// [想定解答 7] // - 想定解答 6 のプログラムを 0.4 秒回し,一番良かった順番を Order[1], Order[2], ..., Order[45] とする. // - その後,Order[36], Order[37], ..., Order[45] の順番を 10! 通り全探索する.(Order[35] 以前の順番は変わらず) // * 上手く処理すれば計算回数は 10! * 10 のオーダーになる. // // - 10! 通りの中で一番良いものを答えとして出力する. // - 82% 程度の得点が得られる. #include #include #include #include #include #include using namespace std; const long long MaxVal = 500000000000000000LL * 2LL; const long long Target = 500000000000000000LL; void Operation(vector& A, vector& B, int idx1, int idx2) { long long avg1 = (A[idx1] + A[idx2]) / 2LL; long long avg2 = (B[idx1] + B[idx2]) / 2LL; A[idx1] = avg1; B[idx1] = avg2; A[idx2] = avg1; B[idx2] = avg2; } long long BinarySearch(int N, vector X, vector Order, int border) { long long cl = 0; long long cr = Target * 2LL; long long cm; for (int i = 0; i < 65; i++) { cm = (cl + cr) / 2LL; vector Y = X; Y[Order[border]] = cm; vector Z = X; Z[Order[border]] = cm; for (int j = border - 1; j >= 0; j--) Operation(Y, Z, Order[j], Order[j + 1]); if (Y[0] >= Target) cr = cm; else cl = cm; } return cm; } int main() { // Step 1. 入力 vector A(50, 0); vector B(50, 0); long long N; cin >> N; for (int i = 0; i < N; i++) cin >> A[i] >> B[i]; // Step 3. 最初のステップ long long MinV = (1LL << 60); long long MinID = -1; for (int i = 1; i < N; i++) { long long v1 = (A[0] + A[i]) / 2LL; long long v2 = (B[0] + B[i]) / 2LL; long long err = max(abs(v1 - Target), abs(v2 - Target)); if (MinV > err) { MinV = err; MinID = i; } } Operation(A, B, 0, MinID); // Step 4. ランダム貪欲 vector MinOrder; int StartTime = clock(); long long RecordScore = Target; while (clock() - StartTime < 40 * CLOCKS_PER_SEC / 100) { vector C = A; vector D = B; long long RemainC = Target * 2 - C[0]; long long RemainD = Target * 2 - D[0]; vector Used(N, false); vector Order; Order.push_back(0); // 貪欲法スタート while (true) { vector> Vec; for (int i = 1; i < N; i++) { if (Used[i] == true) continue; long long v1 = abs(RemainC - C[i]); if (v1 >= RemainC) continue; long long v2 = abs(RemainD - D[i]); if (v2 >= RemainD) continue; Vec.push_back(make_pair(max(v1, v2), i)); } sort(Vec.begin(), Vec.end()); if (Vec.size() == 0) break; int idx = Vec[rand() % max(1, min(3, (int)Vec.size() / 3))].second; RemainC = min(6LL * Target, 2LL * RemainC - C[idx]); RemainD = min(6LL * Target, 2LL * RemainD - D[idx]); Order.push_back(idx); Used[idx] = true; } for (int i = 1; i < N; i++) { if (Used[i] == false) Order.push_back(i); } // スコアを出す vector> CurrentAns; CurrentAns.push_back(make_pair(0, MinID)); for (int i = N - 2; i >= 0; i--) { CurrentAns.push_back(make_pair(Order[i], Order[i + 1])); Operation(C, D, Order[i], Order[i + 1]); } // スコアを比較 long long CandScore = max(abs(Target - C[0]), abs(Target - D[0])); if (RecordScore > CandScore) { RecordScore = CandScore; MinOrder = Order; } } // Step 5. 二分探索 long long BaseA = BinarySearch(N, A, MinOrder, N - 10); long long BaseB = BinarySearch(N, B, MinOrder, N - 10); // Step 6. 指数探索 long long BestScore = (1LL << 60); vector LastOrder; vector BestOrder; for (int i = N - 10; i < N; i++) LastOrder.push_back(MinOrder[i]); sort(LastOrder.begin(), LastOrder.end()); do { vector C = A; vector D = B; for (int i = LastOrder.size() - 2; i >= 0; i--) Operation(C, D, LastOrder[i], LastOrder[i + 1]); long long err_c = abs(BaseA - C[LastOrder[0]]); long long err_d = abs(BaseB - D[LastOrder[0]]); long long score = max(err_c, err_d); if (BestScore > score) { BestScore = score; BestOrder = LastOrder; } } while (next_permutation(LastOrder.begin(), LastOrder.end())); // Step 7. 答えを得る vector> Answer; vector FinalOrder; for (int i = 0; i < N - 10; i++) FinalOrder.push_back(MinOrder[i]); for (int idx : BestOrder) FinalOrder.push_back(idx); Answer.push_back(make_pair(0, MinID)); for (int i = FinalOrder.size() - 2; i >= 0; i--) { Answer.push_back(make_pair(FinalOrder[i], FinalOrder[i + 1])); } // Step 8. シミュレーション vector SimA = A; vector SimB = B; for (int i = 1; i < Answer.size(); i++) Operation(SimA, SimB, Answer[i].first, Answer[i].second); // Step 9. 出力 cout << Answer.size() << endl; for (int i = 0; i < Answer.size(); i++) cout << Answer[i].first + 1 << " " << Answer[i].second + 1 << endl; return 0; }