from buckets import fill_buckets
from sympy import init_printing
from solvers import *
import warnings
warnings.filterwarnings('ignore')
init_printing()

# returns a length-(n+1) array <sizes>, where sizes[i] represents
# the expected number of sequences which do not park at spot i=0,...,n.
n = 3
fill_buckets(n, "pmf")

# returns a length-n array <sizes>, where sizes[i] represents
# the expected number of sequences which bump i=0,...,n-1 times
n = 3
fill_buckets(n, "bumps")

## Research Paper Outline

recurrence(4)

print_polynomial(4)

sums_of_products(4)

balls_bins(3)