結果
問題 | No.2505 matriX cOnstRuction |
ユーザー | 👑 emthrm |
提出日時 | 2023-07-26 19:33:17 |
言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 305 ms / 2,500 ms |
コード長 | 5,363 bytes |
コンパイル時間 | 1,310 ms |
コンパイル使用メモリ | 129,944 KB |
実行使用メモリ | 9,912 KB |
最終ジャッジ日時 | 2023-10-13 18:17:31 |
合計ジャッジ時間 | 7,068 ms |
ジャッジサーバーID (参考情報) |
judge15 / judge13 |
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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
4,352 KB |
testcase_01 | AC | 58 ms
4,348 KB |
testcase_02 | AC | 49 ms
4,352 KB |
testcase_03 | AC | 47 ms
4,352 KB |
testcase_04 | AC | 47 ms
4,352 KB |
testcase_05 | AC | 49 ms
4,348 KB |
testcase_06 | AC | 58 ms
4,352 KB |
testcase_07 | AC | 31 ms
4,348 KB |
testcase_08 | AC | 30 ms
4,348 KB |
testcase_09 | AC | 31 ms
4,348 KB |
testcase_10 | AC | 32 ms
4,348 KB |
testcase_11 | AC | 31 ms
4,352 KB |
testcase_12 | AC | 30 ms
4,352 KB |
testcase_13 | AC | 30 ms
4,352 KB |
testcase_14 | AC | 30 ms
4,348 KB |
testcase_15 | AC | 29 ms
4,352 KB |
testcase_16 | AC | 30 ms
4,348 KB |
testcase_17 | AC | 30 ms
4,348 KB |
testcase_18 | AC | 30 ms
4,348 KB |
testcase_19 | AC | 30 ms
4,348 KB |
testcase_20 | AC | 30 ms
4,348 KB |
testcase_21 | AC | 30 ms
4,348 KB |
testcase_22 | AC | 32 ms
4,352 KB |
testcase_23 | AC | 30 ms
4,348 KB |
testcase_24 | AC | 31 ms
4,352 KB |
testcase_25 | AC | 30 ms
4,348 KB |
testcase_26 | AC | 31 ms
4,352 KB |
testcase_27 | AC | 31 ms
4,348 KB |
testcase_28 | AC | 31 ms
4,348 KB |
testcase_29 | AC | 32 ms
4,348 KB |
testcase_30 | AC | 17 ms
4,348 KB |
testcase_31 | AC | 17 ms
4,348 KB |
testcase_32 | AC | 17 ms
4,348 KB |
testcase_33 | AC | 17 ms
4,352 KB |
testcase_34 | AC | 23 ms
4,348 KB |
testcase_35 | AC | 20 ms
4,352 KB |
testcase_36 | AC | 21 ms
4,352 KB |
testcase_37 | AC | 22 ms
4,352 KB |
testcase_38 | AC | 25 ms
4,352 KB |
testcase_39 | AC | 29 ms
4,352 KB |
testcase_40 | AC | 24 ms
4,348 KB |
testcase_41 | AC | 52 ms
4,376 KB |
testcase_42 | AC | 24 ms
4,352 KB |
testcase_43 | AC | 58 ms
6,984 KB |
testcase_44 | AC | 50 ms
4,536 KB |
testcase_45 | AC | 58 ms
6,996 KB |
testcase_46 | AC | 48 ms
4,524 KB |
testcase_47 | AC | 57 ms
7,052 KB |
testcase_48 | AC | 34 ms
4,352 KB |
testcase_49 | AC | 69 ms
4,928 KB |
testcase_50 | AC | 70 ms
4,788 KB |
testcase_51 | AC | 305 ms
4,348 KB |
testcase_52 | AC | 81 ms
9,248 KB |
testcase_53 | AC | 72 ms
7,228 KB |
testcase_54 | AC | 82 ms
9,912 KB |
testcase_55 | AC | 25 ms
4,348 KB |
testcase_56 | AC | 25 ms
4,348 KB |
testcase_57 | AC | 24 ms
4,348 KB |
testcase_58 | AC | 25 ms
4,348 KB |
testcase_59 | AC | 25 ms
4,348 KB |
testcase_60 | AC | 26 ms
4,352 KB |
testcase_61 | AC | 25 ms
4,348 KB |
testcase_62 | AC | 24 ms
4,348 KB |
testcase_63 | AC | 18 ms
4,352 KB |
ソースコード
#include <algorithm> #include <array> #include <bit> #include <bitset> #include <cassert> #include <iostream> #include <iterator> #include <numeric> #include <tuple> #include <vector> int KthBit(const int x, const int k) { return x >> k & 1; } // <AC> // できる限り枝刈りを行っている。 template <int D> int Solve(const std::vector<int>& rc, const std::vector<std::vector<int>>& a) { const int n = a.size(), m = a.front().size(); assert(std::ssize(rc) == n + m); // ビットごと 2 グループに分ける std::vector group(n + m, std::bitset<D>()); for (int bit = 0; bit < D; ++bit) { const int criteria = KthBit(a.front().front(), bit); for (int i = 1; i < n; ++i) { const int is_diff = (KthBit(a[i].front(), bit) != criteria ? 1 : 0); for (int j = 1; j < m; ++j) { if (KthBit(a.front()[j], bit) ^ is_diff != KthBit(a[i][j], bit)) { return -1; } } if (is_diff == 1) group[i].set(bit); } if (criteria == 1) group[n].set(bit); for (int j = 1; j < m; ++j) { const int is_diff = (KthBit(a.front()[j], bit) != criteria ? 1 : 0); for (int i = 1; i < n; ++i) { if (KthBit(a[i].front(), bit) ^ is_diff != KthBit(a[i][j], bit)) { return -1; } } if (KthBit(a.front()[j], bit) == 1) group[j + n].set(bit); } } const auto Operation = [&rc, &group]( const int bit, const int choice, const std::vector<int>& or_012, const std::vector<int>& or_01, const std::vector<int>& or_12) -> std::tuple<bool, int, std::vector<int>, std::vector<int>, std::vector<int>> { int cost = 0; std::vector<int> next_or_012, next_or_01, next_or_12; for (const int i : or_012) { if (group[i][bit] == choice) { // 1 if (KthBit(rc[i], bit) == 0) { return {false, 0, std::vector<int>{}, std::vector<int>{}, std::vector<int>{}}; } ++cost; next_or_12.emplace_back(i); } else { // 0 (KthBit(rc[i], bit) == 1 ? next_or_01 : next_or_012).emplace_back(i); } } for (const int i : or_01) { if (group[i][bit] == choice) { ++cost; } else { next_or_01.emplace_back(i); } } for (const int i : or_12) { const int bit_of_i = (group[i][bit] == choice ? 1 : 0); const int bit_of_rc = KthBit(rc[i], bit); if (bit_of_i > bit_of_rc) { ++cost; } else if (bit_of_i == bit_of_rc) { next_or_12.emplace_back(i); } } return {true, cost, next_or_012, next_or_01, next_or_12}; }; const int argmin = std::distance(rc.begin(), std::ranges::min_element(rc)); const int need_to_choose = // これより上位のビットは自由に選べない std::bit_width(static_cast<unsigned int>(rc[argmin])); int current_cost = 0; std::vector<int> or_012(n + m), or_01, or_12; std::iota(or_012.begin(), or_012.end(), 0); for (int bit = D - 1; bit >= need_to_choose; --bit) { const int choice = group[argmin][bit] ^ 1; bool is_valid; int added_cost; std::tie(is_valid, added_cost, or_012, or_01, or_12) = Operation(bit, choice, or_012, or_01, or_12); if (!is_valid) return -1; current_cost += added_cost; } int min_cost = (n + m) * 2 + 1; // 上位からグループを決定する const auto dfs = [Operation, &min_cost]( auto dfs, const int bit, const int current_cost, 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_cost = std::min(min_cost, current_cost); return; } std::array<int, 2> next_cost{}; std::array<std::vector<int>, 2> next_or_012{}, next_or_01{}, next_or_12{}; for (const int choice : std::array<int, 2>{0, 1}) { std::tie(std::ignore, next_cost[choice], next_or_012[choice], next_or_01[choice], next_or_12[choice]) = Operation(bit, choice, or_012, or_01, or_12); next_cost[choice] += current_cost; } const int earlier = (next_cost[0] + next_or_012[0].size() + next_or_01[0].size() < next_cost[1] + next_or_012[1].size() + next_or_01[1].size() ? 0 : 1); for (const int parity : std::array<int, 2>{0, 1}) { const int choice = parity ^ earlier; if (next_cost[choice] >= min_cost) continue; // 枝刈り dfs(dfs, bit - 1, next_cost[choice], next_or_012[choice], next_or_01[choice], next_or_12[choice]); } }; dfs(dfs, need_to_choose - 1, current_cost, or_012, or_01, or_12); return min_cost; } 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> rc(n + m); for (int i = 0; i < n + m; ++i) { std::cin >> rc[i]; assert(0 <= rc[i] && rc[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>(rc, a) << '\n'; } return 0; }