結果

問題 No.2895 Zero XOR Subset
コンテスト
ユーザー 👑 binap
提出日時 2024-09-22 06:23:15
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
RE  
実行時間 -
コード長 5,841 bytes
コンパイル時間 4,467 ms
コンパイル使用メモリ 268,220 KB
最終ジャッジ日時 2025-02-24 11:28:56
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1 RE * 1
other MLE * 1 -- * 34
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ソースコード

diff # 

#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,n) for(int i=0;i<n;i++)
using namespace std;
using namespace atcoder;
typedef long long ll;
typedef vector<int> vi;
typedef vector<long long> vl;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef long double ld;
typedef pair<int, int> P;

ostream& operator<<(ostream& os, const modint& a) {os << a.val(); return os;}
template <int m> ostream& operator<<(ostream& os, const static_modint<m>& a) {os << a.val(); return os;}
template <int m> ostream& operator<<(ostream& os, const dynamic_modint<m>& a) {os << a.val(); return os;}
template<typename T> istream& operator>>(istream& is, vector<T>& v){int n = v.size(); assert(n > 0); rep(i, n) is >> v[i]; return is;}
template<typename U, typename T> ostream& operator<<(ostream& os, const pair<U, T>& p){os << p.first << ' ' << p.second; return os;}
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : " "); return os;}
template<typename T> ostream& operator<<(ostream& os, const vector<vector<T>>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : ""); return os;}
template<typename T> ostream& operator<<(ostream& os, const set<T>& se){for(T x : se) os << x << " "; os << "\n"; return os;}
template<typename T> ostream& operator<<(ostream& os, const unordered_set<T>& se){for(T x : se) os << x << " "; os << "\n"; return os;}
template<typename S, auto op, auto e> ostream& operator<<(ostream& os, const atcoder::segtree<S, op, e>& seg){int n = seg.max_right(0, [](S){return true;}); rep(i, n) os << seg.get(i) << (i == n - 1 ? "\n" : " "); return os;}
template<typename S, auto op, auto e, typename F, auto mapping, auto composition, auto id> ostream& operator<<(ostream& os, const atcoder::lazy_segtree<S, op, e, F, mapping, composition, id>& seg){int n = seg.max_right(0, [](S){return true;}); rep(i, n) os << seg.get(i) << (i == n - 1 ? "\n" : " "); return os;}

template<typename T> void chmin(T& a, T b){a = min(a, b);}
template<typename T> void chmax(T& a, T b){a = max(a, b);}

// https://youtu.be/ylWYSurx10A?t=2352
template<typename T>
struct Matrix  : vector<vector<T>> {
	int h, w;
	Matrix(int h, int w, T val=0): vector<vector<T>>(h, vector<T>(w, val)), h(h), w(w) {}
	Matrix(initializer_list<initializer_list<T>> a) : vector<vector<T>>(a.begin(), a.end()){
		assert(int(this->size()) >= 1);
		assert(int((*this)[0].size()) >= 1);
		h = this->size();
		w = (*this)[0].size();
		rep(i, h) assert(int((*this)[i].size()) == w);
	}
	Matrix& unit() {
		assert(h == w);
		rep(i,h) (*this)[i][i] = 1;
		return *this;
	}
	Matrix operator*=(const Matrix& M){
		assert(w == M.h);
		Matrix r(h, M.w);
		rep(i,h) rep(k,w) rep(j, M.w){
			r[i][j] += (*this)[i][k] * M[k][j];
		}
		swap(*this, r);
		return *this;
	}
	Matrix operator*(const Matrix& M) const {return (Matrix(*this) *= M);}
	Matrix operator*=(const T& a) {
		for(int i = 0; i < h; i++) for(int j = 0; j < w; j++) (*this)[i][j] *= a;
		return *this;
	}
	Matrix operator*(const T& a) const {return (Matrix(*this) *= a);}
	Matrix operator+=(const Matrix& M){
		assert(h == M.h and w == M.w);
		for(int i = 0; i < h; i++) for(int j = 0; j < w; j++) (*this)[i][j] += M[i][j];
		return *this;
	}
	Matrix operator+(const Matrix& M) const {return (Matrix(*this) += M);}
	Matrix pow(long long t) const {
		assert(h == w);
		if (!t) return Matrix(h,h).unit();
		if (t == 1) return *this;
		Matrix r = pow(t>>1);r = r*r;
		if (t&1) r = r*(*this);
		return r;
	}
};

template<typename T>
pair<int, Matrix<T>> eliminate(Matrix<T> a){
	int h = a.h;
	int w = a.w;
	
	int ny = 0;
	rep(x, w){
		for(int y = ny; y < h; y++){
			if(a[y][x] != T(0)){
				swap(a[y], a[ny]);
				break;
			}
		}
		if(a[ny][x] == T(0)) continue;
		rep(y, h){
			if(y != ny and a[y][x] != T(0)){
				T c = a[y][x] / a[ny][x];
				rep(x, w){
					a[y][x] -= a[ny][x] * c;
				}
			}
		}
		ny++;
		if(ny == h) break;
	}
	return make_pair(ny, a);
};

// time: O(HW + rank(W - rank))
// space: O(HW + W(W - rank))
// solve aM = b
// a = a_0 + Sum_{i=1,...,w - rank} c_i a_i
// c_i is arbitrary constant

template<typename T>
tuple<int, vector<T>, vector<vector<T>>> solve(Matrix<T> mat, vector<T> b){
	int h = mat.h;
	int w = mat.w;
	assert(h == int(b.size()));
	
	{
		Matrix<T> mat_new(h, w + 1);
		rep(y, h) rep(x, w) mat_new[y][x] = mat[y][x];
		rep(y, h) mat_new[y][w] = b[y];
		swap(mat, mat_new);
	}
	
	int rank;
	
	{
		auto res = eliminate(mat);
		rank = res.first;
		mat = res.second;
	}
	
	
	
	vector<int> fixed;
	vector<int> unfixed;
	
	{
		int y = 0;
		rep(x, w){
			if(y == h){
				unfixed.push_back(x);
				continue;
			}
			if(mat[y][x] == T(0)){
				unfixed.push_back(x);
			}else{
				fixed.push_back(x);
				y++;
			}
		}
		for(; y < h; y++){
			if(mat[y][w] != T(0)){
					return make_tuple(-1, vector<T>(0), vector<vector<T>>(0));
			}
		}
	}
	
	int freedom = w - rank;
	
	vector<T> a_0(w);
	vector<vector<T>> a_vec(freedom);
	rep(i, freedom) a_vec[i].resize(w);
	
	{
		rep(y, rank) a_0[fixed[y]] = mat[y][w] / mat[y][fixed[y]];
	}
	rep(i, freedom){
		a_vec[i][unfixed[i]] = 1;
		rep(y, rank) a_vec[i][fixed[y]] = -(mat[y][unfixed[i]]) / mat[y][fixed[y]];
		break;
	}
	return make_tuple(freedom, a_0, a_vec);
}


using mint = modint;

const int M = 60;

int main(){
	mint::set_mod(2);
	
	int n;
	cin >> n;
	
	vector<long long> a(n);
	cin >> a;
	
	Matrix<mint> mat(M, n);
	rep(i, n){
		rep(j, M){
			if((a[i] >> j) & 1) mat[j][i] = 1;
		}
	}
	vector<mint> zero(M);
	
	auto [freedom, a_0, a_vec] = solve(mat, zero);
	if(freedom == -1){
		cout << "-1\n";
		return 0;
	}else{
		{
			int i = 0;
			vector<int> ans;
			rep(j, n) if(a_vec[i][j] != mint(0)) ans.push_back(j);
			cout << ans.size() <<" \n";
			for(int idx : ans) cout << idx + 1 << ' ';
		}
	}
	return 0;
}
0