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Koch Curve
http://acm.zju.edu.cn/show_problem.php?pid=1575
Time limit: 1 Seconds
Memory limit: 32768K
Koch Curve is very common in fractal. It has infinite length. The figure above illustrates the creation of a Koch Curve. A line segment L1 (a->d) is given. It is cut into three equal parts. L2 is obtained by rotating the middle part counter-clockwise to vector s->d. The length satisfies the constraint p0p1 = p1p2 = p2p3 = p3p4. We further process on p0->p1, p1->p2, p2->p3, p3->p4 to obtain L3. We proceed with such iteration to obtain Koch Curve. Since the length is increased by 4/3 each iteration, the length of Koch Curve is infinite. With given s and d, you are to provide the result of the n-th iteration.
1. Input
There are multiple tests, in each test.
The first line contains an integer n (1 <= n <= 7).
The second line contains four floating numbers sx, sy, dx, dy.
2. Output
For each test print the vertex in the order from s to d. Keep two digits after decimal point.
Print a blank line after each case.
3. Sample Input
1 0 0 3 0 1 3 0 0 0
4. Sample Output
0.00 0.00 1.00 0.00 1.50 0.87 2.00 0.00 3.00 0.00 3.00 0.00 2.00 0.00 1.50 -0.87 1.00 0.00 0.00 0.00
Author: DU, Peng
Problem Source: ZOJ Monthly, April 2003
1 /*Written by czk*/
2 #include <iostream>
3 #include <iomanip>
4 using namespace std;
5
6 void koch(int n, double sx, double sy, double dx, double dy, bool print) {
7 if(n < 0) return;
8 double x1 = (sx * 2+ dx) / 3;
9 double y1 = (sy * 2+ dy) / 3;
10
11
12 double x2 = ( sx + 2 * dx) / 3;
13 double y2 = ( sy + 2 * dy) / 3;
14
15 double xm = x1 + 0.5*(x2-x1) - 1.7320508075688772935274463415059/2*(y2-y1);
16 double ym = y1 + 1.7320508075688772935274463415059/2 * (x2 - x1) + 0.5 * (y2-y1);
17
18 koch(n-1, sx, sy, x1, y1, true);
19 koch(n-1, x1, y1, xm, ym, true);
20 koch(n-1, xm, ym, x2, y2, true);
21 koch(n-1, x2, y2, dx, dy, false);
22 if(print)
23 cout <<setprecision(2)<< fixed<< dx << " "<< dy << '\n';
24 }
25
26 int main() {
27 while(1) {
28 int n;
29 double sx, sy, dx, dy;
30 cin >> n >> sx >> sy >> dx >> dy;
31 if(cin.eof())
32 break;
33 cout <<setprecision(2)<< fixed<< sx << " "<< sy << '\n';
34 koch(n, sx, sy, dx, dy, true);
35 cout << endl;
36 }
37 }