#895425 (C++23) No.2505 matriX cOnstRuction

• 問題: No.2505 matriX cOnstRuction
• ユーザー: 👑 emthrm
• 提出日時: 2023-07-26 21:41:48
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 500 ms / 2,500 ms
• コード長: 3,178 bytes
• コンパイル時間: 1,200 ms
• コンパイル使用メモリ: 113,192 KB
• 実行使用メモリ: 12,544 KB
• 最終ジャッジ日時: 2024-09-15 14:06:50
• 合計ジャッジ時間: 6,309 ms
• ジャッジサーバーID （参考情報）: judge6 / judge5

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	62 ms; 5,376 KB
testcase_02	AC	53 ms; 5,376 KB
testcase_03	AC	52 ms; 5,376 KB
testcase_04	AC	52 ms; 5,376 KB
testcase_05	AC	53 ms; 5,376 KB
testcase_06	AC	62 ms; 5,376 KB
testcase_07	AC	34 ms; 5,376 KB
testcase_08	AC	35 ms; 5,376 KB
testcase_09	AC	34 ms; 5,376 KB
testcase_10	AC	35 ms; 5,376 KB
testcase_11	AC	34 ms; 5,376 KB
testcase_12	AC	35 ms; 5,376 KB
testcase_13	AC	35 ms; 5,376 KB
testcase_14	AC	35 ms; 5,376 KB
testcase_15	AC	35 ms; 5,376 KB
testcase_16	AC	34 ms; 5,376 KB
testcase_17	AC	34 ms; 5,376 KB
testcase_18	AC	34 ms; 5,376 KB
testcase_19	AC	34 ms; 5,376 KB
testcase_20	AC	34 ms; 5,376 KB
testcase_21	AC	35 ms; 5,376 KB
testcase_22	AC	34 ms; 5,376 KB
testcase_23	AC	34 ms; 5,376 KB
testcase_24	AC	35 ms; 5,376 KB
testcase_25	AC	34 ms; 5,376 KB
testcase_26	AC	33 ms; 5,376 KB
testcase_27	AC	35 ms; 5,376 KB
testcase_28	AC	33 ms; 5,376 KB
testcase_29	AC	35 ms; 5,376 KB
testcase_30	AC	18 ms; 5,376 KB
testcase_31	AC	19 ms; 5,376 KB
testcase_32	AC	18 ms; 5,376 KB
testcase_33	AC	19 ms; 5,376 KB
testcase_34	AC	26 ms; 5,376 KB
testcase_35	AC	20 ms; 5,376 KB
testcase_36	AC	26 ms; 5,376 KB
testcase_37	AC	24 ms; 5,376 KB
testcase_38	AC	23 ms; 5,376 KB
testcase_39	AC	26 ms; 5,376 KB
testcase_40	AC	23 ms; 5,376 KB
testcase_41	AC	45 ms; 5,376 KB
testcase_42	AC	23 ms; 5,376 KB
testcase_43	AC	50 ms; 7,296 KB
testcase_44	AC	45 ms; 5,376 KB
testcase_45	AC	50 ms; 7,168 KB
testcase_46	AC	46 ms; 5,376 KB
testcase_47	AC	50 ms; 7,296 KB
testcase_48	AC	30 ms; 5,376 KB
testcase_49	AC	215 ms; 5,376 KB
testcase_50	AC	214 ms; 5,376 KB
testcase_51	AC	500 ms; 5,376 KB
testcase_52	AC	75 ms; 12,544 KB
testcase_53	AC	70 ms; 10,064 KB
testcase_54	AC	77 ms; 12,544 KB
testcase_55	AC	23 ms; 5,376 KB
testcase_56	AC	23 ms; 5,376 KB
testcase_57	AC	24 ms; 5,376 KB
testcase_58	AC	24 ms; 5,376 KB
testcase_59	AC	24 ms; 5,376 KB
testcase_60	AC	24 ms; 5,376 KB
testcase_61	AC	24 ms; 5,376 KB
testcase_62	AC	24 ms; 5,376 KB
testcase_63	AC	16 ms; 5,376 KB

ソースコード

#include <algorithm>
#include <array>
#include <cassert>
#include <iostream>
#include <iterator>
#include <numeric>
#include <tuple>
#include <vector>

int KthBit(const int x, const int k) { return x >> k & 1; }

template <int D>
int Solve(const std::vector<int>& z, const std::vector<std::vector<int>>& a) {
  const int n = a.size(), m = a.front().size();
  assert(std::ssize(z) == n + m);

  // A から S, T を決める
  std::vector<int> y(n + m, 0);
  for (int i = 1; i < n; ++i) {
    y[i] = a[i].front() ^ a.front().front();
  }
  for (int j = 0; j < m; ++j) {
    y[j + n] = a.front()[j];
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      if ((y[i] ^ y[j + n]) != a[i][j]) return -1;
    }
  }

  int min_fx = (n + m) * 2 + 1;

  // 上位から x を決める
  const auto dfs = [&z, &y, &min_fx](
      auto dfs, const int bit, const int fx, const std::vector<int>& or_012,
      const std::vector<int>& or_01, const std::vector<int>& or_12) -> void {
    if ((or_012.empty() && or_01.empty() && or_12.empty()) || bit < 0) {
      min_fx = std::min(min_fx, fx);
      return;
    }
    for (const int x_bit : std::array<int, 2>{0, 1}) {
      bool is_valid = true;
      int next_fx = fx;
      std::vector<int> next_or_012, next_or_01, next_or_12;
      for (const int i : or_012) {
        if (KthBit(y[i], bit) != x_bit) {  // (x ⊕ Y[i])[bit] = 1
          if (KthBit(z[i], bit) == 0) {
            is_valid = false;
            break;
          }
          ++next_fx;
          next_or_12.emplace_back(i);
        } else {  // (x ⊕ Y[i])[bit] = 0
          (KthBit(z[i], bit) == 1 ? next_or_01 : next_or_012).emplace_back(i);
        }
      }
      if (!is_valid) continue;
      for (const int i : or_01) {
        if (KthBit(y[i], bit) != x_bit) {  // (x ⊕ Y[i])[bit] = 1
          ++next_fx;
        } else {  // (x ⊕ Y[i])[bit] = 0
          next_or_01.emplace_back(i);
        }
      }
      for (const int i : or_12) {
        const int x_xor_y = (KthBit(y[i], bit) != x_bit ? 1 : 0);
        const int z_bit = KthBit(z[i], bit);
        if (x_xor_y > z_bit) {
          ++next_fx;
        } else if (x_xor_y == z_bit) {
          next_or_12.emplace_back(i);
        }
      }
      dfs(dfs, bit - 1, next_fx, next_or_012, next_or_01, next_or_12);
    }
  };
  std::vector<int> or_012(n + m);
  std::iota(or_012.begin(), or_012.end(), 0);
  dfs(dfs, D - 1, 0, or_012, std::vector<int>{}, std::vector<int>{});

  return min_fx > (n + m) * 2 ? -1 : min_fx;
}

int main() {
  constexpr int kMaxT = 50000, kMaxNM = 50000, kDigits = 30;

  int t;
  std::cin >> t;
  assert(1 <= t && t <= kMaxT);

  while (t--) {
    int n, m;
    std::cin >> n >> m;
    assert(1 <= n && 1 <= m && n * m <= kMaxNM);
    std::vector<int> z(n + m);
    for (int i = 0; i < n + m; ++i) {
      std::cin >> z[i];
      assert(0 <= z[i] && z[i] < (1 << kDigits));
    }
    std::vector a(n, std::vector(m, 0));
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < m; ++j) {
        std::cin >> a[i][j];
        assert(0 <= a[i][j] && a[i][j] < (1 << kDigits));
      }
    }
    std::cout << Solve<kDigits>(z, a) << '\n';
  }
  return 0;
}