Solved problem 4

0004-palindrome.py

@@ -0,0 +1,41 @@
+"""
+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
+"""
+def traditional():
+    """
+    Nothing fancy in this function, just checks for palindromes
+    """
+    palindromes = []
+    for i in range(999, 100, -1):
+        for j in range(i, 100, -1):
+            product = i * j
+            product_str = str(product)
+            if product_str == product_str[::-1]:
+                palindromes.append(product)
+    return max(palindromes)
+
+def a_little_step_up():
+    """
+    Tiny optimizations over the previous approach
+    """
+    palindromes = []
+    for i in range(999, 100, -1):
+        if i % 11 == 0:
+            # If i is divisible by 11, check for all j's
+            x = range(i, 100, -1)
+        else:
+            # If i is not divisible by 11, check for all j's divisible by 11
+            x = range(i - (i % 11), 100, -11)
+
+        for j in x:
+            product = i * j
+            product_str = str(product)
+            if product_str == product_str[::-1]:
+                palindromes.append(product)
+    return max(palindromes)
+
+
+print "Answer by traditional method: ", traditional()
+print "Answer by optimized method: ", a_little_step_up()