結果

問題 No.2608 Divide into two
ユーザー AerenAeren
提出日時 2024-01-19 21:26:48
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 14 ms / 1,000 ms
コード長 4,807 bytes
コンパイル時間 3,686 ms
コンパイル使用メモリ 278,352 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-28 03:57:12
合計ジャッジ時間 4,349 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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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 AC 2 ms
5,248 KB
testcase_01 AC 5 ms
5,376 KB
testcase_02 AC 14 ms
5,376 KB
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ソースコード

diff # 

#include <bits/stdc++.h>
// #include <x86intrin.h>
using namespace std;
#if __cplusplus >= 202002L
using namespace numbers;
#endif

// Given a set of items where i-th item has non-negative weight w[i],
// find a subset S such that \sum_{i \in S} w[i] <= threshold and \sum_{i \in S} w[i] is maximized
struct subset_sum{
	vector<int> _pref;
	vector<vector<int>> _dp;
	vector<vector<array<int, 2>>> _prev;
	// w[i] < weight_bound
	// O(n * bound)
	void run_for_bounded_weight(const vector<int> &w, int weight_bound, int threshold){
		assert(weight_bound > 0 && threshold >= 0);
		for(auto x: w) assert(0 <= x && x < weight_bound);
		int n = (int)w.size();
		_pref = {0};
		while((int)_pref.size() - 1 < n && _pref.back() + w[(int)_pref.size() - 1] <= threshold) _pref.push_back(_pref.back() + w[(int)_pref.size() - 1]);
		const int cut = (int)_pref.size() - 1;
		if(n == cut){
			subset_weight = _pref[n];
			in_subset.assign(n, true);
			subset.resize(n);
			iota(subset.begin(), subset.end(), 0);
			return;
		}
		_dp.assign(n - cut + 1, vector<int>(weight_bound << 1));
		_prev.assign(n - cut + 1, vector<array<int, 2>>(weight_bound << 1, {-1, -1}));
		fill(_dp[0].begin() + weight_bound, _dp[0].end(), 0);
		_dp[0][weight_bound - 1] = cut + 1;
		for(auto x = weight_bound - 1; x >= 0; -- x) if(_dp[0][x]) for(auto l = _dp[0][x] - 1; l >= 1; -- l){
			if(x >= w[l - 1] && _dp[0][x - w[l - 1]] < l){
				_dp[0][x - w[l - 1]] = l;
				_prev[0][x - w[l - 1]] = {0, x};
			}
		}
		for(auto r = 1; r <= n - cut; ++ r) for(auto x = 2 * weight_bound - 1; x >= 0; -- x){
			if(_dp[r][x] < _dp[r - 1][x]){
				_dp[r][x] = _dp[r - 1][x];
				_prev[r][x] = {r - 1, x};
			}
			if(x >= w[cut + r - 1] && _dp[r][x] < _dp[r - 1][x - w[cut + r - 1]]){
				_dp[r][x] = _dp[r - 1][x - w[cut + r - 1]];
				_prev[r][x] = {r - 1, x - w[cut + r - 1]};
			}
			for(auto l = _dp[r][x] - 1; l >= max(1, _dp[r - 1][x]); -- l) if(x >= w[l - 1] && _dp[r][x - w[l - 1]] < l){
				_dp[r][x - w[l - 1]] = l;
				_prev[r][x - w[l - 1]] = {r, x};
			}
		}
		subset_weight = threshold;
		while(!_dp[n - cut][subset_weight - _pref.back() + weight_bound - 1]) -- subset_weight;
		in_subset.assign(n, false);
		fill(in_subset.begin(), in_subset.begin() + cut, true);
		for(auto r = n - cut, weight = subset_weight - _pref.back() + weight_bound - 1; ; ){
			auto [nr, nweight] = _prev[r][weight];
			if(!~nr) break;
			if(r == nr) in_subset[_dp[r][weight] - 1] = false;
			else if(weight != nweight) in_subset[cut + r - 1] = true;
			r = nr, weight = nweight;
		}
		subset.clear();
		for(auto i = 0; i < n; ++ i) if(in_subset[i]) subset.push_back(i);
	}
	// O(n * log(\sum{w}) + SZ * sqrt(\sum{w}) / bit_width)
	template<size_t SZ>
	void run_for_small_total_weight(const vector<int> &w, int threshold){
		assert(threshold >= 0 && threshold < SZ);
		int n = (int)w.size();
		map<int, list<list<int>>> mp;
		for(auto i = 0; i < (int)w.size(); ++ i) mp[w[i]].push_back({i});
		vector<pair<int, list<int>>> ordered_pool;
		while(!mp.empty()){
			int weight = mp.begin()->first;
			auto &from = mp.begin()->second;
			if((int)from.size() >= 3){
				auto &to = mp[weight << 1];
				while((int)from.size() >= 3){
					next(from.begin())->splice(next(from.begin())->begin(), from.front());
					from.pop_front();
					to.push_back(move(from.front()));
					from.pop_front();
				}
			}
			for(; !from.empty(); from.pop_front()) ordered_pool.push_back({weight, move(from.front())});
			mp.erase(mp.begin());
		}
		vector<int> first_appear(threshold + 1, -1);
		bitset<SZ> dp{};
		dp[0] = true;
		for(auto i = 0; i < (int)ordered_pool.size(); ++ i){
			int weight = ordered_pool[i].first;
			auto dp_next = dp | dp << weight;
			auto dif = dp ^ dp_next;
			for(auto x = dif._Find_first(); x <= threshold; x = dif._Find_next(x)) first_appear[x] = i;
			dp = dp_next;
		}
		subset_weight = threshold;
		while(!dp[subset_weight]) -- subset_weight;
		in_subset.assign(n, false);
		subset.clear();
		for(auto weight = subset_weight; weight; ){
			int i = first_appear[weight];
			for(auto ind: ordered_pool[i].second){
				in_subset[ind] = true;
				subset.push_back(ind);
			}
			weight -= ordered_pool[i].first;
		}
	}
	int subset_weight;
	vector<int> in_subset, subset;
};

int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(ios::badbit | ios::failbit);
	auto __solve_tc = [&](auto __tc_num)->int{
		int n;
		cin >> n;
		if(n * (n + 1) / 2 & 1){
			cout << "-1\n";
			return 0;
		}
		subset_sum ss;
		vector<int> a(n);
		iota(a.begin(), a.end(), 1);
		ss.run_for_small_total_weight<10001>(a, n * (n + 1) / 4);
		ranges::copy(ss.in_subset, ostream_iterator<int>(cout, ""));
		cout << "\n";
		return 0;
	};
	int __tc_cnt;
	cin >> __tc_cnt;
	for(auto __tc_num = 0; __tc_num < __tc_cnt; ++ __tc_num){
		__solve_tc(__tc_num);
	}
	return 0;
}

/*

*/
0