 71             --top;
 72         Result[++top] = Tree[i];
 73     }
 74     mint = top;
 75     Result[++top] = Tree[N - 2];
 76     for (i = N - 3; i >= 0; i--)
 77     {
 78         while (top != mint && del(top, i))
 79             --top;
 80         Result[++top] = Tree[i];
 81     }
 82     return top;
 83 }
 84 
 85 int main()
 86 {
 87     int i;
 88     double sum;
 89     while (1)
 90     {
 91         cin >> N;
 92         if (!N)
 93             break;
 94 
 95         for (i = 0; i < N; i++)
 96             cin >> Tree[i].x >> Tree[i].y;
 97         
 98         // 快排
 99         qsort(Tree, N, sizeof(Tree[0]), cmp);
100         sum = 0;
101 
102         if (N == 1)
103             cout << "0.00\n";
104         else if (N == 2)
105         {
106             sum = Distance(Tree[0].x,Tree[0].y,Tree[1].x,Tree[1].y);
107             cout << sum << endl;
108         }
109         else
110         {
111             P = graham();
112             for (i = 0; i < P; i++)
113                 sum += Distance(Result[i].x, Result[i].y, Result[i + 1].x, Result[i + 1].y);
114             cout << sum << endl;
115         }
116     }
117     
118     return 0;
119 }