/
problem329.py
executable file
·58 lines (50 loc) · 2 KB
/
problem329.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
#!/usr/bin/env python3
########################################################################
# Solves problem 329 from projectEuler.net.
# Calculates the probability of a series of croaks.
# Copyright (C) 2011 Santiago Alessandri
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# You can contact me at san.lt.ss@gmail.com
# Visit my wiki at http://wiki.san-ss.com.ar
# Visit my blog at http://blog.san-ss.com.ar
########################################################################
from CommonFunctions import find_primes_less_than
from fractions import Fraction
d = {}
primes = set(find_primes_less_than(501))
for i in range(1, 501):
if i in primes:
d[(i, 'P')] = Fraction(2, 3)
d[(i, 'N')] = Fraction(1, 3)
else:
d[(i, 'P')] = Fraction(1, 3)
d[(i, 'N')] = Fraction(2, 3)
def calc_prob(i, string):
if (i, string) in d:
return d[(i, string)]
if (i == 1):
prob = d[(i, string[0])] * calc_prob(i + 1, string[1:])
elif (i == 500):
prob = d[(i, string[0])] * calc_prob(i - 1, string[1:])
else:
prob = d[(i, string[0])] * (calc_prob(i + 1, string[1:]) * Fraction(1, 2) + calc_prob(i - 1, string[1:]) * Fraction(1, 2))
d[(i, string)] = prob
return prob
if __name__ == '__main__':
result = Fraction(0, 1)
for i in range(1, 501):
result += calc_prob(i, 'PPPPNNPPPNPPNPN')
print("The result is:", result / 500)