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Submission #1066534

# Submission time Handle Problem Language Result Execution time Memory
1066534 2024-08-20T00:45:13 Z myst6 Ancient Machine 2 (JOI23_ancient2) C++17
98 / 100
 74 ms 1780 KB 
#include "ancient2.h"

#include <bits/stdc++.h>

using namespace std;
using ll = long long;

const int MAX_BITS = 1000;
const int BOUND = 56;

#define bs bitset<MAX_BITS>

vector<pair<bs,array<ll,3>>> MIS(const vector<pair<bs,array<ll,3>>>& vectors) {
    vector<bs> basis;  // Store the basis vectors here
    vector<pair<bs,array<ll,3>>> mis;

    for (const auto& vec : vectors) {
        bs v = vec.first;  // Copy the vector

        // Try to eliminate the current vector with the basis vectors
        for (const auto& b : basis) {
            if (v.none()) break;  // If the vector is already zero, skip
            if (v.test(b._Find_first())) {  // If leading bit matches
                v ^= b;  // Subtract the basis vector (add in GF(2))
            }
        }

        // If the vector is not zero after elimination, it's linearly independent
        if (v.any()) {
            basis.push_back(v);
            mis.push_back(vec);  // Add the original vector to the mis 
        }
    }

    return mis;
}

void gaussian_elimination(vector<bs> &A, bs &S, bs &b, int N) {
    int row = 0;

    for (int col = 0; col < N; ++col) {
        // Find pivot row
        int pivot = -1;
        for (int i = row; i < N; ++i) {
            if (A[i][col]) {
                pivot = i;
                break;
            }
        }
        if (pivot == -1) continue; // No pivot found, move to the next column

        // Swap pivot row with the current row
        swap(A[row], A[pivot]);
        // swap(b[row], b[pivot]);
        int tmp = b[row];
        b[row] = b[pivot];
        b[pivot] = tmp;

        // Eliminate below
        for (int i = row + 1; i < N; ++i) {
            if (A[i][col]) {
                A[i] ^= A[row];
                // b[i] ^= b[row];
                if (b[row]) b[i] = !b[i];
            }
        }
        ++row;
    }

    // Backward substitution
    S.reset();
    for (int i = row - 1; i >= 0; --i) {
        if (A[i].any()) {
            int leading_one = A[i]._Find_first();
            S[leading_one] = b[i];
            for (int j = leading_one + 1; j < N; ++j) {
                if (A[i][j]) {
                    // S[leading_one] ^= S[j];
                    if (S[j]) S[leading_one] = !S[leading_one];
                }
            }
        }
    }
}

string solve(int N, vector<pair<bs,int>> &info) {
    // Create bitsets
    vector<bs> A(N);
    bs S, b;

    // Populate the matrix A and vector b with parity information
    for (int i=0; i<N; i++) {
        A[i] = info[i].first;
        b[i] = info[i].second;
    }

    // Perform Gaussian elimination
    gaussian_elimination(A, S, b, N);

    // Output the reconstructed binary string
    string s = S.to_string();
    reverse(s.begin(), s.end());
    return s.substr(0, N);
}

string Solve(int N) {
    vector<pair<bs,int>> info;
    function<int(ll,int)> solve1 = [&](ll mask, int j) -> int {
        int m = 2 * j;
        vector<int> a(m), b(m);
        for (int r=0; r<j; r++) {
            a[r] = (r + 1) % j;
            b[r] = (r + 1) % j;
            a[j + r] = j + ((r + 1) % j);
            b[j + r] = j + ((r + 1) % j);
            if (mask & (1LL << r)) {
                swap(b[r], b[j + r]);
            }
        }
        return Query(m, a, b) / j;
    }; 
    function<int(int)> solve2 = [&](int k) -> int {
        int m = k + 3;
        vector<int> a(m), b(m);
        for (int r=0; r<k; r++) {
            a[r] = r + 1;
            b[r] = r + 1;
        }
        a[k] = k + 1;
        b[k] = k + 2;
        a[k + 1] = b[k + 1] = k + 1;
        a[k + 2] = b[k + 2] = k + 2;
        return Query(m, a, b) - k - 1;
    };
    vector<pair<bs,array<ll,3>>> all;
    for (int j=1; j<=BOUND; j++) {
        for (int i=0; i<j; i++) {
            bs here;
            for (int k=0; k<N; k++) {
                if (k % j == i) {
                    here[k] = 1;
                }
            }
            all.push_back({here, {0, 1LL << i, j}});
        }
    }
    for (int i=0; i<=min(99,N); i++) {
        bs here;
        here[i] = 1;
        all.push_back({here, {1, i, i}});
    }
    for (int j=1; j<=BOUND; j++) {
        for (int i=1; i<j; i++) {
            bs here;
            for (int k=i; k<j; k+=i) {
                here[k] = 1;
            }
            here[i] = 1;
            all.push_back({here, {2, i, j}});
        }
    }
    int A = all.size();
    vector<pair<bs,array<ll,3>>> mis = MIS(all);
    for (auto &[HELP, bruh] : mis) {
        if (bruh[0] == 0) {
            info.push_back({HELP, solve1(bruh[1], bruh[2])});
        } else if (bruh[0] == 1) {
            info.push_back({HELP, solve2(bruh[1])});
        } else if (bruh[0] == 2) {
            // info.push_back({HELP, solve3(bruh[1], bruh[2])});
        } else {
            assert(false);
        }
    }
    // cout << info.size() << "\n";
    return solve(N, info);
}

Compilation message

ancient2.cpp: In function 'std::string Solve(int)':
ancient2.cpp:162:9: warning: unused variable 'A' [-Wunused-variable]
  162 |     int A = all.size();
      |         ^

Subtask #1
98.0 / 100.0

# Verdict Execution time Memory Grader output
1 Partially correct 64 ms 1384 KB Output is partially correct
2 Partially correct 62 ms 1320 KB Output is partially correct
3 Partially correct 64 ms 1264 KB Output is partially correct
4 Partially correct 61 ms 1300 KB Output is partially correct
5 Partially correct 65 ms 1536 KB Output is partially correct
6 Partially correct 66 ms 1256 KB Output is partially correct
7 Partially correct 64 ms 1380 KB Output is partially correct
8 Partially correct 66 ms 1304 KB Output is partially correct
9 Partially correct 66 ms 1380 KB Output is partially correct
10 Partially correct 63 ms 1384 KB Output is partially correct
11 Partially correct 63 ms 1380 KB Output is partially correct
12 Partially correct 64 ms 1264 KB Output is partially correct
13 Partially correct 66 ms 1640 KB Output is partially correct
14 Partially correct 65 ms 1384 KB Output is partially correct
15 Partially correct 66 ms 1272 KB Output is partially correct
16 Partially correct 63 ms 1384 KB Output is partially correct
17 Partially correct 66 ms 1384 KB Output is partially correct
18 Partially correct 63 ms 1540 KB Output is partially correct
19 Partially correct 68 ms 1780 KB Output is partially correct
20 Partially correct 62 ms 1380 KB Output is partially correct
21 Partially correct 64 ms 1264 KB Output is partially correct
22 Partially correct 63 ms 1384 KB Output is partially correct
23 Partially correct 64 ms 1384 KB Output is partially correct
24 Partially correct 63 ms 1284 KB Output is partially correct
25 Partially correct 65 ms 1380 KB Output is partially correct
26 Partially correct 69 ms 1544 KB Output is partially correct
27 Partially correct 73 ms 1384 KB Output is partially correct
28 Partially correct 62 ms 1248 KB Output is partially correct
29 Partially correct 63 ms 1512 KB Output is partially correct
30 Partially correct 65 ms 1384 KB Output is partially correct
31 Partially correct 64 ms 1384 KB Output is partially correct
32 Partially correct 64 ms 1260 KB Output is partially correct
33 Partially correct 64 ms 1384 KB Output is partially correct
34 Partially correct 63 ms 1324 KB Output is partially correct
35 Partially correct 65 ms 1280 KB Output is partially correct
36 Partially correct 71 ms 1260 KB Output is partially correct
37 Partially correct 70 ms 1380 KB Output is partially correct
38 Partially correct 71 ms 1276 KB Output is partially correct
39 Partially correct 64 ms 1548 KB Output is partially correct
40 Partially correct 74 ms 1384 KB Output is partially correct
41 Partially correct 65 ms 1276 KB Output is partially correct
42 Partially correct 67 ms 1264 KB Output is partially correct
43 Partially correct 65 ms 1384 KB Output is partially correct
44 Partially correct 64 ms 1268 KB Output is partially correct
45 Partially correct 65 ms 1540 KB Output is partially correct
46 Partially correct 63 ms 1384 KB Output is partially correct
47 Partially correct 66 ms 1380 KB Output is partially correct
48 Partially correct 66 ms 1264 KB Output is partially correct
49 Partially correct 67 ms 1268 KB Output is partially correct
50 Partially correct 70 ms 1544 KB Output is partially correct
51 Partially correct 64 ms 1632 KB Output is partially correct
52 Partially correct 64 ms 1532 KB Output is partially correct
53 Partially correct 64 ms 1384 KB Output is partially correct
54 Partially correct 66 ms 1520 KB Output is partially correct
55 Partially correct 70 ms 1324 KB Output is partially correct
56 Partially correct 64 ms 1252 KB Output is partially correct
57 Partially correct 64 ms 1384 KB Output is partially correct
58 Partially correct 66 ms 1528 KB Output is partially correct
59 Partially correct 66 ms 1520 KB Output is partially correct
60 Partially correct 68 ms 1380 KB Output is partially correct
61 Partially correct 65 ms 1384 KB Output is partially correct
62 Partially correct 69 ms 1384 KB Output is partially correct
63 Partially correct 66 ms 1268 KB Output is partially correct