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problems/004_problem/004_problem.py

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+#!/usr/bin/env python
+
+#  Problem 4:
+#
+#  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
+
+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)]
+	
+	# 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):
+		flipped_candidate[-i-1] = flipped_candidate[i]
+	flipped_candidate[-1] = flipped_candidate[0]
+
+	# Compare if the flipped version and the original
+	# candidate are identical.
+	# The function returns this test result...		
+	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
+	
+	# Initialize loop parameters...
+	n = max_factor
+	m = max_factor
+	n_has_token = False
+	test_passed = False
+	palindrome_list=[]
+	
+
+	while (n*m)>1:
+	
+		# Loop over all possible pairs of
+		# integers, testing for "palindrom-iness" ...
+		print("{} * {} = {}".format(n,m,n*m))
+		test_passed = is_palindrome(n*m)
+
+		if test_passed:
+			palindrome_list.append(n*m)
+			if n_has_token:
+				n -= 1
+				if n ==0:
+					n_has_token = False
+					n = m-1
+			if not n_has_token:
+				m -= 1
+				if m ==1:
+					n_has_token = True
+					m = n-1
+
+		
+		if not test_passed:
+			if n_has_token:
+				n -= 1
+				if n ==0:
+					n_has_token = False
+					n = m-1
+			if not n_has_token:
+				m -= 1
+				if m ==1:
+					n_has_token = True
+					m = n-1
+
+	print("The largest palindrome number which is a product of two numbers of length {} is {} ... ".format(factor_length,max(palindrome_list)))
+
+main()