To solve the problem one could just store two arrays hused[j] and vused[j] sized n and filled with false initially. Then process intersections one by one from 1 to n, and if for i-th intersections both hused[h_i] and vused[v_i] are false, add i to answer and set both hused[h_i] and vused[v_i] with true meaning that h_i-th horizontal and v_i-th vertical roads are now asphalted, and skip asphalting the intersection roads otherwise. Such solution has O(n²) complexity.