def main():
rollingTotal = 1 # 1 ** 2 is special as it's palindromic, but it's only 1 number.
# so start the total at 1 to avoid special casiing in the algo.
palindromes = set([])
LIMIT = 10**8
END = int(floor((sqrt(4 - 4 * 2 * (1 - LIMIT)) + 2) /
4)) # solve x ** 2 + (x - 1) ** 2 = LIMIT
# this establishes the very last squared number
# that, when added to the 2nd-to-last squared number,
# produces a number < LIMIT.
for i in xrange(2, END + 1):
rollingTotal += i**2
if rollingTotal < LIMIT and isNumberPalindromic(rollingTotal):
palindromes.add(rollingTotal)
copyOfTotal = rollingTotal
for j in xrange(1, i - 1): # the sum is of at least two values.
copyOfTotal -= j**2
if copyOfTotal < LIMIT and isNumberPalindromic(copyOfTotal):
palindromes.add(copyOfTotal)
print "Sum of all palindromes:", sum(palindromes)
def main():
rollingTotal = 1 # 1 ** 2 is special as it's palindromic, but it's only 1 number.
# so start the total at 1 to avoid special casiing in the algo.
palindromes = set([])
LIMIT = 10 ** 8
END = int(floor((sqrt(4 - 4 * 2 * (1 - LIMIT)) + 2) / 4)) # solve x ** 2 + (x - 1) ** 2 = LIMIT
# this establishes the very last squared number
# that, when added to the 2nd-to-last squared number,
# produces a number < LIMIT.
for i in xrange(2, END + 1):
rollingTotal += i ** 2
if rollingTotal < LIMIT and isNumberPalindromic(rollingTotal):
palindromes.add(rollingTotal)
copyOfTotal = rollingTotal
for j in xrange(1, i - 1): # the sum is of at least two values.
copyOfTotal -= j ** 2
if copyOfTotal < LIMIT and isNumberPalindromic(copyOfTotal):
palindromes.add(copyOfTotal)
print "Sum of all palindromes:", sum(palindromes)
def main():
start = time()
solutions = set([])
for i in xrange(1, LIMIT):
if isNumberPalindromic(i) and isNumberPalindromic(str(bin(i))[2:]):
solutions.add(i)
print "Sum of solution set: ", sum(solutions)
end = time()
print "Runtime: ", end - start, " seconds."
def main():
start = time()
solutions = set([])
for i in xrange(1, LIMIT):
if isNumberPalindromic(i) and isNumberPalindromic(str(bin(i))[2:]):
solutions.add(i)
print "Sum of solution set: ", sum(solutions)
end = time()
print "Runtime: ", end - start, " seconds."
def main():
start = time()
solutionSet = set([])
numbersLeadingToPalindromes = set([])
for i in xrange(1, LIMIT):
iterationNumber = 0
candidate = i
possibleLychrel = True
iterationIntermediates = set([i])
while iterationNumber < ITERATION_LIMIT:
mirroredNumber = int(str(candidate)[::-1])
newCandidate = candidate + mirroredNumber
iterationIntermediates.add(newCandidate)
if newCandidate in numbersLeadingToPalindromes or isNumberPalindromic(newCandidate):
possibleLychrel = False
numbersLeadingToPalindromes |= iterationIntermediates
break
candidate = newCandidate
iterationNumber += 1
if possibleLychrel:
solutionSet.add(i)
end = time()
print "Potential Lychrel numbers < ", LIMIT, " : ", len(solutionSet)
print "Runtime: ", end - start, " seconds."
def main():
start = time()
solutionSet = set([])
numbersLeadingToPalindromes = set([])
for i in xrange(1, LIMIT):
iterationNumber = 0
candidate = i
possibleLychrel = True
iterationIntermediates = set([i])
while iterationNumber < ITERATION_LIMIT:
mirroredNumber = int(str(candidate)[::-1])
newCandidate = candidate + mirroredNumber
iterationIntermediates.add(newCandidate)
if newCandidate in numbersLeadingToPalindromes or isNumberPalindromic(
newCandidate):
possibleLychrel = False
numbersLeadingToPalindromes |= iterationIntermediates
break
candidate = newCandidate
iterationNumber += 1
if possibleLychrel:
solutionSet.add(i)
end = time()
print "Potential Lychrel numbers < ", LIMIT, " : ", len(solutionSet)
print "Runtime: ", end - start, " seconds."