"""euler4.py

 https://projecteuler.net/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.

in python class | Oct 29 2019
"""

def is_palindrome(number):
    """ return True if number is a palindrome base 10 
        >>> is_palindrome(123)
        False
        >>> is_palindrome(121)
        True
    """
    n_str = str(number)
    n_reverse = n_str[::-1]
    return n_str == n_reverse

def search(low, high):
    """ search for a,b between low an high
        to find palidrome with largest a*b 
        >>> search(10, 99)
        (91, 99)
    """
    best_product = 1
    best_a = 0
    best_b = 0
    for a in range(low, high+1):
        for b in range(a, high+1):
            product = a*b
            #print("a={}, b={}, product={}".format(a,b,product))
            if is_palindrome(product):
                #print("  palindrome! ")
                if product > best_product:
                    #print(" NEW BEST ")
                    best_product = product
                    best_a = a
                    best_b = b
    return (best_a, best_b)

def main():
    print(" -- project euler 4 --")
    (a, b) = search(100, 999)
    print("a, b = ", a, b)

if __name__ == '__main__':
    import doctest
    doctest.testmod()
    main()