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Project Euler Problem 68
from itertools import permutations
from itertools import combinations
# array of candidate solutions empty at the beginning
record = []
# choose 5 numbers for inner cells between 1 and 9; there are 9C5 combinations
# the problem ask for a 16-digit number, so 10 is not to be included in inner cells
cells = range(1,10)
inner_cells = [map(int,comb) for comb in combinations(cells,5)]
# code to calculate min and max couple in an array
def minCouple(array):
answer = array[0]+array[-1]
for i in xrange(len(array)-1):
coupleSum = array[i] + array[i+1]
if coupleSum < answer:
answer = coupleSum
return answer
def maxCouple(array):
answer = 0
for i in xrange(len(array)-1):
if i==0:
coupleSum = array[0]+ array[-1]
if coupleSum > answer:
answer = coupleSum
coupleSum = array[i]+ array[i+1]
if coupleSum > answer:
answer = coupleSum
return answer
# Algorithm
for array in inner_cells:
pivot = array[0]
perm_array = array[1:]
perms = [map(int,perm) for perm in permutations(perm_array,4)]
for perm in perms:
checkArray = perm
outerRing = [el for el in range(1,11) if el not in checkArray]
xMax = minCouple(checkArray) + max(outerRing)
xMin = maxCouple(checkArray) + min(outerRing)
if xMax >= xMin:
for x in xrange(xMin, xMax+1):
i = checkArray[0]
j = checkArray[1]
k = checkArray[2]
l = checkArray[3]
m = checkArray[4]
alpha = x-i-j
beta = x-j-k
gamma = x-k-l
delta = x-l-m
theta = x-m-i
outerCalculated = [alpha, beta, gamma, delta, theta]
if sorted(outerCalculated) == sorted(outerRing):
a = [alpha, i, j]
b = [beta, j, k]
c = [gamma, k, l]
d = [delta, l, m]
e = [theta, m, i]
min_val = min(alpha, beta, gamma, delta, theta)
if alpha == min_val:
append = a+b+c+d+e
elif beta == min_val:
append = b+c+d+e+a
elif gamma == min_val:
append = c+d+e+a+b
elif delta == min_val:
append = d+e+a+b+c
elif theta == min_val:
append = e+a+b+c+d
l = [str(i) for i in append]
s = ''.join(l)
integer_list = int(s)
print max(record)
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