Submission #987599

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
987599	2024-05-23T06:52:59 Z	HienTD	Ancient Machine 2 (JOI23_ancient2)	C++17	100 / 100	72 ms	1984 KB

ancient2

#include "ancient2.h"
#include <bits/stdc++.h>

#define MAX_N 1000
#define M_UPPERBOUND 102

using bitvec = std::bitset<MAX_N>;

struct basis_manager {
	std::vector<std::pair<int, bitvec> > basis;
	bool add(bitvec v) {
		for (auto i : basis) if (v[i.first]) v ^= i.second;
		if (v.any()) {
			basis.push_back({v._Find_first(), v});
			return true;
		}
		return false;
	}
};

// {mod, remainder, actual 01 vector}
// {-1, i,          actual 01 vector} : i-th
// {-2, i,          actual 01 vector} : i-th from the back
std::vector<std::tuple<int, int, bitvec> > list_needed_vecs(int n) {
	std::vector<std::vector<std::tuple<int, int, bitvec> > > cands(M_UPPERBOUND + 1);
	// periodic
	for (int mod = 1; mod <= M_UPPERBOUND / 2; mod++) {
		for (int rem = 0; rem < mod; rem++) {
			bitvec x;
			for (int i = rem; i < n; i += mod) x[i] = 1;
			cands[2 * mod].push_back(std::make_tuple(mod, rem, x));
		}
	}
	// prefix
	for (int i = 0; i + 3 <= M_UPPERBOUND; i++) {
		bitvec x;
		x[i] = 1;
		cands[i + 3].push_back(std::make_tuple(-1, i, x));
	}
	// suffix
	for (int i = 0; i + 2 <= M_UPPERBOUND; i++) {
		bitvec x;
		x[n - 1 - i] = 1;
		cands[i + 2].push_back({-2, i, x});
	}
	basis_manager basis;
	std::vector<std::tuple<int, int, bitvec> > res;
	for (int i = 0; i <= M_UPPERBOUND; i++) {
		for (auto j : cands[i]) {
			if (basis.add(std::get<2>(j))) res.push_back(j);
			if ((int) basis.basis.size() == n) break;
		}
		if ((int) basis.basis.size() == n) break;
	}
	return res;
}
std::vector<bool> solve_linear_equation(std::vector<bitvec> &a, std::vector<bool> &b) {
	int n = a.size();
	for (int i = 0; i < n; i++) {
		int id = -1;
		for (int j = i; j < n; j++) if (a[j][i]) { id = j; break; }
		assert(id != -1);
		std::swap(a[i], a[id]);
		swap(b[i], b[id]);
		for (int j = 0; j < n; j++) if (j != i && a[j][i]) a[j] ^= a[i], b[j] = b[j] ^ b[i];
	}
	return b;
}


std::string Solve(int n) {
	auto list = list_needed_vecs(n);
	
	std::vector<bitvec> mat;
	std::vector<bool> res;
	std::vector<bool> back_res;
	for (auto i : list) {
		int mod = std::get<0>(i);
		int rem = std::get<1>(i);
		auto query_mod = [&] () {
			int m = mod * 2;
			std::vector<int> a(m), b(m);
			for (int j = 0; j < mod; j++) {
				int next = (j + 1) % mod;
				a[j] = b[j] = next;
				a[j + mod] = b[j + mod] = next + mod;
				if (j == rem) std::swap(b[j], b[j + mod]);
			}
			return Query(m, a, b) >= mod;
		};
		auto query_forward = [&] () {
			int m = rem + 3;
			std::vector<int> a(m), b(m);
			for (int j = 0; j < rem; j++) a[j] = b[j] = j + 1;
			a[rem] = rem + 1;
			b[rem] = rem + 2;
			a[rem + 1] = b[rem + 1] = rem + 1;
			a[rem + 2] = b[rem + 2] = rem + 2;
			return Query(m, a, b) == rem + 2;
		};
		auto query_back = [&] () {
			assert(rem == (int) back_res.size());
			back_res.insert(back_res.begin(), 0);
			int m = rem + 2;
			std::vector<int> a(m), b(m);
			for (int i = 0; i <= rem + 1; i++) {
				auto get = [&] (bool next) {
					auto cur = std::vector<bool>(back_res.begin(), back_res.begin() + i);
					cur.push_back(next);
					for (int j = std::min(rem + 1, i + 1); j; j--)
						if (std::vector<bool>(cur.end() - j, cur.end()) ==
							std::vector<bool>(back_res.begin(), back_res.begin() + j)) return j;
					return 0;
				};
				a[i] = get(0);
				b[i] = get(1);
			}
			bool res = Query(m, a, b) != rem + 1;
			back_res[0] = res;
			return res;
		};
		mat.push_back(std::get<2>(i));
		res.push_back(mod >= 1 ? query_mod() : mod == -1 ? query_forward() : query_back());
	}
	res = solve_linear_equation(mat, res);
	
	std::string res_str;
	for (auto i : res) res_str.push_back('0' + i);
	
	return res_str;
}

Subtask #1

100.0 / 100.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	59 ms	1984 KB	Output is correct
2	Correct	51 ms	1696 KB	Output is correct
3	Correct	50 ms	1460 KB	Output is correct
4	Correct	55 ms	968 KB	Output is correct
5	Correct	60 ms	1220 KB	Output is correct
6	Correct	61 ms	1456 KB	Output is correct
7	Correct	50 ms	1468 KB	Output is correct
8	Correct	54 ms	1220 KB	Output is correct
9	Correct	57 ms	1216 KB	Output is correct
10	Correct	66 ms	1224 KB	Output is correct
11	Correct	54 ms	1180 KB	Output is correct
12	Correct	64 ms	1220 KB	Output is correct
13	Correct	59 ms	1436 KB	Output is correct
14	Correct	58 ms	1208 KB	Output is correct
15	Correct	65 ms	1952 KB	Output is correct
16	Correct	58 ms	1460 KB	Output is correct
17	Correct	57 ms	964 KB	Output is correct
18	Correct	58 ms	1444 KB	Output is correct
19	Correct	63 ms	1708 KB	Output is correct
20	Correct	63 ms	960 KB	Output is correct
21	Correct	51 ms	1480 KB	Output is correct
22	Correct	61 ms	1456 KB	Output is correct
23	Correct	53 ms	1208 KB	Output is correct
24	Correct	72 ms	1468 KB	Output is correct
25	Correct	56 ms	1192 KB	Output is correct
26	Correct	60 ms	1444 KB	Output is correct
27	Correct	64 ms	1452 KB	Output is correct
28	Correct	58 ms	1452 KB	Output is correct
29	Correct	57 ms	1208 KB	Output is correct
30	Correct	52 ms	956 KB	Output is correct
31	Correct	71 ms	1200 KB	Output is correct
32	Correct	58 ms	1448 KB	Output is correct
33	Correct	69 ms	1456 KB	Output is correct
34	Correct	53 ms	1448 KB	Output is correct
35	Correct	53 ms	1180 KB	Output is correct
36	Correct	60 ms	1212 KB	Output is correct
37	Correct	56 ms	1204 KB	Output is correct
38	Correct	58 ms	1448 KB	Output is correct
39	Correct	61 ms	1436 KB	Output is correct
40	Correct	61 ms	1460 KB	Output is correct
41	Correct	61 ms	1452 KB	Output is correct
42	Correct	59 ms	1464 KB	Output is correct
43	Correct	63 ms	1180 KB	Output is correct
44	Correct	59 ms	1440 KB	Output is correct
45	Correct	57 ms	968 KB	Output is correct
46	Correct	59 ms	1464 KB	Output is correct
47	Correct	68 ms	1436 KB	Output is correct
48	Correct	71 ms	964 KB	Output is correct
49	Correct	58 ms	1204 KB	Output is correct
50	Correct	56 ms	1196 KB	Output is correct
51	Correct	63 ms	1208 KB	Output is correct
52	Correct	61 ms	1192 KB	Output is correct
53	Correct	63 ms	1196 KB	Output is correct
54	Correct	65 ms	1200 KB	Output is correct
55	Correct	66 ms	1220 KB	Output is correct
56	Correct	61 ms	1180 KB	Output is correct
57	Correct	58 ms	1448 KB	Output is correct
58	Correct	53 ms	1212 KB	Output is correct
59	Correct	61 ms	1216 KB	Output is correct
60	Correct	57 ms	1192 KB	Output is correct
61	Correct	57 ms	1444 KB	Output is correct
62	Correct	58 ms	1736 KB	Output is correct
63	Correct	58 ms	964 KB	Output is correct