#include #include #include #include using namespace std; void log_vector(const vector& vec, const string& prefix = "") { clog << prefix; for (const int i : vec) { clog << i << " "; } clog << endl; } vector get_divisors(const int n) { vector small_divisors = {1}; vector big_factors = {n}; for (int i = 2; i * i <= n; i++) { if (n % i == 0) { small_divisors.push_back(i); big_factors.push_back(n / i); } } // reverse(small_divisors.begin(), small_divisors.end()); // big_factors.insert(big_factors.end(), small_divisors.begin(), small_divisors.end()); // return big_factors; reverse(big_factors.begin(), big_factors.end()); small_divisors.insert(small_divisors.end(), big_factors.begin(), big_factors.end()); return small_divisors; } /// 需要保证 sorted_cut_sticks 有序;需要保证 target_length 是总长度的因数 bool verify_length_greedy(vector sorted_cut_sticks, const int target_length) { // if (target_times == 0) { return true; } // if (sorted_cut_sticks.empty()) { throw logic_error("Invalid target_times"); } if (sorted_cut_sticks.empty()) { return true; } if (sorted_cut_sticks.back() > target_length) { return false; } int remaining_length = target_length - sorted_cut_sticks.back(); sorted_cut_sticks.pop_back(); if (remaining_length == 0) { return verify_length_greedy(sorted_cut_sticks, target_length); } while (true) { auto closest_iter = lower_bound(sorted_cut_sticks.begin(), sorted_cut_sticks.end(), remaining_length); if (closest_iter != sorted_cut_sticks.end() && *closest_iter == remaining_length) { sorted_cut_sticks.erase(closest_iter); // log_vector(sorted_cut_sticks, "after erase: "); return verify_length_greedy(sorted_cut_sticks, target_length); } if (closest_iter == sorted_cut_sticks.begin()) { // 都太长了! return false; } closest_iter -= 1; // 第一个小于 remaining_length 的元素的 iter remaining_length -= *closest_iter; sorted_cut_sticks.erase(closest_iter); } } int get_shortest_original_length(vector cut_sticks) { sort(cut_sticks.begin(), cut_sticks.end()); const int total_length = accumulate(cut_sticks.begin(), cut_sticks.end(), 0); const vector divisors = get_divisors(total_length); log_vector(divisors, "divisors: "); for (const int divisor : divisors) { if (verify_length_greedy(cut_sticks, divisor)) { return divisor; } } return -1; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int cut_sticks_amount; while (cin >> cut_sticks_amount && cut_sticks_amount) { vector cut_sticks(cut_sticks_amount); for (int i = 0; i < cut_sticks_amount; i++) { cin >> cut_sticks[i]; } sort(cut_sticks.begin(), cut_sticks.end()); log_vector(cut_sticks, "cut_sticks: "); // int target_length; // cin >> target_length; // cout << (verify_length_greedy(cut_sticks, target_length) ? "Yes" : "No") << endl; cout << get_shortest_original_length(cut_sticks) << endl; } return 0; }