import numpy as np

def buffon$\_$needle$\_$simulation$($num$\_$tries, seed$)$:

np$.$random.seed$($seed$)$

# Length of the needle

needle$\_$length $=1\mathrm{.}0$

# Distance between the lines

line$\_$distance $=1\mathrm{.}0$

num$\_$crosses $=0$

for $\_$ in range$($num$\_$tries$)$:

# Drop the needle

center$\_$position $=$ np$.$random.uniform$(0,$ line$\_$distance $/2)$

angle $=$ np$.$random.uniform$(0,$ np$.$pi $/2)$

# Check if the needle crosses a line

if center$\_$position $<=($needle$\_$length $/2)*$ np$.$sin$($angle$)$:

num$\_$crosses $+=1$

# Use Buffon's needle formula to approximate pi

pi$\_$approximation $=(2*$ needle$\_$length $*$ num$\_$tries$)/($num$\_$crosses $*$ line$\_$distance$)$

return pi$\_$approximation

# Example usage

seed $=123$

num$\_$tries $=1000000$ # Number of times the needle is dropped

pi$\_$approx $=$ buffon$\_$needle$\_$simulation$($num$\_$tries, seed$)$

print$($f$"$Approximation for pi with seed $\{$seed$\}$: $\{$pi$\_$approx$\}")$