#953599 (C++14) No.5020 Averaging

提出ソース

結果

問題	No.5020 Averaging
ユーザー	e869120
提出日時	2024-02-22 13:59:22
言語	C++14 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	922 ms / 1,000 ms
コード長	6,468 bytes
コンパイル時間	1,378 ms
コンパイル使用メモリ	101,180 KB
実行使用メモリ	423,184 KB
スコア	90,633,758
最終ジャッジ日時	2024-02-25 12:53:21
合計ジャッジ時間	49,781 ms
ジャッジサーバーID （参考情報）	judge15 / judge11
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ファイルパターン	結果
other	AC * 50

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ソースコード

raw source code

#include <iostream>
#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<int> FinalOrder;
int Masks[1 << 20];
vector<tuple<int, int, int>> List[15600][1000];

// ========================================================================================================== 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<int>& Order) {
	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 < Order.size(); i++) {
		long long avgA = (LA[1] + LA[Order[i]]) / 2LL;
		long long avgB = (LB[1] + LB[Order[i]]) / 2LL;
		LA[1] = avgA; LA[Order[i]] = avgA;
		LB[1] = avgB; LB[Order[i]] = 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 <= 25 * 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;

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 > 70 * CLOCKS_PER_SEC / 100) return;
	}
	NumLoops += 1;
	if (depth <= 5) {
		int idx = Masks[(1 << Cand.size()) - 1 - mask];
		int Remain = max(0LL, min(999LL, (Target - CurrentA) / 2000LL));
		for (tuple<int, int, int> tup : List[idx][Remain]) {
			long long gosaA = abs(Target - (CurrentA + 1LL * get<1>(tup)));
			long long gosaB = abs(Target - (CurrentB + 1LL * get<0>(tup)));
			if (max(gosaA, gosaB) > FinalScore + 100LL) continue;
			vector<int> Final;
			for (int i = 0; i < 5; i++) Final.push_back(Cand[(get<2>(tup) >> (5 * i)) & 31]);
			for (int i = CurrentOrder.size() - 1; i >= 0; i--) Final.push_back(CurrentOrder[i]);
			for (int i = 0; i < PostOrder.size(); i++) Final.push_back(PostOrder[i]);
			long long Score = GetActual(Final);
			if (FinalScore > Score) {
				FinalScore = Score;
				FinalOrder = Final;
			}
		}
		return;
	}

	// 枝刈り探索
	int dep = PostOrder.size() + CurrentOrder.size() + 1;
	long long Border1 = 12LL * (MaxVal >> dep) / 10LL;
	long long Border2 = 10000LL;
	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 < Target - Border1) continue;
		if (NextB < Target - Border1) continue;
		if (NextA > Target + Border2) continue;
		if (NextB > Target + Border2) continue;
		CurrentOrder.push_back(Cand[i]);
		dfs(depth - 1, mask + (1 << i), NextA, NextB, Cand, PostOrder);
		CurrentOrder.pop_back();
	}
}

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

	// Step 2. 焼きなまし法
	StartTime = clock();
	vector<int> BestOrder = GetBestOrder();

	// Step 3. 終盤探索 (初期化)
	int IndexCount = 0;
	for (int i = 0; i < 20; i++) {
		for (int j = i + 1; j < 20; j++) {
			for (int k = j + 1; k < 20; k++) {
				for (int l = k + 1; l < 20; l++) {
					for (int m = l + 1; m < 20; m++) {
						vector<int> Order = { i, j, k, l, m };
						do {
							long long sumA = 0;
							long long sumB = 0;
							for (int idx = 0; idx < Order.size(); idx++) {
								sumA += A[BestOrder[Order[idx]]] >> (N - 1 - idx);
								sumB += B[BestOrder[Order[idx]]] >> (N - 1 - idx);
							}
							List[IndexCount][sumA / 2000LL].push_back(make_tuple(sumB, sumA, Order[0] + (Order[1] << 5) + (Order[2] << 10) + (Order[3] << 15) + (Order[4] << 20)));
						} while (next_permutation(Order.begin(), Order.end()));
						for (int n = 0; n < 1000; n++) {
							if (List[IndexCount][n].size() <= 1) continue;
							sort(List[IndexCount][n].begin(), List[IndexCount][n].end());
						}
						Masks[(1 << i) + (1 << j) + (1 << k) + (1 << l) + (1 << m)] = IndexCount;
						IndexCount += 1;
					}
				}
			}
		}
	}

	// Step 3. 終盤探索
	for (int depth = 6; depth <= 18; depth++) {
		long long SumA = (A[1] >> (N - 1));
		long long SumB = (B[1] >> (N - 1));
		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));
		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 > 70 * CLOCKS_PER_SEC / 100) break;
	}

	// Step 4. 出力
	vector<pair<int, int>> Answer;
	for (int i = 0; i < FinalOrder.size(); i++) Answer.push_back(make_pair(1, FinalOrder[i]));
	cout << Answer.size() << endl;
	for (pair<int, int> ans : Answer) cout << ans.first << " " << ans.second << endl;
	return 0;
}

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結果

ソースコード