Finding the largest palindrome of the product of two 3-digit numbers in Python

Question

So the challenge I'm trying to solve is to find the largest palindrome made from the product of two 3-digit numbers. I'm new to Python and so my code is not elegant or refracted yet, but there is a logical error that I can't seem to find.

def ispalindrome(n):
    rev_n = str(n)[::-1]
    if n == rev_n:
        return True
    else:
        return False


first_num = 100
second_num = 100
mylist=[]
while first_num < 1000:
    while second_num < 1000:
        item = first_num * second_num
        mylist.append(item)
        second_num += 1
    second_num = 100
    first_num +=1
# print (mylist)
num_as_string = []
for i in mylist:
    i = str(i)
    num_as_string.append(i)
print("Total products of two 3-digit numbers: {}").format(len(num_as_string))
print("-----------------------------------------------------")

def convert_to_num_list(string_list):
    new_num_list = []
    item = int(string_list)
    new_num_list.append(item)
    return new_num_list



palindrome_list = []

for j in num_as_string:
    if ispalindrome(j) == True:
        palindrome_list.append(j)
        palindrome_list.sort()
        # print(palindrome_list)
        x = convert_to_num_list(j)
        largest_palindrome = max(x)

print("Total palindroms of product of two 3-digit numers: {}").format(len(palindrome_list))

print("Largest palindrome = {}").format(largest_palindrome)

The problem is that I'm getting the largest palindrome as 580085, which is 995*583 but is NOT the largest palindrome. I believe the largest palindrome is 906609, which is 993*913, but my code is not finding this. Can anyone help me with the flaw in my logic?

Answer 1

Your code does a lot of unnecessary conversion between numbers and strings, which made the error hard to find. The only place in the code that needs a string representation is when determining if the number is a palindrome or not. So that should be the only place that the code does the conversion.

The logic error is in your function convert_to_num_list(). It takes a string representation of one number and returns a 1-list containing that number. So, "123321" gets returned as [123321]. You then take the max() of that 1-list, which is always the value that was passed to convert_to_num_list(). So the code never keeps the largest value because if a smaller value comes in later it will be overwritten. The code reports 995*583 as the largest because it comes in later than 993*913, which in turn is because 995 > 993.

You can fix that error with an if statement, but the program is overcomplicated and may well contain other bugs. I recommend reducing the code to the essential task of producing the largest palindrome, without printing out the intermediate results, because the simpler the code the easier it is to see a logic error.

def ispalindrome(n):
    return str(n) == str(n)[::-1]

mylist=[]
for first_num in range(100,1000):
    for second_num in range(100,1000):
        item = first_num*second_num
        if ispalindrome(item):
            mylist.append(item)
print(max(mylist))

This gives your expected answer:

906609