import numpy as np
import scipy as scp

from matplotlib import pyplot as plt

from RubberBand import RubberBand

NUM_BANDS = int(1E5)
N = 100

length_dist = np.zeros((NUM_BANDS,))
for i in range(NUM_BANDS):
    band = RubberBand(N, a=1)
    length_dist[i] = band.length/band.a

P_true = lambda N, L: scp.special.binom(N, (L+N)/2) / 2**N
L_norm = np.linspace(-N, N, 100) # normalised (no Link length a) range

plt.plot(L_norm, P_true(N, L_norm))
plt.hist(length_dist, range=(-N, N), bins=N, density=True)
plt.xlabel("$L/a$")
plt.ylabel("P($L/a$)")
plt.show()