POJ1696 Space Ant（贪心、向量叉乘、向量极角、线段相交、点在线段上）

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <algorithm>
 4 #include <cstring>
 5 #include <cmath>
 6 using namespace std;
 7 
 8 const double EPS = 1e-10;    //精度系数
 9 const int INF = 0x3f3f3f3f;
10 const double PI = acos(-1.0);
11 const int N = 55;
12 
13 struct Point {
14     double x, y;
15     Point(double x = 0, double y = 0) :x(x), y(y) {}
16 };    //点的定义
17 
18 typedef Point Vector;    //向量的定义
19 
20 Vector operator - (Vector A, Vector B) { return Vector(A.x - B.x, A.y - B.y); }    //向量减法
21 
22 int dcmp(double x) {
23     if (fabs(x) < EPS)return 0; else return x < 0 ? -1 : 1;
24 }    //与0的关系
25 
26 double Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; }    //向量叉乘
27 double Dot(Vector A, Vector B) { return A.x*B.x + A.y*B.y; }    //向量点乘
28 double Length(Vector A) { return sqrt(Dot(A, A)); }    //向量长度
29 
30 double Angle(Vector A, Vector B) {
31     double ans = atan2(A.y, A.x) - atan2(B.y, B.x);
32     return ans + (ans < 0 ? 2 * PI : 0);
33 }    //向量夹角（ 范围[0, 2π) ）
34 
35 bool SegmentProperIntersection(Point& a1, Point& a2, Point& b1, Point& b2) {
36     double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1),
37         c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1);
38     return dcmp(c1)*dcmp(c2) < 0 && dcmp(c3)*dcmp(c4) < 0;
39 }    //判断两线段相交（恰有一个公共点且不在端点）
40 
41 bool OnSegment(Point& p, Point& a1, Point& a2) {
42     return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) < 0;
43 }    //判断点是否在一条线段上（不含端点）
44 
45 int n, index[N], best, ans[N], res[N];
46 Point P[N];
47 bool vis[N];
48 
49 bool ok(int cur, int next, int now) {
50     Point last(0, P[res[0]].y);
51     for (int i = 0; i < cur; ++i) {
52         if (SegmentProperIntersection(last, P[res[i]], P[now], P[next])
53             || OnSegment(P[res[i]], P[now], P[next]))return false;
54         last = P[res[i]];
55     }
56     return true;
57 }
58 
59 void solve(int cur, int id, Vector v) {
60     double MIN = INF, L = INF;
61     int next = 0;
62     for (int i = 1; i <= n; ++i)if (!vis[i]) {    //如果没有访问过
63         double agl = Angle(P[i] - P[id], v);    //夹角
64         if (agl >= PI || !ok(cur, i, id))continue;    //保证方向，且与之前线段不相交
65         if (agl < MIN || (dcmp(agl - MIN) == 0 && Length(P[i] - P[id]) < L))    //扫描夹角最小的
66             MIN = agl, next = i, L = Length(P[i] - P[id]);
67     }
68     if (next) {
69         vis[next] = true;
70         res[cur] = next;
71         solve(cur + 1, next, P[next] - P[id]);
72         vis[next] = false;
73     } else if (cur > best) {    //不能再继续
74         best = cur;
75         memcpy(ans, res, sizeof(ans));
76     }
77 }
78 
79 int main() {
80     int t;
81     cin >> t;
82     while (t--) {
83         memset(vis, 0, sizeof(vis));
84         best = 0;
85         cin >> n;
86         double tmp = INF;
87         int m;
88         for (int i = 1; i <= n; ++i) {
89             scanf("%d%lf%lf", &index[i], &P[i].x, &P[i].y);
90             if (P[i].y < tmp) { tmp = P[i].y, m = i; }    //找到y坐标最小的点
91         }
92         vis[m] = true;
93         res[0] = m;
94         solve(1, m, Vector(P[m].x, 0));
95         printf("%d", best);
96         for (int i = 0; i < best; ++i)printf(" %d", index[ans[i]]);
97         printf("\n");
98     }
99 }