import random as rd
import math as mt
import matplotlib.pyplot as plt


## count how many lines you've crossed

def find_int_between(x,y):
    if y > x:
        return max(0,mt.ceil(y) - mt.floor(x)-1)
    else:
        return max(0, mt.ceil(x) - mt.floor(y)-1)


## set this to whatever
distance = 1
n = 100
success = 0

for i in range(n):

    x = rd.random()*10000
    y = rd.random()*10000

    start_pt = [x,y]

    angle = rd.uniform(0, 360)
    x_1 = x + distance * mt.cos(angle)
    y_1 = y + distance * mt.sin(angle)

    end_pt = [x_1,y_1]

    distance_check = mt.sqrt(((start_pt[0]-end_pt[0])**2)+((start_pt[1]-end_pt[1])**2) )

    x_axis_cross = find_int_between(end_pt[0],(start_pt[0]))
    y_axis_cross = find_int_between(end_pt[1],(start_pt[1]))

    ## number of lines crossed
    total_cross = abs(x_axis_cross) + abs(y_axis_cross)
    if total_cross == 1:
        success+=1
    # print(total_cross)

print(success)
print(success/n)
## check
# print(start_pt)
# print(distance_check)
# print(end_pt)
# print(angle)

## check to visualize what you're doing

# x = [start_pt[0],end_pt[0]]
# y = [start_pt[1],end_pt[1]]
# plt.plot(x, y)
# plt.grid(True)
# plt.show()