POJ2194 Stacking Cylinders（向量旋转）

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <algorithm>
 4 #include <cmath>
 5 #include <cstring>
 6 using namespace std;
 7 
 8 const int N = 12;
 9 const double EPS = 1e-10;        //精度系数
10 const double PI = acos(-1.0);    //π
11 
12 struct Point {
13     double x, y;
14     Point(double x = 0, double y = 0) :x(x), y(y) {}
15     const bool operator < (Point A)const {
16         return x == A.x ? y < A.y : x < A.x;
17     }
18 };    //点的定义
19 
20 typedef Point Vector;    //向量的定义
21 
22 Vector operator + (Vector A, Vector B) { return Vector(A.x + B.x, A.y + B.y); }    //向量加法
23 Vector operator - (Vector A, Vector B) { return Vector(A.x - B.x, A.y - B.y); }    //向量减法
24 Vector operator * (Vector A, double p) { return Vector(A.x*p, A.y*p); }        //向量数乘
25 
26 int dcmp(double x) {
27     if (fabs(x) < EPS)return 0; else return x < 0 ? -1 : 1;
28 }    //与0的关系
29 
30 Vector Rotate(Vector A, double rad) {
31     return Vector(A.x*cos(rad) - A.y*sin(rad), A.x*sin(rad) + A.y*cos(rad));
32 }    //逆时针旋转rad度
33 
34 double Dot(Vector A, Vector B) { return A.x*B.x + A.y*B.y; }    //向量点乘
35 double Length(Vector A) { return sqrt(Dot(A, A)); }    //向量长度
36 
37 Point Up(Point A, Point B) {
38     Vector v = B - A;
39     double L = Length(v), rad = acos(L / 4);
40     Vector u = Rotate(v, rad);
41     return A + u*(2 / L);
42 }
43 
44 int main() {
45     int n;
46     Point P[N][N];
47     while (cin >> n && n) {
48         for (int i = 0; i < n; ++i)
49             scanf("%lf", &P[0][i].x), P[0][i].y = 1;
50         sort(P[0], P[0] + n);
51         for (int i = 1; i < n; ++i)
52             for (int j = 0; j < n - i; ++j)
53                 P[i][j] = Up(P[i - 1][j], P[i - 1][j + 1]);
54         printf("%.4lf %.4lf\n", P[n - 1][0].x, P[n - 1][0].y);
55     }
56 }