結果
| 問題 | No.3736 Purely Bool Hell |
| コンテスト | |
| ユーザー |
 cn_449
|
| 提出日時 | 2026-09-19 16:35:48 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0 + ACL) |
| 結果 |
RE
不安定
|
| 実行時間 | - |
| コード長 | 13,790 bytes |
| 記録 | |
| コンパイル時間 | 5,641 ms |
| コンパイル使用メモリ | 382,412 KB |
| 実行使用メモリ | 10,056 KB |
| 最終ジャッジ日時 | 2026-09-19 16:36:05 |
| 合計ジャッジ時間 | 13,496 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge3_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 13 RE * 26 |
ソースコード
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <string>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <array>
#include <iomanip>
#include <utility>
#include <tuple>
#include <functional>
#include <bitset>
#include <cassert>
#include <complex>
#include <stdio.h>
#include <time.h>
#include <numeric>
#include <random>
#include <unordered_set>
#include <unordered_map>
#include <cstring>
#include <bit>
#include <chrono>
using namespace std;
#define all(a) (a).begin(), (a).end()
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define For(i, a, b) for (ll i = (a); i < (b); i++)
#define debug(...) cerr << __LINE__ << " | ", debug_out(#__VA_ARGS__, __VA_ARGS__)
#define test_only(x, y, ...) do { if ((x) != (y)) { debug(x, y, ##__VA_ARGS__); } } while (0)
#define test_same(x, y, ...) do { if ((x) != (y)) { debug(x, y, ##__VA_ARGS__); abort(); } } while (0)
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef long double ld;
template<class T> using P = pair<T, T>;
template<class T> using pri_l = priority_queue<T>;
template<class T> using pri_s = priority_queue<T, vector<T>, greater<T>>;
constexpr int inf = 1000000010;
constexpr ll INF = 1000000000000000010;
constexpr int mod1e9 = 1000000007;
constexpr int mod998 = 998244353;
constexpr ld eps = 1e-12;
constexpr ld pi = 3.141592653589793238;
constexpr ll ten(int n) { return n ? 10 * ten(n - 1) : 1; };
int dx[] = { 1,0,-1,0,1,1,-1,-1,0 }; int dy[] = { 0,1,0,-1,1,-1,1,-1,0 };
ll safe_mul(ll a, ll b, ll LIM = INF) { return (b != 0 && a > LIM / b ? LIM : a * b); }
void fail() { cout << "-1\n"; exit(0); } void no() { cout << "No\n"; exit(0); }
template<class T> void er(T a) { cout << a << '\n'; exit(0); }
template<class T, class U> inline bool chmax(T& a, const U& b) { if (a < b) { a = b; return true; } return false; }
template<class T, class U> inline bool chmin(T& a, const U& b) { if (a > b) { a = b; return true; } return false; }
template<class T, class U> ostream& operator << (ostream& s, const pair<T, U>& p) { s << p.first << ' ' << p.second; return s; }
template<class T> istream& operator >>(istream& s, vector<T>& v) { for (auto& e : v) s >> e; return s; }
template<class T> ostream& operator <<(ostream& s, const vector<T>& v) { for (auto& e : v) s << e << ' '; return s; }
struct fastio {
fastio() {
cin.tie(0); cout.tie(0);
ios::sync_with_stdio(false);
cout << fixed << setprecision(20);
cerr << fixed << setprecision(20);
}
}fastio_;
namespace rdv {
random_device seed_gen;
mt19937_64 engine(seed_gen());
ll rnum(ll r) { return engine() % r; } // [0, r)
ll rnum(ll l, ll r) { return rnum(r - l) + l; } // [l, r)
ll rng(ll l, ll r) { return rnum(l, r + 1); } // [l, r]
double rng01() { return engine() * pow(2, -64); }
template<class T> void shuf(vector<T>& v) { shuffle(all(v), engine); }
void shuf(string& s) { shuffle(all(s), engine); }
}
using namespace rdv;
template<class T> vector<int> compress(vector<T>& v) {
int n = ssize(v);
vector<T> tmp = v;
sort(tmp.begin(), tmp.end());
tmp.erase(unique(tmp.begin(), tmp.end()), tmp.end());
vector<int> res(n);
for (int i = 0; i < n; i++) res[i] = lower_bound(tmp.begin(), tmp.end(), v[i]) - tmp.begin();
return res;
}
#ifdef _MSC_VER
using lint = ll;
#else
using lint = __int128_t;
#endif
#include <atcoder/all>
using namespace atcoder;
constexpr ll mod = mod998;
using mint = static_modint<mod>;
istream& operator >>(istream& s, mint& m) { ll y; s >> y; m = y; return s; }
istream& operator >>(istream& s, vector<mint>& v) { for (auto& e : v) { ll y; s >> y; e = y; } return s; }
ostream& operator <<(ostream& s, const mint& m) { return s << m.val(); }
ostream& operator <<(ostream& s, const vector<mint>& v) { for (auto& e : v) s << e.val() << ' '; return s; }
void debug_out(const char*) { cerr << "\n"; }
template <typename T, typename... Args> void debug_out(const char* names, T value, Args... args) {
while (*names == ' ') ++names;
const char* comma = strchr(names, ',');
if (!comma) { cerr << names << ":" << value << "\n"; }
else { cerr.write(names, comma - names) << ":" << value << ", "; debug_out(comma + 1, args...); }
}
vector<mint> fac, inv, facinv;
void modcalc(int n) {
assert(fac.empty()); assert(inv.empty()); assert(facinv.empty());
fac.resize(n); inv.resize(n); facinv.resize(n);
fac[0] = 1; fac[1] = 1; inv[1] = 1;
facinv[0] = 1; facinv[1] = 1;
for (ll i = 2; i < n; i++) {
fac[i] = fac[i - 1] * i;
inv[i] = -inv[mod % i] * (mod / i);
facinv[i] = facinv[i - 1] * inv[i];
}
}
mint comb(ll n, ll k) {
if (n < 0 or k < 0 or n < k) return 0;
return fac[n] * facinv[k] * facinv[n - k];
}
mint perm(ll n, ll k) {
if (n < 0 or k < 0 or n < k) return 0;
return fac[n] * facinv[n - k];
}
mint hom(ll n, ll k) {
if (n < 0 or k < 0 or (n == 0 && k > 0)) return 0;
if (n == 0 && k == 0) return 1;
return fac[n + k - 1] * facinv[k] * facinv[n - 1];
}
int main() {
[[maybe_unused]] bool DEBUG = false;
int TEST = 1;
cin >> TEST;
while (TEST--) {
int n;
if (DEBUG) n = rng(1, 4);
else cin >> n;
vector<int> x(n), y(n), z(2 * n - 1);
if (DEBUG) {
rep(i, n) {
x[i] = rng(0, 1);
y[i] = rng(0, 1);
}
rep(i, 2 * n - 1) z[i] = rng(0, 1);
}
else cin >> x >> y >> z;
vector a(n, vector<int>(n));
if (n == 1) {
if (x[0] == y[0] && y[0] == z[0]) {
cout << x[0] << '\n';
continue;
}
else {
cout << "-1\n";
continue;
}
continue;
}
assert(n >= 2);
bool bad = false;
rep(d, 30) {
vector f(n, vector<int>(n, -1));
bool and_1 = false, or_0 = false;
rep(i, n) if (x[i] >> d & 1) and_1 = true;
rep(i, n) if (!(y[i] >> d & 1)) or_0 = true;
if (and_1 && or_0) {
bad = true;
break;
}
if (and_1) {
rep(i, n) {
if (x[i] >> d & 1) {
rep(j, n) f[i][j] = 1;
}
}
int p = -1, q = -1;
rep(i, n) {
if (!(x[i] >> d & 1)) {
if (p == -1) p = i;
else if (q == -1) q = i;
else f[i][n - 1 - i] = 0;
}
}
// p, q 行目以外は適当に埋める
// k = n-1 はどちらでも発生
// p, q 行目を両方 0 にできるなら終わり
// 目標が 1 のとき、片方しか 0 にできない
// 両方全 1 のときにのみ困っている
// 1, 1 という埋め方をしないというルールを付けると、p=0, q=n-1 以外では困らない
// 逆に p=0,q=n-1 のときは選択の余地がないからいいはず
// あー、適当すぎると大きいところで xor 条件に違反する
int LIM;
if (q != -1) LIM = q + 1;
else if (p != -1) LIM = p + 1;
else LIM = 0;
vector<int> r(2 * n - 1);
rep(i, 2 * n - 1) r[i] = z[i] >> d & 1;
rep(i, n) rep(j, n) if (f[i][j] != -1) r[i + j] ^= f[i][j];
for (int i = n - 1; i >= LIM; i--) {
for (int j = n - 1; i + j >= n; j--) {
if (f[i][j] != -1) continue;
f[i][j] = r[i + j];
r[i + j] = 0;
}
}
// debug(p, q, f);
vector<int> ord;
rep(k, 2 * n - 1) {
if (k != n - 1) ord.push_back(k);
}
ord.push_back(n - 1);
for (int k : ord) {
vector<P<int>> pos;
int sum = z[k] >> d & 1;
rep(i, n) {
int j = k - i;
if (!(0 <= j && j < n)) continue;
if (f[i][j] != -1) sum ^= f[i][j];
else pos.push_back({ i, j });
}
if (pos.empty() && sum != 0) bad = true;
// debug(d, k, sum, pos);
assert(ssize(pos) <= 2);
if (ssize(pos) == 1) {
if (k == n - 1) {
assert(q == -1);
bool have_0_p = false;
rep(j, n) if (f[p][j] == 0) have_0_p = true;
if (sum == 1 && !have_0_p) bad = true;
}
f[pos[0].first][pos[0].second] = sum;
}
else if (ssize(pos) == 2) {
if (sum == 0) {
f[pos[0].first][pos[0].second] = 0;
f[pos[1].first][pos[1].second] = 0;
}
else {
bool have_0_p = false, have_0_q = false;
rep(j, n) {
if (f[p][j] == 0) have_0_p = true;
if (f[q][j] == 0) have_0_q = true;
}
if (!have_0_p && !have_0_q) {
if (k == n - 1) {
assert(p == 0 && q == n - 1);
bad = true;
}
else {
f[pos[0].first][pos[0].second] = 0;
f[pos[1].first][pos[1].second] = 1;
}
}
else if (have_0_p) {
f[pos[0].first][pos[0].second] = 1;
f[pos[1].first][pos[1].second] = 0;
}
else {
f[pos[0].first][pos[0].second] = 0;
f[pos[1].first][pos[1].second] = 1;
}
}
}
}
}
else if (or_0) {
rep(j, n) {
if (!(y[j] >> d & 1)) {
rep(i, n) f[i][j] = 0;
}
}
int p = -1, q = -1;
rep(j, n) {
if (y[j] >> d & 1) {
if (p == -1) p = j;
else if (q == -1) q = j;
else f[n - 1 - j][j] = 1;
}
}
int LIM;
if (q != -1) LIM = q + 1;
else if (p != -1) LIM = p + 1;
else LIM = 0;
vector<int> r(2 * n - 1);
rep(i, 2 * n - 1) r[i] = z[i] >> d & 1;
rep(i, n) rep(j, n) if (f[i][j] != -1) r[i + j] ^= f[i][j];
for (int j = n - 1; j >= LIM; j--) {
for (int i = n - 1; i + j >= n; i--) {
if (f[i][j] != -1) continue;
f[i][j] = r[i + j];
r[i + j] = 0;
}
}
vector<int> ord;
rep(k, 2 * n - 1) {
if (k != n - 1) ord.push_back(k);
}
ord.push_back(n - 1);
for (int k : ord) {
vector<P<int>> pos;
int sum = z[k] >> d & 1;
rep(j, n) {
int i = k - j;
if (!(0 <= i && i < n)) continue;
if (f[i][j] != -1) sum ^= f[i][j];
else pos.push_back({ i, j });
}
if (pos.empty() && sum != 0) bad = true;
assert(ssize(pos) <= 2);
if (ssize(pos) == 1) {
if (k == n - 1) {
assert(q == -1);
bool have_1_p = false;
rep(i, n) if (f[i][p] == 1) have_1_p = true;
if (sum == 0 && !have_1_p) bad = true;
}
f[pos[0].first][pos[0].second] = sum;
}
else if (ssize(pos) == 2) {
if (sum == 0) {
f[pos[0].first][pos[0].second] = 1;
f[pos[1].first][pos[1].second] = 1;
}
else {
bool have_1_p = false, have_1_q = false;
rep(i, n) {
if (f[i][p] == 1) have_1_p = true;
if (f[i][q] == 1) have_1_q = true;
}
if (!have_1_p && !have_1_q) {
if (k == n - 1) {
assert(p == 0 && q == n - 1);
bad = true;
}
else {
f[pos[0].first][pos[0].second] = 1;
f[pos[1].first][pos[1].second] = 0;
}
}
else if (have_1_p) {
f[pos[0].first][pos[0].second] = 0;
f[pos[1].first][pos[1].second] = 1;
}
else {
f[pos[0].first][pos[0].second] = 1;
f[pos[1].first][pos[1].second] = 0;
}
}
}
}
}
else {
if (n == 2) {
int z0 = z[0] >> d & 1;
int z1 = z[1] >> d & 1;
int z2 = z[2] >> d & 1;
if (z0 == 0 && z1 == 0 && z2 == 0) {
f[0][0] = 0, f[0][1] = 1, f[1][0] = 1, f[1][1] = 0;
}
else if (z0 == 1 && z1 == 0 && z2 == 1) {
f[0][0] = 1, f[0][1] = 0, f[1][0] = 0, f[1][1] = 1;
}
else {
bad = true;
break;
}
}
else if (n == 3) {
f[0][0] = z[0] >> d & 1;
f[2][2] = z[4] >> d & 1;
bool valid = false;
rep(bt, 16) {
int f01 = bt >> 0 & 1;
int f02 = bt >> 1 & 1;
int f11 = bt >> 2 & 1;
int f12 = bt >> 3 & 1;
int f00 = f[0][0], f22 = f[2][2];
int f10 = (z[1] >> d & 1) ^ f01;
int f20 = (z[2] >> d & 1) ^ f02 ^ f11;
int f21 = (z[3] >> d & 1) ^ f12;
bool x0 = f00 == 0 or f01 == 0 or f02 == 0;
bool x1 = f10 == 0 or f11 == 0 or f12 == 0;
bool x2 = f20 == 0 or f21 == 0 or f22 == 0;
bool y0 = f00 == 1 or f10 == 1 or f20 == 1;
bool y1 = f01 == 1 or f11 == 1 or f21 == 1;
bool y2 = f02 == 1 or f12 == 1 or f22 == 1;
if (x0 && x1 && x2 && y0 && y1 && y2) {
valid = true;
f[0][1] = f01, f[0][2] = f02;
f[1][0] = f10, f[1][1] = f11, f[1][2] = f12;
f[2][0] = f20, f[2][1] = f21;
break;
}
}
if (!valid) bad = true;
}
else if (n >= 4) {
rep(i, n) {
f[(i + 1) % n][i] = 0;
f[(i + 2) % n][i] = 1;
}
rep(k, 2 * n - 1) {
int sum = z[k] >> d & 1;
vector<P<int>> pos;
rep(i, n) {
int j = k - i;
if (!(0 <= j && j < n)) continue;
if (f[i][j] != -1) sum ^= f[i][j];
else pos.push_back({ i, j });
}
assert(!pos.empty());
f[pos[0].first][pos[0].second] = sum;
For(i, 1, ssize(pos)) f[pos[i].first][pos[i].second] = 0;
}
}
}
if (bad) break;
// debug(f);
rep(i, n) rep(j, n) assert(f[i][j] != -1);
rep(i, n) rep(j, n) a[i][j] += f[i][j] << d;
}
/*{
vector<int> X(n, (1 << 30) - 1), Y(n), Z(2 * n - 1);
rep(i, n) rep(j, n) {
X[i] &= a[i][j];
Y[j] |= a[i][j];
Z[i + j] ^= a[i][j];
}
if (!(x == X && y == Y && z == Z)) bad = true;
}*/
if (bad) {
cout << "-1\n";
if (DEBUG && n <= 4) {
rep(bt, 1 << (n * n)) {
vector<int> X(n, 1), Y(n), Z(2 * n - 1);
rep(i, n) rep(j, n) {
int w = bt >> (i * n + j) & 1;
X[i] &= w;
Y[j] |= w;
Z[i + j] ^= w;
}
if (x == X && y == Y && z == Z) {
debug(a, x, y, z);
assert(false);
}
}
}
}
else {
rep(i, n) rep(j, n) cout << a[i][j] << " \n"[j == n - 1];
if (DEBUG) {
vector<int> X(n, (1 << 30) - 1), Y(n), Z(2 * n - 1);
rep(i, n) rep(j, n) {
X[i] &= a[i][j];
Y[j] |= a[i][j];
Z[i + j] ^= a[i][j];
}
if (!(x == X && y == Y && z == Z)) {
debug(x, y, z, X, Y, Z);
}
}
}
}
}