<reponame>lcsm29/project-euler<filename>py/py_0392_enmeshed_unit_circle.py<gh_stars>0
# Solution of;
# Project Euler Problem 392: Enmeshed unit circle
# https://projecteuler.net/problem=392
# 
# A rectilinear grid is an orthogonal grid where the spacing between the 
# gridlines does not have to be equidistant. An example of such grid is 
# logarithmic graph paper. Consider rectilinear grids in the Cartesian 
# coordinate system with the following properties:The gridlines are parallel 
# to the axes of the Cartesian coordinate system. There are N+2 vertical and 
# N+2 horizontal gridlines. Hence there are (N+1) x (N+1) rectangular cells. 
# The equations of the two outer vertical gridlines are x = -1 and x = 1. The 
# equations of the two outer horizontal gridlines are y = -1 and y = 1. The 
# grid cells are colored red if they overlap with the unit circle, black 
# otherwise. For this problem we would like you to find the positions of the 
# remaining N inner horizontal and N inner vertical gridlines so that the area 
# occupied by the red cells is minimized. E. g. here is a picture of the 
# solution for N = 10:The area occupied by the red cells for N = 10 rounded to 
# 10 digits behind the decimal point is 3. 3469640797. Find the positions for 
# N = 400. Give as your answer the area occupied by the red cells rounded to 
# 10 digits behind the decimal point.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 392
    timed.caller(dummy, n, i, prob_id)
