#include #include #include #include #include #include using namespace std; const long long MaxVal = 500000000000000000LL * 2LL; const long long Target = 500000000000000000LL; vector> ValList[10][10][10][10][100]; vector> backtrack, backtrack_valid; int backtrack_finish; vector>> Possibility; map Possibility_Record; 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; } void init_dfs(int depth, vector ArrayA) { if (Possibility_Record[ArrayA[0]] == false) { Possibility_Record[ArrayA[0]] = true; Possibility.push_back(backtrack); } if (depth == 7) return; for (int i = 0; i < 4; i++) { for (int j = i + 1; j < 4; j++) { if (ArrayA[i] == ArrayA[j]) continue; vector 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 idx, vector ArrayA, vector ArrayB) { for (int i = 0; i < 4; i++) { for (vector> track : Possibility) { vector ArrayC = ArrayA; vector ArrayD = ArrayB; for (pair 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 idx, vector ArrayA, vector ArrayB, long long tgt_a, long long tgt_b) { for (vector> track : Possibility) { vector ArrayC = ArrayA; vector ArrayD = ArrayB; for (pair 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() { // 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 2. 初期化 vector 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 MinOrder; int StartTime = clock(); long long RecordScore = Target; while (clock() - StartTime < 4 * CLOCKS_PER_SEC / 10) { 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; } } // ============================================================================================================================== シナリオ 1 long long FinalScore = (1LL << 60); vector> FinalAns; if (true) { // Step 5. 二分探索 long long BaseA = BinarySearch(N, A, MinOrder, N - 10); long long BaseB = BinarySearch(N, B, MinOrder, N - 10); long long BestScore = (1LL << 60); vector LastOrder, Ord; for (int i = N - 10; i < N; i++) LastOrder.push_back(MinOrder[i]); for (int i = 0; i < 10; i++) Ord.push_back(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{i, j, k, l}, vector{A[LastOrder[i]], A[LastOrder[j]], A[LastOrder[k]], A[LastOrder[l]]}, vector{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); int cnts = 0; do { if (cnts % 24 == 0) { vector C = A; C[LastOrder[Ord[6]]] = 0; vector D = B; D[LastOrder[Ord[6]]] = 0; for (int i = 5; 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 / 64LL ? MaxVal - 1LL : err_c * 64LL)); long long goal_d = (err_d < 0LL ? 0LL : (err_d >= MaxVal / 64LL ? MaxVal - 1LL : err_d * 64LL)); if (goal_c <= 0LL || goal_c >= MaxVal - 1LL) continue; if (goal_d <= 0LL || goal_d >= MaxVal - 1LL) continue; // 探索準備 vector tmp = { Ord[6], Ord[7], Ord[8], Ord[9] }; sort(tmp.begin(), tmp.end()); int pos1 = goal_c / (MaxVal / 100LL); tuple Record = make_tuple(1LL << 60, -1, -1); // 探索 for (int i = pos1 - 4; i <= pos1 + 4; 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{A[LastOrder[tmp[0]]], A[LastOrder[tmp[1]]], A[LastOrder[tmp[2]]], A[LastOrder[tmp[3]]]}, vector{B[LastOrder[tmp[0]]], B[LastOrder[tmp[1]]], B[LastOrder[tmp[2]]], B[LastOrder[tmp[3]]]}, tgt_a, tgt_b); vector> 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 NewOrder; for (int i = 0; i < N - 10; i++) NewOrder.push_back(MinOrder[i]); for (int i = 0; i < 6; 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 SimA = A; vector 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; } } } cnts += 1; } while (next_permutation(Ord.begin(), Ord.end())); } // ============================================================================================================================== 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 LastOrder; vector BestOrder; for (int i = N - 9; 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 10. 答えを得る vector> Answer; vector 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 SimA = A; vector 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; }