結果
問題 | No.5020 Averaging |
ユーザー | e869120 |
提出日時 | 2024-02-20 12:40:55 |
言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
結果 |
TLE
(最新)
AC
(最初)
|
実行時間 | - |
コード長 | 12,783 bytes |
コンパイル時間 | 3,285 ms |
コンパイル使用メモリ | 140,860 KB |
実行使用メモリ | 89,532 KB |
スコア | 0 |
最終ジャッジ日時 | 2024-02-25 12:42:03 |
合計ジャッジ時間 | 74,540 ms |
ジャッジサーバーID (参考情報) |
judge13 / judge12 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | TLE | - |
testcase_01 | TLE | - |
testcase_02 | TLE | - |
testcase_03 | TLE | - |
testcase_04 | TLE | - |
testcase_05 | TLE | - |
testcase_06 | TLE | - |
testcase_07 | TLE | - |
testcase_08 | TLE | - |
testcase_09 | TLE | - |
testcase_10 | TLE | - |
testcase_11 | TLE | - |
testcase_12 | TLE | - |
testcase_13 | TLE | - |
testcase_14 | TLE | - |
testcase_15 | TLE | - |
testcase_16 | TLE | - |
testcase_17 | TLE | - |
testcase_18 | TLE | - |
testcase_19 | TLE | - |
testcase_20 | TLE | - |
testcase_21 | TLE | - |
testcase_22 | TLE | - |
testcase_23 | TLE | - |
testcase_24 | TLE | - |
testcase_25 | TLE | - |
testcase_26 | TLE | - |
testcase_27 | TLE | - |
testcase_28 | TLE | - |
testcase_29 | TLE | - |
testcase_30 | TLE | - |
testcase_31 | TLE | - |
testcase_32 | TLE | - |
testcase_33 | TLE | - |
testcase_34 | TLE | - |
testcase_35 | TLE | - |
testcase_36 | TLE | - |
testcase_37 | TLE | - |
testcase_38 | TLE | - |
testcase_39 | TLE | - |
testcase_40 | TLE | - |
testcase_41 | TLE | - |
testcase_42 | TLE | - |
testcase_43 | TLE | - |
testcase_44 | TLE | - |
testcase_45 | TLE | - |
testcase_46 | TLE | - |
testcase_47 | TLE | - |
testcase_48 | TLE | - |
testcase_49 | TLE | - |
ソースコード
#include <iostream> #include <map> #include <cmath> #include <ctime> #include <tuple> #include <vector> #include <algorithm> using namespace std; const long long MaxVal = 500000000000000000LL * 2LL; const long long Target = 500000000000000000LL; vector<pair<long long, long long>> ValList[11][11][11][11][100]; vector<pair<int, int>> backtrack, backtrack_valid; int backtrack_finish; vector<vector<pair<int, int>>> Possibility; map<long long, bool> Possibility_Record; void Operation(vector<long long>& A, vector<long long>& 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<long long> X, vector<int> 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<long long> Y = X; Y[Order[border]] = cm; vector<long long> 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; } void init_dfs(int depth, vector<long long> ArrayA) { if (Possibility_Record[ArrayA[0]] == false) { Possibility_Record[ArrayA[0]] = true; Possibility.push_back(backtrack); } if (depth == 8) return; for (int i = 0; i < 4; i++) { for (int j = i + 1; j < 4; j++) { if (ArrayA[i] == ArrayA[j]) continue; vector<long long> ArrayC = ArrayA; long long avg1 = (ArrayC[i] + ArrayC[j]) / 2LL; ArrayC[i] = avg1; ArrayC[j] = avg1; backtrack.push_back(make_pair(i, j)); init_dfs(depth + 1, ArrayC); backtrack.pop_back(); } } } void brute_force(int depth, vector<int> idx, vector<long long> ArrayA, vector<long long> ArrayB) { for (int i = 0; i < 4; i++) { for (vector<pair<int, int>> track : Possibility) { vector<long long> ArrayC = ArrayA; vector<long long> ArrayD = ArrayB; for (pair<int, int> place : track) { int idx1 = (place.first + i) % 4; int idx2 = (place.second + i) % 4; long long avg1 = (ArrayC[idx1] + ArrayC[idx2]) / 2LL; long long avg2 = (ArrayD[idx1] + ArrayD[idx2]) / 2LL; ArrayC[idx1] = avg1; ArrayD[idx1] = avg2; ArrayC[idx2] = avg1; ArrayD[idx2] = avg2; } ValList[idx[0]][idx[1]][idx[2]][idx[3]][ArrayC[i] / (MaxVal / 100LL)].push_back(make_pair(ArrayD[i], ArrayC[i])); } } } void search(int depth, vector<int> idx, vector<long long> ArrayA, vector<long long> ArrayB, long long tgt_a, long long tgt_b) { for (vector<pair<int, int>> track : Possibility) { vector<long long> ArrayC = ArrayA; vector<long long> ArrayD = ArrayB; for (pair<int, int> idx : track) { long long avg1 = (ArrayC[idx.first] + ArrayC[idx.second]) / 2LL; long long avg2 = (ArrayD[idx.first] + ArrayD[idx.second]) / 2LL; ArrayC[idx.first] = avg1; ArrayD[idx.first] = avg2; ArrayC[idx.second] = avg1; ArrayD[idx.second] = avg2; } if (ArrayC[0] == tgt_a && ArrayD[0] == tgt_b) { backtrack_valid = track; backtrack_finish = 0; return; } if (ArrayC[1] == tgt_a && ArrayD[1] == tgt_b) { backtrack_valid = track; backtrack_finish = 1; return; } if (ArrayC[2] == tgt_a && ArrayD[2] == tgt_b) { backtrack_valid = track; backtrack_finish = 2; return; } if (ArrayC[3] == tgt_a && ArrayD[3] == tgt_b) { backtrack_valid = track; backtrack_finish = 3; return; } } } int main() { srand((unsigned)time(NULL)); // Step 1. 入力 vector<long long> A(50, 0); vector<long long> B(50, 0); long long N; cin >> N; for (int i = 0; i < N; i++) cin >> A[i] >> B[i]; // Step 2. 初期化 vector<long long> Random(4, 0); for (int i = 0; i < 4; i++) { for (int j = 0; j < 18; j++) Random[i] += 10LL * Random[i] + 1LL * (rand() % 10LL); } init_dfs(0, Random); // 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<int> MinOrder; int StartTime = clock(); long long RecordScore = Target; while (clock() - StartTime < 60 * CLOCKS_PER_SEC / 100) { vector<long long> C = A; vector<long long> D = B; long long RemainC = Target * 2 - C[0]; long long RemainD = Target * 2 - D[0]; vector<bool> Used(N, false); vector<int> Order; Order.push_back(0); // 貪欲法スタート int param1 = rand() % 3 + 2; int param2 = rand() % 3 + 2; int param3 = rand() % 7; while (true) { vector<pair<long long, int>> 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; double keisuu = 1.0 - 0.1 * param3 * max(abs(C[i] - Target), abs(D[i] - Target)) / Target; Vec.push_back(make_pair(max(v1, v2) * keisuu, i)); } sort(Vec.begin(), Vec.end()); if (Vec.size() == 0) break; int idx = Vec[rand() % max(1, min(param1, (int)Vec.size() / param2))].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<pair<int, int>> 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; } } // ============================================================================================================================== シナリオ 1 long long FinalScore = (1LL << 60); vector<pair<int, int>> FinalAns; if (true) { // Step 5. 二分探索 long long BaseA = BinarySearch(N, A, MinOrder, N - 11); long long BaseB = BinarySearch(N, B, MinOrder, N - 11); long long BestScore = (1LL << 60); vector<int> LastOrder; vector<int> Ord(11, 0); for (int i = N - 11; i < N; i++) LastOrder.push_back(MinOrder[i]); for (int i = 0; i < 11; i++) Ord[i] = i; sort(LastOrder.begin(), LastOrder.end()); // Step 6. 指数探索の前計算 for (int i = 0; i < LastOrder.size(); i++) { for (int j = i + 1; j < LastOrder.size(); j++) { for (int k = j + 1; k < LastOrder.size(); k++) { for (int l = k + 1; l < LastOrder.size(); l++) { brute_force(0, vector<int>{i, j, k, l}, vector<long long>{A[LastOrder[i]], A[LastOrder[j]], A[LastOrder[k]], A[LastOrder[l]]}, vector<long long>{B[LastOrder[i]], B[LastOrder[j]], B[LastOrder[k]], B[LastOrder[l]]}); for (int m = 0; m < 100; m++) sort(ValList[i][j][k][l][m].begin(), ValList[i][j][k][l][m].end()); for (int m = 0; m < 100; m++) ValList[i][j][k][l][m].erase(unique(ValList[i][j][k][l][m].begin(), ValList[i][j][k][l][m].end()), ValList[i][j][k][l][m].end()); } } } } // Step 7. 指数探索 long long CurrentBest = (1LL << 60); while (true) { // Ord の更新 swap(Ord[7], Ord[10]); swap(Ord[8], Ord[9]); int c1 = 6; int c2 = 0; while (c1 >= 0 && Ord[c1] > Ord[c1 + 1]) c1 -= 1; if (c1 == -1) break; c2 = c1 + 1; while (c2 <= 9 && Ord[c1] < Ord[c2 + 1]) c2 += 1; swap(Ord[c1], Ord[c2]); sort(Ord.begin() + (c1 + 1), Ord.end()); // 誤差の計算 vector<long long> C = A; C[LastOrder[Ord[7]]] = 0; vector<long long> D = B; D[LastOrder[Ord[7]]] = 0; for (int i = 6; i >= 0; i--) Operation(C, D, LastOrder[Ord[i]], LastOrder[Ord[i + 1]]); long long err_c = BaseA - C[LastOrder[Ord[0]]]; long long err_d = BaseB - D[LastOrder[Ord[0]]]; long long goal_c = (err_c < 0LL ? 0LL : (err_c >= MaxVal / 128LL ? MaxVal - 1LL : err_c * 128LL)); long long goal_d = (err_d < 0LL ? 0LL : (err_d >= MaxVal / 128LL ? MaxVal - 1LL : err_d * 128LL)); if (goal_c <= 0LL || goal_c >= MaxVal - 1LL) continue; if (goal_d <= 0LL || goal_d >= MaxVal - 1LL) continue; // 探索準備 vector<int> tmp = { Ord[7], Ord[8], Ord[9], Ord[10] }; sort(tmp.begin(), tmp.end()); int pos1 = goal_c / (MaxVal / 100LL); tuple<long long, int, int> Record = make_tuple(1LL << 60, -1, -1); // 探索 for (int i = pos1 - 10; i <= pos1 + 9; i++) { if (i < 0 || i >= 100) continue; int pos2 = lower_bound(ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][i].begin(), ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][i].end(), make_pair(goal_d, 0LL)) - ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][i].begin(); for (int j = pos2 - 5; j <= pos2 + 4; j++) { if (j < 0 || j >= ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][i].size()) continue; long long diff_a = abs(goal_c - ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][i][j].second); long long diff_b = abs(goal_d - ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][i][j].first); Record = min(Record, make_tuple(max(diff_a, diff_b), i, j)); } } // 記録更新の場合 if (CurrentBest > get<0>(Record)) { CurrentBest = get<0>(Record); long long tgt_a = ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][get<1>(Record)][get<2>(Record)].second; long long tgt_b = ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][get<1>(Record)][get<2>(Record)].first; search(0, tmp, vector<long long>{A[LastOrder[tmp[0]]], A[LastOrder[tmp[1]]], A[LastOrder[tmp[2]]], A[LastOrder[tmp[3]]]}, vector<long long>{B[LastOrder[tmp[0]]], B[LastOrder[tmp[1]]], B[LastOrder[tmp[2]]], B[LastOrder[tmp[3]]]}, tgt_a, tgt_b); vector<pair<int, int>> Answer; Answer.push_back(make_pair(0, MinID)); for (int i = 0; i < backtrack_valid.size(); i++) Answer.push_back(make_pair(LastOrder[tmp[backtrack_valid[i].first]], LastOrder[tmp[backtrack_valid[i].second]])); vector<int> NewOrder; for (int i = 0; i < N - 11; i++) NewOrder.push_back(MinOrder[i]); for (int i = 0; i < 7; i++) NewOrder.push_back(LastOrder[Ord[i]]); NewOrder.push_back(LastOrder[tmp[backtrack_finish]]); for (int i = NewOrder.size() - 2; i >= 0; i--) Answer.push_back(make_pair(NewOrder[i], NewOrder[i + 1])); vector<long long> SimA = A; vector<long long> SimB = B; for (int i = 1; i < Answer.size(); i++) Operation(SimA, SimB, Answer[i].first, Answer[i].second); long long diff_a = abs(Target - SimA[0]); long long diff_b = abs(Target - SimB[0]); if (FinalScore > max(diff_a, diff_b)) { FinalScore = max(diff_a, diff_b); FinalAns = Answer; } } } } // ============================================================================================================================== シナリオ 2 if (true) { // Step 8. 二分探索 long long BaseA = BinarySearch(N, A, MinOrder, N - 9); long long BaseB = BinarySearch(N, B, MinOrder, N - 9); // Step 9. 指数探索 long long BestScore = (1LL << 60); vector<int> LastOrder; vector<int> BestOrder; for (int i = N - 9; i < N; i++) LastOrder.push_back(MinOrder[i]); sort(LastOrder.begin(), LastOrder.end()); do { vector<long long> C = A; vector<long long> 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 10. 答えを得る vector<pair<int, int>> Answer; vector<int> FinalOrder; for (int i = 0; i < N - 9; 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 11. シミュレーション vector<long long> SimA = A; vector<long long> SimB = B; for (int i = 1; i < Answer.size(); i++) Operation(SimA, SimB, Answer[i].first, Answer[i].second); long long diff_a = abs(Target - SimA[0]); long long diff_b = abs(Target - SimB[0]); if (FinalScore > max(diff_a, diff_b)) { FinalScore = max(diff_a, diff_b); FinalAns = Answer; } } // ============================================================================================================================== 出力 cout << FinalAns.size() << endl; for (int i = 0; i < FinalAns.size(); i++) cout << FinalAns[i].first + 1 << " " << FinalAns[i].second + 1 << endl; return 0; }