Add all the natural numbers below one thousand that are multiples of 3 or 5.

On the walk home, I found myself thinking about the problem and I wondered if it would be possible to use C++ template meta-programming to obtain the solution at compile time. Here's what I came up with:

template< int n >

struct sum_integers_up_to

{

static const int result =

(n * (n + 1)) / 2;

};

template< int upper_limit, int x >

struct sum_multiples

{

static const int result =

x * sum_integers_up_to< (upper_limit - 1)/ x >::result;

};

template< int upper_limit, int x, int y >

struct sum_two_multiples

{

static const int sum_of_multiples_of_x =

sum_multiples< upper_limit, x >::result;

static const int sum_of_multiples_of_y =

sum_multiples< upper_limit, y >::result;

static const int sum_of_multiples_of_xy =

sum_multiples< upper_limit, x*y >::result;

static const int result =

sum_of_multiples_of_x + sum_of_multiples_of_y - sum_of_multiples_of_xy;

};

int main()

{

return sum_two_multiples< 1000, 3, 5 >::result;

}

Having a look at the assembly code generated by MSVC, we see that it's about as minimal as it gets (spoiler alert!):

_main PROC

mov eax, 233168

ret 0

_main ENDP

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