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// Notes: // - queries are [l, r] // - add(int array_id) -> void // - undo() -> void // - get(QueryT query) -> ResultT // // Tested: // - https://www.spoj.com/problems/FREQ2/ (submission ID: 30602190) // - https://www.spoj.com/problems/KDOMINO/ (submission ID: 30602247) // - https://www.spoj.com/problems/ZQUERY/ // // Mo algorithm with undo DS {{{ template<typename QueryT, typename ResultT, typename Add, typename Undo, typename Get> vector<ResultT> mo_with_undo(int n, std::vector<QueryT> queries, Add add, Undo undo, Get get) { int s = max((int) 1, (int) sqrt(n + 0.5)); int q = queries.size(); vector<ResultT> res(q); // For each block, stores vector of (query, id) std::vector<std::vector<int>> blocks(n / s + 1); for (int i = 0; i < q; ++i) { blocks[queries[i].l / s].push_back(i); } // Process each block int block_start = 0, block_end = s - 1; for (auto& block : blocks) { sort(block.begin(), block.end(), [&] (int q1, int q2) { return queries[q1].r < queries[q2].r; }); int cur_r = block_end; for (int qid : block) { const auto& query = queries[qid]; assert(block_start <= query.l && query.l <= block_end); // For query that is entirely inside this block, we just process it // and then undo immediately if (query.r <= block_end) { for (int i = query.l; i <= query.r; ++i) add(i); res[qid] = get(query); for (int i = query.l; i <= query.r; ++i) undo(); continue; } // Order: // 1. add(i) for i in block_end + 1 .. query.r // 2. add(i) for i in query.l .. block_end // 3. get() // 4. undo() for i in query.l .. block_end => all of (2) is undo for (int i = cur_r + 1; i <= query.r; ++i) add(i); for (int i = query.l; i <= block_end; ++i) add(i); res[qid] = get(query); for (int i = query.l; i <= block_end; ++i) undo(); cur_r = query.r; } for (int i = cur_r; i > block_end; --i) undo(); block_start += s; block_end += s; } return res; } // Example struct Query { int l, r; // QueryT must have l, r }; // Usage // auto res = mo_with_undo<Query, int, decltype(add), decltype(undo), decltype(get)> // (n, queries, add, undo, get); // }}}
#line 1 "DataStructure/Mo/MoAlgorithmWithUndo.h" // Notes: // - queries are [l, r] // - add(int array_id) -> void // - undo() -> void // - get(QueryT query) -> ResultT // // Tested: // - https://www.spoj.com/problems/FREQ2/ (submission ID: 30602190) // - https://www.spoj.com/problems/KDOMINO/ (submission ID: 30602247) // - https://www.spoj.com/problems/ZQUERY/ // // Mo algorithm with undo DS {{{ template<typename QueryT, typename ResultT, typename Add, typename Undo, typename Get> vector<ResultT> mo_with_undo(int n, std::vector<QueryT> queries, Add add, Undo undo, Get get) { int s = max((int) 1, (int) sqrt(n + 0.5)); int q = queries.size(); vector<ResultT> res(q); // For each block, stores vector of (query, id) std::vector<std::vector<int>> blocks(n / s + 1); for (int i = 0; i < q; ++i) { blocks[queries[i].l / s].push_back(i); } // Process each block int block_start = 0, block_end = s - 1; for (auto& block : blocks) { sort(block.begin(), block.end(), [&] (int q1, int q2) { return queries[q1].r < queries[q2].r; }); int cur_r = block_end; for (int qid : block) { const auto& query = queries[qid]; assert(block_start <= query.l && query.l <= block_end); // For query that is entirely inside this block, we just process it // and then undo immediately if (query.r <= block_end) { for (int i = query.l; i <= query.r; ++i) add(i); res[qid] = get(query); for (int i = query.l; i <= query.r; ++i) undo(); continue; } // Order: // 1. add(i) for i in block_end + 1 .. query.r // 2. add(i) for i in query.l .. block_end // 3. get() // 4. undo() for i in query.l .. block_end => all of (2) is undo for (int i = cur_r + 1; i <= query.r; ++i) add(i); for (int i = query.l; i <= block_end; ++i) add(i); res[qid] = get(query); for (int i = query.l; i <= block_end; ++i) undo(); cur_r = query.r; } for (int i = cur_r; i > block_end; --i) undo(); block_start += s; block_end += s; } return res; } // Example struct Query { int l, r; // QueryT must have l, r }; // Usage // auto res = mo_with_undo<Query, int, decltype(add), decltype(undo), decltype(get)> // (n, queries, add, undo, get); // }}}