It's highly unlikely that you will get anywhere if you do not use some very specific number theory theorem. I think you just need to do some more research, until you stumple upon some particular approach.

I am hitting timeout exception with n=661915703. I have tried solving the problem using DP + memoization and BFS. Both the solution are encountering same timeout issue. I am unable to identify whats wrong. Any pointers will be great.

Thanks.

it's most probably a bug in c++ version of the kata. please check if adding include <cmath> in your solution helps, even if you don't use it.

What are these errors? I don't have these on my file. (C++)

In file included from main.cpp:7:
./tests.cpp:7:35: error: no member named 'sqrt' in namespace 'std'
return n == std::pow(int(std::sqrt(n)), 2);
~~~~~^
./tests.cpp:7:22: error: no member named 'pow' in namespace 'std'
return n == std::pow(int(std::sqrt(n)), 2);
~~~~~^
./tests.cpp:20:27: error: no member named 'sqrt' in namespace 'std'
int sqrt_n = int(std::sqrt(n));
~~~~~^
3 errors generated.

Assert::That(sum_of_squares(661915703), Equals(4));

I am using C++ to attempt this problem.

It would be good if you stated the langauge you are attempting, it would help us to check tests.

You can also read this paragraph: https://docs.codewars.com/training/troubleshooting#print-input and the one directly following it.

For SumsOfPerfectSquares problem, all my test-cases are passing expect "maximally_hard_test_case1". This test-case is failing with time-out error. Is there a way to find which test in this test-set is failing?