mirror of
https://github.com/jlengrand/project_euler.git
synced 2026-03-10 08:41:20 +00:00
a173f16dcb
Could be refactored a bit to avoid code redondance. Uses my list of primes numbers Performs calculations in less than one minute.
69 lines
2.0 KiB
Python
69 lines
2.0 KiB
Python
#!/usr/bin/env python
|
|
'''
|
|
Created on 10 feb. 2012
|
|
|
|
@author: Julien Lengrand-Lambert
|
|
|
|
DESCRIPTION: Solves problem 37 of Project Euler
|
|
The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.
|
|
|
|
Find the sum of the only eleven primes that are both truncatable from left to right and right to left.
|
|
|
|
NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
|
|
'''
|
|
import pickle
|
|
|
|
plist = pickle.load(open("primes_list.dup", "rb"))
|
|
|
|
def is_prime(val):
|
|
"""
|
|
Returns True if the number is prime
|
|
"""
|
|
return (val in plist)
|
|
|
|
def trunc_left(val):
|
|
"""
|
|
Returns true if the prime number is truncatable from left to right
|
|
"""
|
|
if not is_prime(val):
|
|
return False
|
|
if len(str(val)) == 1:
|
|
return True
|
|
else:
|
|
return trunc_left(int(str(val)[1:]))
|
|
|
|
def trunc_right(val):
|
|
"""
|
|
Returns true if the prime number is truncatable from left to right
|
|
"""
|
|
if not is_prime(val):
|
|
return False
|
|
if len(str(val)) == 1:
|
|
return True
|
|
else:
|
|
return trunc_right(int(str(val)[:-1]))
|
|
|
|
def trunc_primes():
|
|
"""
|
|
Returns the complete list of primes that are both truncatable from left to right and right to left
|
|
"""
|
|
# there we already have to 1 million.
|
|
inplist = list(plist)
|
|
out_list = []
|
|
|
|
for p in inplist:
|
|
if p > 11:
|
|
if (trunc_left(p) and trunc_right(p)):
|
|
print "Found one : %d" %(p)
|
|
out_list.append(p)
|
|
|
|
if len(out_list) > 10 : #already found them all
|
|
return out_list
|
|
|
|
print "End of the line. Should go higher than one million !"
|
|
return out_list
|
|
|
|
if __name__ == '__main__':
|
|
# We know that there are only 11 of them. Lets try to find them
|
|
print trunc_primes()
|
|
print "Answer : %d " % (sum(trunc_primes())) |