結果
| 問題 |
No.5020 Averaging
|
| コンテスト | |
| ユーザー |
 e869120
|
| 提出日時 | 2024-02-20 11:58:02 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 981 ms / 1,000 ms |
| コード長 | 13,026 bytes |
| コンパイル時間 | 2,394 ms |
| コンパイル使用メモリ | 140,860 KB |
| 実行使用メモリ | 277,436 KB |
| スコア | 85,348,471 |
| 最終ジャッジ日時 | 2024-02-25 12:41:16 |
| 合計ジャッジ時間 | 54,180 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge11 |
| 純コード判定しない問題か言語 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 50 |
ソースコード
#include <iostream>
#include <map>
#include <cmath>
#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[10][10][10][10][10][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 == 5) return;
for (int i = 0; i < 5; i++) {
for (int j = i + 1; j < 5; 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 < 5; 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) % 5;
int idx2 = (place.second + i) % 5;
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]][idx[4]][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; }
if (ArrayC[4] == tgt_a && ArrayD[4] == tgt_b) { backtrack_valid = track; backtrack_finish = 4; return; }
}
}
int main() {
srand((unsigned)time(NULL));
// Step 1. 入力
vector<long long> A(45, 0);
vector<long long> B(45, 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(5, 0);
for (int i = 0; i < 5; 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 < 5 * CLOCKS_PER_SEC / 10) {
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 - 10);
long long BaseB = BinarySearch(N, B, MinOrder, N - 10);
long long BestScore = (1LL << 60);
vector<int> 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++) {
for (int m = l + 1; m < LastOrder.size(); m++) {
brute_force(0, vector<int>{i, j, k, l, m}, vector<long long>{A[LastOrder[i]], A[LastOrder[j]], A[LastOrder[k]], A[LastOrder[l]], A[LastOrder[m]]}, vector<long long>{B[LastOrder[i]], B[LastOrder[j]], B[LastOrder[k]], B[LastOrder[l]], B[LastOrder[m]]});
for (int n = 0; n < 100; n++) sort(ValList[i][j][k][l][m][n].begin(), ValList[i][j][k][l][m][n].end());
for (int n = 0; n < 100; n++) ValList[i][j][k][l][m][n].erase(unique(ValList[i][j][k][l][m][n].begin(), ValList[i][j][k][l][m][n].end()), ValList[i][j][k][l][m][n].end());
}
}
}
}
}
// Step 7. 指数探索
long long CurrentBest = (1LL << 60);
int cnts = 0;
do {
if (cnts % 120 == 0) {
for (int loops = 0; loops < 1; loops++) {
vector<long long> C = A; C[LastOrder[Ord[5]]] = 0;
vector<long long> D = B; D[LastOrder[Ord[5]]] = 0;
for (int i = 4; 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 / 32LL ? MaxVal - 1LL : err_c * 32LL));
long long goal_d = (err_d < 0LL ? 0LL : (err_d >= MaxVal / 32LL ? MaxVal - 1LL : err_d * 32LL));
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[5], Ord[6], Ord[7], Ord[8], Ord[9] };
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 - 5; i <= pos1 + 4; i++) {
if (i < 0 || i >= 100) continue;
int pos2 = lower_bound(ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][i].begin(), ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][i].end(), make_pair(goal_d, 0LL)) - ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][i].begin();
for (int j = pos2 - 5; j <= pos2 + 4; j++) {
if (j < 0 || j >= ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][i].size()) continue;
long long diff_a = abs(goal_c - ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][i][j].second);
long long diff_b = abs(goal_d - ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][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]][tmp[4]][get<1>(Record)][get<2>(Record)].second;
long long tgt_b = ValList[tmp[0]][tmp[1]][tmp[2]][tmp[3]][tmp[4]][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]]], A[LastOrder[tmp[4]]]}, vector<long long>{B[LastOrder[tmp[0]]], B[LastOrder[tmp[1]]], B[LastOrder[tmp[2]]], B[LastOrder[tmp[3]]], B[LastOrder[tmp[4]]]}, 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 - 10; i++) NewOrder.push_back(MinOrder[i]);
for (int i = 0; i < 5; 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;
}
}
}
}
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<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;
}