Since I spend most of my day thinking in C++ I thought I would inject a little of that perspective. So here is a quick version that uses standard C++ only.

#include <iostream>
#include <set>
#include <algorithm>
#include <iterator>

int the_alphas[] = { 9, 4, 3, 2, 22,  13, 7,  140, 95, 278 };
int the_betas[]  = { 8, 3, 4, 1, 278, 94, 15, 7,   19, 200 };

const int the_alphas_size = sizeof(the_alphas) / sizeof(the_alphas[0])
+;
const int the_betas_size = sizeof(the_betas) / sizeof(the_betas[0]);

int main(int argc, char** argv)
{
    std::set<int> alphas(the_alphas, the_alphas + the_alphas_size);
    std::set<int> betas(the_betas, the_betas + the_betas_size);

    std::set<int> results;
    std::set_intersection(alphas.begin(), alphas.end(),
              betas.begin(), betas.end(),
              std::inserter(results, results.begin()));

    std::cout << "set_intersection: ";
    std::copy(results.begin(), results.end(),
          std::ostream_iterator<int>(std::cout, " "));
    std::cout << std::endl;

    return 0;
}
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Owl looked at him, and wondered whether to push him off the tree; but, feeling that he could always do it afterwards, he tried once more to find out what they were talking about.