#954959 (C++14) No.5020 Averaging

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問題	No.5020 Averaging
ユーザー	e869120
提出日時	2024-02-24 13:27:56
言語	C++14 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	927 ms / 1,000 ms
コード長	11,382 bytes
コンパイル時間	1,936 ms
コンパイル使用メモリ	119,116 KB
実行使用メモリ	284,628 KB
スコア	96,145,988
最終ジャッジ日時	2024-02-25 13:00:38
合計ジャッジ時間	50,318 ms
ジャッジサーバーID （参考情報）	judge12 / judge11
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ファイルパターン	結果
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ソースコード

raw source code
#include <iostream>
#include <map>
#include <cmath>
#include <ctime>
#include <tuple>
#include <vector>
#include <algorithm>
using namespace std;

const long long MaxVal = 1000000000000000000LL;
const long long MinVal = 100000000000000000LL;
const long long Target = 500000000000000000LL;
long long N;
long long A[59], LA[59];
long long B[59], LB[59];
long long FinalScore = MaxVal;
vector<pair<int, int>> FinalAns;

// 終盤探索用
vector<int> backtrack;
vector<pair<vector<int>, int>> Possibility;
map<long long, bool> Possibility_Record;
int IndexCount = 0;
int Masks[1 << 20];
long long MaximumA[1 << 20], MaximumB[1 << 20];
long long MinimumA[1 << 20], MinimumB[1 << 20];
int ListIndex[5000][2009];
int ListCount[5000][2009];
tuple<int, int, int> List[5000][2009];
tuple<int, int, int> ListTemp[5000][2009];

// ========================================================================================================== 初期解探索
void init_dfs(int depth, vector<long long> ArrayA) {
	for (int i = 0; i < 4; i++) {
		if (Possibility_Record[ArrayA[i]] == false) {
			Possibility_Record[ArrayA[i]] = true;
			backtrack.push_back(i + 1);
			int hash_val = 0;
			for (int j = 0; j < backtrack.size(); j++) hash_val += (backtrack[j] << (3 * j));
			Possibility.push_back(make_pair(backtrack, hash_val));
			backtrack.pop_back();
		}
	}
	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((i == 0 && j == 1 ? 1 : (i == 0 && j == 2 ? 2 : (i == 0 && j == 3 ? 3 : (i == 1 && j == 2 ? 4 : (i == 1 && j == 3 ? 5 : 6))))));
			init_dfs(depth + 1, ArrayC);
			backtrack.pop_back();
		}
	}
}

void Initialize(int mask, vector<int> idx) {
	Masks[mask] = IndexCount;
	vector<long long> ArrayA(4, 0);
	vector<long long> ArrayB(4, 0);

	// Enumerate Part
	int cnt = 0;
	for (int i = 0; i < Possibility.size(); i++) {
		ArrayA[0] = A[idx[0]]; ArrayB[0] = B[idx[0]];
		ArrayA[1] = A[idx[1]]; ArrayB[1] = B[idx[1]];
		ArrayA[2] = A[idx[2]]; ArrayB[2] = B[idx[2]];
		ArrayA[3] = A[idx[3]]; ArrayB[3] = B[idx[3]];
		for (int j = 0; j < Possibility[i].first.size(); j++) {
			if (j + 1 == Possibility[i].first.size()) {
				int num = Possibility[i].first[j] - 1;
				ListIndex[IndexCount][(ArrayA[num] >> 49) + 1]++;
				ListTemp[IndexCount][cnt] = make_tuple(ArrayB[num] >> 41, ArrayA[num] >> 41, Possibility[i].second);
				cnt += 1;
			}
			else {
				int idxA = (Possibility[i].first[j] < 4 ? 0 : (Possibility[i].first[j] < 6 ? 1 : 2));
				int idxB = Possibility[i].first[j] - (Possibility[i].first[j] < 4 ? 0 : (Possibility[i].first[j] < 6 ? 2 : 3));
				long long avgA = (ArrayA[idxA] + ArrayA[idxB]) >> 1;
				long long avgB = (ArrayB[idxA] + ArrayB[idxB]) >> 1;
				ArrayA[idxA] = avgA; ArrayB[idxA] = avgB;
				ArrayA[idxB] = avgA; ArrayB[idxB] = avgB;
			}
		}
	}

	// Add Part
	for (int i = 1; i <= 2000; i++) ListIndex[IndexCount][i] += ListIndex[IndexCount][i - 1];
	for (int i = 0; i <= 2000; i++) ListCount[IndexCount][i] = ListIndex[IndexCount][i];
	for (int i = 0; i < cnt; i++) {
		int idx = get<1>(ListTemp[IndexCount][i]) >> 8;
		List[IndexCount][ListCount[IndexCount][idx]] = ListTemp[IndexCount][i];
		ListCount[IndexCount][idx]++;
	}
}

// ========================================================================================================== 基本関数
long long GetScore(vector<int>& Order) {
	long long TotalScore1 = (A[1] >> (N - 1));
	long long TotalScore2 = (B[1] >> (N - 1));
	for (int i = 0; i < N - 1; i++) TotalScore1 += (A[Order[i]] >> (N - 1 - i));
	for (int i = 0; i < N - 1; i++) TotalScore2 += (B[Order[i]] >> (N - 1 - i));
	return max(abs(Target - TotalScore1), abs(Target - TotalScore2));
}

long long GetActual(vector<pair<int, int>>& Operation) {
	for (int i = 1; i <= N; i++) LA[i] = A[i];
	for (int i = 1; i <= N; i++) LB[i] = B[i];
	for (int i = 0; i < Operation.size(); i++) {
		int idx1 = Operation[i].first;
		int idx2 = Operation[i].second;
		long long avgA = (LA[idx1] + LA[idx2]) / 2LL;
		long long avgB = (LB[idx1] + LB[idx2]) / 2LL;
		LA[idx1] = avgA; LA[idx2] = avgA;
		LB[idx1] = avgB; LB[idx2] = avgB;
	}
	long long gosa = max(abs(Target - LA[1]), abs(Target - LB[1]));
	return gosa;
}

long double Randouble() {
	double s = 0.0, t = 1.0;
	for (int i = 0; i < 3; i++) {
		t /= 1024.0;
		s += 1.0 * (rand() % 1024) * t;
	}
	return s;
}

// ========================================================================================================== 序盤・中盤探索
vector<int> GetBestOrder() {
	vector<int> Order(N - 1, 0);
	vector<int> BestOrder(N - 1, 0);
	for (int i = 0; i < N - 1; i++) Order[i] = i + 2;

	// 準備
	long long CurrentScore = GetScore(Order);
	long long BestScore = CurrentScore;
	int StartTime = clock();

	// 焼きなまし法開始
	while (clock() - StartTime <= 10 * CLOCKS_PER_SEC / 100) {
		int idx1 = rand() % (N - 1);
		int idx2 = rand() % (N - 1);
		swap(Order[idx1], Order[idx2]);
		long long CandScore = GetScore(Order);
		double Diff = log10(CurrentScore) - log10(CandScore);
		if (Randouble() < exp(Diff / 0.17)) {
			if (BestScore > CandScore) {
				BestScore = CandScore;
				BestOrder = Order;
			}
			CurrentScore = CandScore;
		}
		else {
			swap(Order[idx1], Order[idx2]);
		}
	}
	return BestOrder;
}

// ========================================================================================================== 終盤探索
vector<int> CurrentOrder;
int StartTime;
int NumLoops;
const int TIMELIMIT = 80;

void dfs(int depth, int mask, long long CurrentA, long long CurrentB, vector<int>& Cand, vector<int>& PostOrder) {
	if ((NumLoops & 1023) == 0) {
		if (clock() - StartTime > TIMELIMIT * CLOCKS_PER_SEC / 100) return;
	}
	NumLoops += 1;
	if (depth == 4) {
		int idx = Masks[(1 << Cand.size()) - 1 - mask];
		int Remain = max(0LL, min(1999LL, CurrentA >> 8));
		for (int pos = ListIndex[idx][Remain]; pos < ListIndex[idx][Remain + 1]; pos++) {
			long long gosaA = CurrentA - 1LL * get<1>(List[idx][pos]);
			long long gosaB = CurrentB - 1LL * get<0>(List[idx][pos]);
			if (gosaA > FinalScore + 100LL || gosaB > FinalScore + 100LL || gosaA < -FinalScore - 100LL || gosaB < -FinalScore - 100LL) continue;

			// 手順の計算
			vector<int> MaskOrd;
			vector<pair<int, int>> Final;
			for (int i = 0; i < Cand.size(); i++) {
				if (!((mask >> i) & 1)) MaskOrd.push_back(Cand[i]);
			}
			for (int i = 0; i < 10; i++) {
				int val1 = (get<2>(List[idx][pos]) >> (3 * i)) & 7;
				int val2 = (get<2>(List[idx][pos]) >> (3 * i + 3)) & 7;
				if (val2 == 0) {
					Final.push_back(make_pair(1, MaskOrd[val1 - 1]));
					for (int j = CurrentOrder.size() - 1; j >= 0; j--) Final.push_back(make_pair(1, CurrentOrder[j]));
					for (int j = 0; j < PostOrder.size(); j++) Final.push_back(make_pair(1, PostOrder[j]));
					break;
				}
				else {
					int idxA = (val1 < 4 ? 0 : (val1 < 6 ? 1 : 2));
					int idxB = val1 - (val1 < 4 ? 0 : (val1 < 6 ? 2 : 3));
					Final.push_back(make_pair(MaskOrd[idxA], MaskOrd[idxB]));
				}
			}

			// スコアの計算
			long long Score = GetActual(Final);
			if (FinalScore > Score) {
				FinalScore = Score;
				FinalAns = Final;
			}
		}
		return;
	}

	// 枝刈り探索
	int dep = PostOrder.size() + CurrentOrder.size() + 1;
	int cur = (1 << Cand.size()) - 1 - mask;
	for (int i = 0; i < Cand.size(); i++) {
		if ((mask >> i) & 1) continue;
		long long NextA = CurrentA - (A[Cand[i]] >> dep);
		long long NextB = CurrentB - (B[Cand[i]] >> dep);
		if (NextA > MaximumA[cur - (1 << i)] || NextA < MinimumA[cur - (1 << i)]) continue;
		if (NextB > MaximumB[cur - (1 << i)] || NextB < MinimumB[cur - (1 << i)]) continue;
		CurrentOrder.push_back(Cand[i]);
		dfs(depth - 1, mask + (1 << i), NextA, NextB, Cand, PostOrder);
		CurrentOrder.pop_back();
	}
}

// ========================================================================================================== メイン関数
int main() {
	// Step 1. 入力
	cin >> N;
	for (int i = 1; i <= N; i++) cin >> A[i] >> B[i];

	// Step 2. 初期化
	vector<long long> Random(4, 0);
	Random[0] = 123456789123456789;
	Random[1] = 314159265358979323;
	Random[2] = 869120869120869120;
	Random[3] = 999999999999999999;
	init_dfs(0, Random);

	// Step 3. 焼きなまし法
	StartTime = clock();
	vector<int> BestOrder = GetBestOrder();

	// Step 4. 終盤探索
	for (int depth = 6; depth <= 19; depth++) {
		vector<pair<long long, int>> SortedA;
		vector<pair<long long, int>> SortedB;
		for (int i = 0; i < depth; i++) SortedA.push_back(make_pair(A[BestOrder[i]], i));
		for (int i = 0; i < depth; i++) SortedB.push_back(make_pair(B[BestOrder[i]], i));
		sort(SortedA.begin(), SortedA.end());
		sort(SortedB.begin(), SortedB.end());

		// 初期化 1 : MaximumA など
		for (int i = (depth == 6 ? 0 : (1 << (depth - 1))); i < (1 << depth); i++) {
			int cntA = 0;
			int cntB = 0;
			MinimumA[i] = -10000;
			MinimumA[i] = -10000;
			MaximumA[i] = 10000;
			MaximumB[i] = 10000;
			for (int j = depth - 1; j >= 0; j--) {
				if ((i >> SortedA[j].second) & 1) {
					if (cntA <= 3) MinimumA[i] = (SortedA[j].first >> 41);
					else MinimumA[i] += (SortedA[j].first >> (44 - cntA));
					cntA += 1;
				}
				if ((i >> SortedB[j].second) & 1) {
					if (cntB <= 3) MinimumB[i] = (SortedB[j].first >> 41);
					else MinimumB[i] += (SortedB[j].first >> (44 - cntB));
					cntB += 1;
				}
			}
			cntA = 0;
			cntB = 0;
			for (int j = 0; j < depth; j++) {
				if ((i >> SortedA[j].second) & 1) {
					if (cntA <= 3) MaximumA[i] = (SortedA[j].first >> 41);
					else MaximumA[i] += (SortedA[j].first >> (44 - cntA));
					cntA += 1;
				}
				if ((i >> SortedB[j].second) & 1) {
					if (cntB <= 3) MaximumB[i] = (SortedB[j].first >> 41);
					else MaximumB[i] += (SortedB[j].first >> (44 - cntB));
					cntB += 1;
				}
			}
			if ((i & 1023) == 0) {
				if (clock() - StartTime > TIMELIMIT * CLOCKS_PER_SEC / 100) break;
			}
		}

		// 初期化 2 : 終盤のパターン
		for (int i = 0; i < depth; i++) {
			for (int j = i + 1; j < depth; j++) {
				for (int k = j + 1; k < depth; k++) {
					for (int l = k + 1; l < depth; l++) {
						if (depth != 6 && l != depth - 1) continue;
						Initialize((1 << i) + (1 << j) + (1 << k) + (1 << l), vector<int>{BestOrder[i], BestOrder[j], BestOrder[k], BestOrder[l]});
						IndexCount += 1;
					}
				}
			}
			if (clock() - StartTime > TIMELIMIT * CLOCKS_PER_SEC / 100) break;
		}

		// 探索
		long long SumA = (A[1] >> (N - 4));
		long long SumB = (B[1] >> (N - 4));
		for (int i = depth; i < N - 1; i++) SumA += (A[BestOrder[i]] >> (N - 1 - i));
		for (int i = depth; i < N - 1; i++) SumB += (B[BestOrder[i]] >> (N - 1 - i));
		SumA = Target - SumA;
		SumB = Target - SumB;
		vector<int> Vec1;
		vector<int> Vec2;
		for (int i = 0; i < depth; i++) Vec1.push_back(BestOrder[i]);
		for (int i = depth; i < N - 1; i++) Vec2.push_back(BestOrder[i]);
		dfs(depth, 0, SumA, SumB, Vec1, Vec2);
		// printf("% 3d% 9lld% 9d% 7d\n", depth, min(99999999LL, FinalScore), NumLoops, clock() - StartTime);
		if (clock() - StartTime > TIMELIMIT * CLOCKS_PER_SEC / 100) break;
	}

	// Step 5. 出力
	cout << FinalAns.size() << endl;
	for (pair<int, int> ans : FinalAns) cout << ans.first << " " << ans.second << endl;
	return 0;
}
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