Optimization of recursion in C++ - c++

Question

I have a recursive function. And I want to optimize it as less as 10 sec. Higher use of Memory is not an issue.
Currently, it takes around 85 sec on Linux and three times more on Mac.
I could not understand in what way I can proceed?
Here is code:
using namespace std;
double get_wall_time(){
struct timeval time;
if (gettimeofday(&time,NULL)){
// Handle error
return 0;
}
return (double)time.tv_sec + (double)time.tv_usec * .000001;
}
int fun(long long n) {
if (n < 0) {
cout << "Please enter valid number";
return 0;
}
else if (n == 0 || n == 1)
return 1;
else if (n % 2 == 0)
return fun(n / 2);
else if (n % 2 == 1)
return fun(n / 2) + fun(n / 2 - 1);
else
return 0;
}
int main() {
double begin = get_wall_time();
cout << fun(123456789012345678) << std::endl;
double end = get_wall_time();
cout << "Time elapsed : " << double(end - begin);
return 0;
}
EDIT:
If n is even, return f(n/2)
If n is odd, return f(n/2)+f(n/2-1)

Answer 1

I would memoize the results using a std::map, like so:
std::map<long long, int>fun_results;
int fun(long long n) {
try {
return fun_results.at(n);
} catch(const std::out_of_range&) {
if (n < 0) {
cout << "Please enter valid number";
return 0;
}
else if (n == 0 || n == 1)
return fun_results[n] = 1;
else if (n % 2 == 0)
return fun_results[n] = fun(n / 2);
else if (n % 2 == 1)
return fun_results[n] = fun(n / 2) + fun(n / 2 - 1);
else
return 0;
}
}
Result:
1332403
Time elapsed : 0.000710011