<< problem 35 - Circular primes | Truncatable primes - problem 37 >> |
Problem 36: Double-base palindromes
(see projecteuler.net/problem=36)
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.)
My Algorithm
My short function num2str
converts a number x
into a std::string
with base
.
It's more or less the same code I used in previous problems when I wanted to extract right-most digit of a number.
Note that the result "grows" from right-to-left, that's why I always insert a single char at position 0.
The function isPalindrome
uses the STL function std::reverse
to efficiently reverse a string in-place.
If it's identical to the original string, then we have a palindrome.
The main loop checks number with base 10 first, because they are shorter than numbers with base 2 to 9.
In most cases we can abort earlier and save a little time.
Modifications by HackerRank
Base can be anything from 2 to 9.
Note
Of course you can speed up the whole process considerably:
1. generate all numbers from 1
to y
where y
has half as many digits as x
.
2. then convert to an std::string
and append its reverse.
3. convert that string to an integer x
and test with isPalindrome(num2str(x, 2))
whether x
's binary representation is a palindrome, too.
This way you have to check 1000 instead of 1000000 numbers.
I haven't benchmark it but my suspicion is that if num2str
appends digits (instead of prepending) and reverses the string as a final step,
then we might see a speed-up as well.
Interactive test
You can submit your own input to my program and it will be instantly processed at my server:
This is equivalent toecho "100 2" | ./36
Output:
Note: the original problem's input 1000000 2
cannot be entered
because just copying results is a soft skill reserved for idiots.
(this interactive test is still under development, computations will be aborted after one second)
My code
… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too.
#include <iostream>
#include <string>
#include <algorithm>
// base: decimal=10, binary=2
std::string num2str(unsigned int x, unsigned int base)
{
std::string result;
while (x > 0)
{
auto digit = x % base;
x /= base;
result.insert(0, 1, char(digit + '0'));
}
return result;
}
// true if string is a palindrome
bool isPalindrome(const std::string& s)
{
auto other = s;
std::reverse(other.begin(), other.end());
return other == s;
}
// I was quite surprised that the basic brute-force approach is sufficiently fast ...
int main()
{
unsigned int limit, base; // limit = 1000000 and base = 2
std::cin >> limit >> base;
unsigned int sum = 0;
for (unsigned int x = 1; x < limit; x++)
if (isPalindrome(num2str(x, 10)) && // palindrome in base 10 ?
isPalindrome(num2str(x, base))) // palindrome in base k ?
// yes, double palindrome
sum += x;
std::cout << sum << std::endl;
return 0;
}
This solution contains 5 empty lines, 4 comments and 3 preprocessor commands.
Benchmark
The correct solution to the original Project Euler problem was found in 0.3 seconds on an Intel® Core™ i7-2600K CPU @ 3.40GHz.
(compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 -DORIGINAL
)
See here for a comparison of all solutions.
Note: interactive tests run on a weaker (=slower) computer. Some interactive tests are compiled without -DORIGINAL
.
Changelog
February 24, 2017 submitted solution
April 6, 2017 added comments
Hackerrank
see https://www.hackerrank.com/contests/projecteuler/challenges/euler036
My code solves 15 out of 15 test cases (score: 100%)
Difficulty
Project Euler ranks this problem at 5% (out of 100%).
Hackerrank describes this problem as easy.
Note:
Hackerrank has strict execution time limits (typically 2 seconds for C++ code) and often a much wider input range than the original problem.
In my opinion, Hackerrank's modified problems are usually a lot harder to solve. As a rule thumb: brute-force is rarely an option.
Links
projecteuler.net/thread=36 - the best forum on the subject (note: you have to submit the correct solution first)
Code in various languages:
C# www.mathblog.dk/project-euler-36-palindromic-base-10-2/ (written by Kristian Edlund)
C github.com/eagletmt/project-euler-c/blob/master/30-39/problem36.c (written by eagletmt)
Java github.com/nayuki/Project-Euler-solutions/blob/master/java/p036.java (written by Nayuki)
Javascript github.com/dsernst/ProjectEuler/blob/master/36 Double-base palindromes.js (written by David Ernst)
Mathematica github.com/nayuki/Project-Euler-solutions/blob/master/mathematica/p036.mathematica (written by Nayuki)
Haskell github.com/nayuki/Project-Euler-solutions/blob/master/haskell/p036.hs (written by Nayuki)
Scala github.com/samskivert/euler-scala/blob/master/Euler036.scala (written by Michael Bayne)
Perl github.com/gustafe/projecteuler/blob/master/036-Double-base-palindromes.pl (written by Gustaf Erikson)
Those links are just an unordered selection of source code I found with a semi-automatic search script on Google/Bing/GitHub/whatever.
You will probably stumble upon better solutions when searching on your own.
Maybe not all linked resources produce the correct result and/or exceed time/memory limits.
Heatmap
Please click on a problem's number to open my solution to that problem:
green | solutions solve the original Project Euler problem and have a perfect score of 100% at Hackerrank, too | |
yellow | solutions score less than 100% at Hackerrank (but still solve the original problem easily) | |
gray | problems are already solved but I haven't published my solution yet | |
blue | solutions are relevant for Project Euler only: there wasn't a Hackerrank version of it (at the time I solved it) or it differed too much | |
orange | problems are solved but exceed the time limit of one minute or the memory limit of 256 MByte | |
red | problems are not solved yet but I wrote a simulation to approximate the result or verified at least the given example - usually I sketched a few ideas, too | |
black | problems are solved but access to the solution is blocked for a few days until the next problem is published | |
[new] | the flashing problem is the one I solved most recently |
I stopped working on Project Euler problems around the time they released 617.
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I scored 13526 points (out of 15700 possible points, top rank was 17 out of ≈60000 in August 2017) at Hackerrank's Project Euler+.
My username at Project Euler is stephanbrumme while it's stbrumme at Hackerrank.
Look at my progress and performance pages to get more details.
Copyright
I hope you enjoy my code and learn something - or give me feedback how I can improve my solutions.
All of my solutions can be used for any purpose and I am in no way liable for any damages caused.
You can even remove my name and claim it's yours. But then you shall burn in hell.
The problems and most of the problems' images were created by Project Euler.
Thanks for all their endless effort !!!
<< problem 35 - Circular primes | Truncatable primes - problem 37 >> |