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problems/004_problem.py

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+
+#  Problem 3:
+#
+#  A palindromic number reads the same both ways. 
+#  The largest palindrome made from the product 
+#  of two 2-digit numbers is 9009 = 91 × 99.
+#  
+#  Find the largest palindrome made from the 
+#  product of two 3-digit numbers.
+#
+
+import decorators
+import time
+
+# Create function that finds the next
+# prime number when supplied with an
+# intitial integer.
+
+def is_palindrome(candidate):
+	"""
+	Returns a boolean to confirm if the passed
+	integer is a palindrome.
+	
+		is_palindrome(candidate)
+
+			param 'candidate': Integer to test for palindrom-iness.
+			
+	"""
+
+	# Convert maximum candidate to a list ...
+	listed_candidate = [int(i) for i in str(candidate)]
+	flipped_candidate = [int(i) for i in str(candidate)]
+	#print("{}".format(listed_candidate))
+
+	# Determine length of maximum candidate, and manipulate.	
+	num_digits = listed_candidate.__len__()
+	digit_flips = int(num_digits/2)
+
+	for i in range(1,digit_flips):
+		#print("{}".format(i))
+		flipped_candidate[-i-1] = flipped_candidate[i]
+	flipped_candidate[-1] = flipped_candidate[0]
+
+	#print("{}".format(flipped_candidate))
+
+	# Compare ...		
+	if listed_candidate == flipped_candidate:
+		return True
+	else:
+		return False
+
+@decorators.function_timer
+def main():
+
+	# Define the problem inputs... 
+	factor_length = 3
+	
+	# Calculate intermediate inputs...
+	max_factor = 10**(factor_length)-1
+	product_of_factors = max_factor * max_factor # Maximum candidate for palindrome test. 
+	
+	# Initialize loop parameters...
+	n = max_factor
+	m = max_factor
+	n_has_token = False
+	test_passed = False
+	palindrome_list=[]
+
+	while (n*m)>0:
+	
+		# Test for "palindrom-iness" ...
+		print("{} * {} = {}".format(n,m,n*m))
+		test_passed = is_palindrome(n*m)
+#		if not test_passed and n_has_token:	
+#			n -= 1
+#			if n == 1:
+#				n_has_token = False
+#				n = max_factor
+#		elif not test_passed and not n_has_token:
+#			m -= 1
+#			n_has_token = True
+#		else:
+#			palindrome_list.append(n*m)
+#
+		if test_passed:
+			palindrome_list.append(n*m)
+			if n_has_token:
+				n -= 1
+				if n ==1:
+					n_has_token = False
+					n = max_factor
+			if not n_has_token:
+				m -= 1
+				n_has_token = True
+		
+		if not test_passed:
+			if n_has_token:
+				n -= 1
+				if n ==1:
+					n_has_token = False
+					n = max_factor
+			if not n_has_token:
+				m -= 1
+				n_has_token = True
+
+
+			
+
+		
+	print("{}".format(max(palindrome_list)))
+#	print("{} * {} = {}".format(n,m,n*m))
+
+#	print("The largest palindrome number which is a product of two numbers of length {} is {} ... ".format(num_digits,num_digits))
+
+
+
+main()