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Submission #1066524

# Submission time Handle Problem Language Result Execution time Memory
1066524 2024-08-20T00:15:53 Z myst6 Ancient Machine 2 (JOI23_ancient2) C++17
98 / 100
 43 ms 1480 KB 
#include "ancient2.h"

#include <bits/stdc++.h>

using namespace std;

const int MAX_BITS = 1000;
const int BOUND = 54;

#define bs bitset<MAX_BITS>

vector<bs> MIS(const vector<bs>& vectors) {
    vector<bs> basis;  // Store the basis vectors here
    vector<bs> mis;

    for (const auto& vec : vectors) {
        bs v = vec;  // 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(int,int)> solve1 = [&](int i, 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);
        }
        b[i] = j + ((i + 1) % j);
        b[i + j] = (i + 1) % j;
        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<bs> all;
    vector<array<int,2>> ij;
    for (int j=1; j<=BOUND; j++) {
        for (int i=0; i<j; i++) {
            bs here;
            for (int k=i; k<N; k+=j) {
                here[k] = 1;
            }
            all.push_back(here);
            ij.push_back({i, j});
        }
    }
    for (int i=0; i<=min(99,N); i++) {
        bs here;
        here[i] = 1;
        all.push_back(here);
    }
    int A = all.size();
    vector<bs> mis = MIS(all);
    for (bs &HELP : mis) {
        if (HELP.count() == 1) {
            int i = HELP._Find_first();
            info.push_back({HELP, solve2(i)});
        } else {
            for (int i=0; i<A; i++) {
                if (HELP == all[i]) {
                    info.push_back({HELP, solve1(ij[i][0], ij[i][1])});
                    // cout << ij[i][0] << "," << ij[i][1] << "," << solve1(ij[i][0], ij[i][1]) << "\n";
                }
            }
        }
    }
    // cout << info.size() << "\n";
    return solve(N, info);
}

Subtask #1
98.0 / 100.0

# Verdict Execution time Memory Grader output
1 Partially correct 32 ms 980 KB Output is partially correct
2 Partially correct 32 ms 980 KB Output is partially correct
3 Partially correct 31 ms 980 KB Output is partially correct
4 Partially correct 31 ms 1068 KB Output is partially correct
5 Partially correct 36 ms 1072 KB Output is partially correct
6 Partially correct 32 ms 980 KB Output is partially correct
7 Partially correct 37 ms 1100 KB Output is partially correct
8 Partially correct 34 ms 1076 KB Output is partially correct
9 Partially correct 31 ms 1100 KB Output is partially correct
10 Partially correct 33 ms 1080 KB Output is partially correct
11 Partially correct 38 ms 1092 KB Output is partially correct
12 Partially correct 31 ms 980 KB Output is partially correct
13 Partially correct 32 ms 980 KB Output is partially correct
14 Partially correct 33 ms 1200 KB Output is partially correct
15 Partially correct 31 ms 1228 KB Output is partially correct
16 Partially correct 33 ms 980 KB Output is partially correct
17 Partially correct 33 ms 1480 KB Output is partially correct
18 Partially correct 31 ms 1072 KB Output is partially correct
19 Partially correct 35 ms 1096 KB Output is partially correct
20 Partially correct 33 ms 1092 KB Output is partially correct
21 Partially correct 32 ms 980 KB Output is partially correct
22 Partially correct 42 ms 1092 KB Output is partially correct
23 Partially correct 32 ms 1072 KB Output is partially correct
24 Partially correct 32 ms 980 KB Output is partially correct
25 Partially correct 37 ms 1208 KB Output is partially correct
26 Partially correct 32 ms 1200 KB Output is partially correct
27 Partially correct 32 ms 980 KB Output is partially correct
28 Partially correct 42 ms 992 KB Output is partially correct
29 Partially correct 32 ms 1092 KB Output is partially correct
30 Partially correct 32 ms 980 KB Output is partially correct
31 Partially correct 36 ms 1228 KB Output is partially correct
32 Partially correct 32 ms 1072 KB Output is partially correct
33 Partially correct 31 ms 980 KB Output is partially correct
34 Partially correct 32 ms 980 KB Output is partially correct
35 Partially correct 32 ms 980 KB Output is partially correct
36 Partially correct 31 ms 1236 KB Output is partially correct
37 Partially correct 31 ms 1092 KB Output is partially correct
38 Partially correct 35 ms 1088 KB Output is partially correct
39 Partially correct 36 ms 980 KB Output is partially correct
40 Partially correct 37 ms 980 KB Output is partially correct
41 Partially correct 32 ms 1096 KB Output is partially correct
42 Partially correct 32 ms 980 KB Output is partially correct
43 Partially correct 43 ms 980 KB Output is partially correct
44 Partially correct 33 ms 1076 KB Output is partially correct
45 Partially correct 32 ms 1104 KB Output is partially correct
46 Partially correct 42 ms 980 KB Output is partially correct
47 Partially correct 35 ms 1088 KB Output is partially correct
48 Partially correct 33 ms 980 KB Output is partially correct
49 Partially correct 36 ms 980 KB Output is partially correct
50 Partially correct 34 ms 1096 KB Output is partially correct
51 Partially correct 32 ms 980 KB Output is partially correct
52 Partially correct 37 ms 980 KB Output is partially correct
53 Partially correct 33 ms 980 KB Output is partially correct
54 Partially correct 34 ms 1084 KB Output is partially correct
55 Partially correct 34 ms 1236 KB Output is partially correct
56 Partially correct 32 ms 980 KB Output is partially correct
57 Partially correct 41 ms 1080 KB Output is partially correct
58 Partially correct 32 ms 980 KB Output is partially correct
59 Partially correct 33 ms 1084 KB Output is partially correct
60 Partially correct 33 ms 1092 KB Output is partially correct
61 Partially correct 31 ms 1092 KB Output is partially correct
62 Partially correct 38 ms 980 KB Output is partially correct
63 Partially correct 35 ms 1232 KB Output is partially correct