0

Here is slow brute force way to find the largest palindromic product of three digit integers. You could do loop and break out of it if you go under the smaller number (the second one) of best solution found so far to be more efficient etc.

Edited by pyTony

def pali(a):
    return str(a) == str(a)[::-1]

print('Biggest palindromic product of two three digit integers is %i, which is %i * %i.' % 
       max((a*b, a, b) for a in range(999, 100, -1) for b in range(a, 100000//a, -1) if pali(a*b)))
""" Output:
Biggest palindromic product of two three digit integers is 906609, which is 993 * 913.
"""

Specialties:
IT/Science/Contracts/Religious translation/interpreting FIN-ENG-FIN
Python programming

2
Contributors
3
Replies
6
Views
5 Years
Discussion Span
Last Post by hughesadam_87
0

Well that just blew my mind.

Is it actually quicker to define the pali() function than it would be to just put that expression into the generator expression? EG

       max((a*b, a, b) for a in range(999, 100, -1) for b in range(a, 100000//a, -1) if str(a*b))==str(a*b)[::-1])

I ask because sometimes my list comprehensions get really crowded and I never think to do this.

Edited by hughesadam_87

0

It is faster by one function call penalty per iteration to not to use function, but function compensate it by making the code more readable. Your generator version is incorrect, you misplaced a ')':

max((a*b, a, b) for a in range(999, 100, -1) for b in range(a, 100000//a, -1) if str(a*b)==str(a*b)[::-1])

The optimized version with loop, even this above one liner is for me fast enough

def pali(a):
    return str(a) == str(a)[::-1]

m = (0,0,0)
for a in range(999, 100, -1):
    if m[-1] > a:
        #print('Breaking with a = %i' % a)
        break
    for b in range(a, 100000//a, -1):
        if pali(a*b):
            if a * b > m[0]:
                m = a*b, a, b
                #print m
            break


print('Biggest palindromic product of two three digit integers is %i, which is %i * %i.' % m)

""" Debug output:
(580085, 995, 583)
(906609, 993, 913)
Breaking with a = 912
Biggest palindromic product of two three digit integers is 906609, which is 993 * 913.
"""

Edited by pyTony

Have something to contribute to this discussion? Please be thoughtful, detailed and courteous, and be sure to adhere to our posting rules.