0 30
-25.9807621135 -15
25.9807621135 -15

3.711537444785714 10.714285714285715
-11.134612334357143 -2.142857142857144
7.423074889571431 -8.571428571428571
18.557687223928568 23.57142857142857
-29.69229955828571 4.285714285714285
11.134612334357145 -27.857142857142854

#!python3
s = """0 30
-25.9807621135 -15
25.9807621135 -15
3.711537444785714 10.714285714285715
-11.134612334357143 -2.142857142857144
7.423074889571431 -8.571428571428571
18.557687223928568 23.57142857142857
-29.69229955828571 4.285714285714285
11.134612334357145 -27.857142857142854"""

import matplotlib.pyplot as plt
from math import cos, sin, pi
fig = plt.figure()
ax = fig.add_subplot(111,aspect='equal')

r=[[float(a) for a in p.split()] for p in s.split("\n")]
def d(a,b): return (r[a][0]-r[b][0])**2 + (r[a][1]-r[b][1])**2
def z(a,b): return abs(a-b) < 1e-6

a = 0
for i in range(len(r)):
    for j in range(i+1,len(r)):
        for k in range(j+1,len(r)):
            if z(d(i,j),d(i,k)) and z(d(i,j),d(j,k)) and z(d(j,k),d(i,k)):
                a += 1
                x = [r[t][0] + 0.5*cos(2*pi*a/9) for t in (i,j,k,i)]
                y = [r[t][1] + 0.5*sin(2*pi*a/9) for t in (i,j,k,i)]
                plt.plot(x, y, '-')
for p in r: plt.plot(p[0],p[1],'bo')
plt.grid()
plt.show()
print(a)

Can somebody give some tests?
 Thank you..

as topic says^^

Very beautiful problem and very easy to solve it using simple geometric methods of working with vectors and points.

Pay attention to output:
In the first three lines output the coordinates of the points put INSIDE the triangle. In the following three lines output the coordinates of the points put OUTSIDE the triangle.

Edited by author 15.02.2010 18:39

I got WA on 1 test. On sample input my program gives this answer
0.000000000 0.000000000
0.000000000 -30.000000000
25.980762114 15.000000000
-25.980762114 15.000000000
-2.886751346 -5.000000000
2.886751346 -5.000000000
is it true?

can more than 9 3andls be??

If I have a point lie on an edge of triangle, then move it by very small distance, is it considered inside the triangle

[solution cut]

But I got WA1.
What did I misunderstand?

Edited by author 03.11.2008 23:24

Edited by author 03.11.2008 23:24

Edited by author 04.11.2008 05:20

Edited by author 04.11.2008 05:21

Edited by moderator 05.11.2008 14:57

take sample output and
map it affinly to data triangle and you will have AC

Can those points lie on the sides of the triangle?