Problem 2: Symmetry [Brian Dean, 2012]
After taking a modern art class, Farmer John has become interested in
finding geometric patterns in everything around his farm. He carefully
plots the locations of his N cows (2 <= N <= 1000), each one occupying a
distinct point in the 2D plane, and he wonders how many different lines of
symmetry exist for this set of points. A line of symmetry, of course, is a
line across which the points on both sides are mirror images of each-other.
Please help FJ answer this most pressing geometric question.
PROBLEM NAME: symmetry
INPUT FORMAT:
* Line 1: The single integer N.
* Lines 2..1+N: Line i+1 contains two space-separated integers
representing the x and y coordinates of the ith cow (-10,000
<= x,y <= 10,000).
SAMPLE INPUT (file symmetry.in):
4
0 0
0 1
1 0
1 1
INPUT DETAILS:
The 4 cows form the corners of a square.
OUTPUT FORMAT:
* Line 1: The number of different lines of symmetry of the point set.
SAMPLE OUTPUT (file symmetry.out):
4
OUTPUT DETAILS:
There are 4 lines of symmetry -- one vertical, one horizontal, and two
diagonal.