Double-base palindromes
The decimal number, 585 = 10010010012 (binary), is palindromic in both bases.
Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.
(Please note that the palindromic number, in either base, may not include leading zeros.)
Before you continue reading the solution I would recommend you having a look at Palindrome Number Wikipedia, if you don't know what a palindrome number is.
This problem is pretty easy if you have already solved problem 4. You can see my solution to understand the program for this problem. Problem 4 Project Euler Solution with python.
After reading this question it just took me a few minutes to get the solution. Algorithm is simple, use python's inbuilt
bin function and then get the binary version of the number. In the similar way use extended slicing to get the reverse of the number. If you don't want to use extended slicing but to use some other program for getting the reverse of the number, then you might have to look at Reverse a string in python. There are a lot of answer given by the community members.Now coming back to question, as I was not paying a careful attention to the question to the last problem, I wasted some time solving the problem for wrong question. So this time I didn't want to do the same mistake. If you have observed, the last statement in the question says, "Please note that the palindromic number, in either base, may not include leading zeros". There are two conclusions we can make of this statement.
First conclusion I made was regarding the base 10 number, according to which if the number is palindrome then there should not be zeros in the end also. So we can eliminate all the multiples of 10.
Before I came up with the second conclusion, I first revised my concepts with converting Decimal number to Binary number on wikihow. All the even numbers when written in base 2 will have zero at the end. I also checked the same with
bin in the interpreter. As we know that there should not be any zeros in the start of the number then there should not be any zeros at the end of the number also. But all the even numbers when written in binary format have zeros and they can be eliminated from our calculation.Finally I only had to do iterations for odd numbers and it was easy with
xrange, because I only increased the step size to 2. You can see the same in the program also.Program
Program is very simple and also it is very compact. If you remove all the comments and the time stuff from the code you will end up with just 6 lines of code.In the program, I have not checked for Base 2 numbers and Base 10 numbers separately. I simply checked for Base 10 numbers and if the given number is Palindrome in Base 10 then check if the number is Palindrome in Base 2. This has saved me a lot of resources and has also saved a lot of execution time.
As always you can download the source code from Github Gist pep36.py
Output
Summary
The first time I wrote the program for this problem, it came out to be very simple and compact. Performance was also very good and I didn't think of optimizing the code. I am satisfied with this code because even after looping for half a million times the execution time is very less. But there might be some scope for improvement. Even if improved we will have to compromise on the compactness of the code.If you have any doubt or didn't understand anything then comment in the comment box below and I will be glad to help you.
Please do comment in the comment box below if you have found any typo, or have a different or better program or if you have any suggestion. I will be glad to view each of them.
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Thank you. Have a nice day😃.