# 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.

# Solution

#!/usr/bin/env python

def ispal(num): #Check if the number is a palindrome

val = str(num) #Python just does the right thing here. Nice.

for each in range(0,int((len(val)+1)/2)): #Any mismatch return false

if val[len(val)-1-each]!=val[0+each]: return False

return True #otherwise return true

def calc(): #brute force looking for palindromes

temp = 0

largest = 0

for each in range(999,100,-1):

for other in range(999,100,-1):

temp = each * other

if ispal(temp):

largest = max(largest,temp)

return largest

if __name__ == '__main__' :

print (calc())

*The answer is 906609.*

# Approach

This was one of the problems which took almost no time to code. The seamless casting in Python made this one trivial. You just work from both ends and look for mismatches.

Converting to a string worked exactly like it should have and python made it trivial to code. Using some sort of built-in to reverse the string and see if it matches the original sting would probably be faster than a char by char comparison.

# Benchmarks

The benchmarks fell out pretty much like the others. Boring example, Sorry!

Problem #4 Benchmarks

time python palindromes.py

906609

real 0m0.746s

user 0m0.744s

sys 0m0.000s

time python -O palindromes.py

906609

real 0m0.764s

user 0m0.756s

sys 0m0.004s

time python3 palindromes.py

906609

real 0m0.839s

user 0m0.828s

sys 0m0.008s

time python3 -O palindromes.py

906609

real 0m0.875s

user 0m0.868s

sys 0m0.004s

time pypy palindromes.py

906609

real 0m0.090s

user 0m0.080s

sys 0m0.008s

time pypy -O palindromes.py

906609

real 0m0.087s

user 0m0.072s

sys 0m0.012s

time jython palindromes.py

906609

real 0m2.835s

user 0m5.852s

sys 0m0.176s

# Conclusion

Python just worked here. This problem took no time at all to code and worked on the first try. The benchmarks agree with everything else we've seen. The answer is 906609.