#Project euler problem 329 "Prime Frog"

import proj_euler as pe

import numpy as np

cap = 500

croaks = "PPPPNNPPPNPPNPN"

#croaks = "PP"

max_depth = len(croaks)

denom = 500*6**max_depth/2

print "Total possibilities: " + str(denom)

primes,mask = pe.primes_and_mask(cap)

curr = np.ones(cap,dtype=np.int64)

for croak in croaks:

prev = curr

curr = np.ones(cap,dtype=np.int64)

#Count croaks multiplicities. For each path on a prime, P gets croaked twice

#For each on a non-prime, N gets croaked twice

if croak == "P":

for i in xrange(cap):

if mask[i+1]:

prev[i] *= 2

else:

for i in xrange(cap):

if not mask[i+1]:

prev[i] *= 2

#compute transitions

curr[1:cap-1] = prev[:cap-2] + prev[2:cap]

curr[0] = prev[1]

curr[cap-1] = prev[cap-2]

#double count the contributions from the end squares

curr[1] += prev[0]

curr[cap-2] += prev[cap-1]

num = np.sum(prev)

print "Total admissible possibilities " + str(num)

d = pe.gcd(denom,num)

print "Reduced fraction " + str(num/d) + "/" + str(denom/d)