oj.uz

Submission #1066513

# Submission time Handle Problem Language Result Execution time Memory
1066513 2024-08-19T23:50:13 Z myst6 Ancient Machine 2 (JOI23_ancient2) C++17
97 / 100
 129 ms 1788 KB 
#include "ancient2.h"

#include <bits/stdc++.h>

using namespace std;

const int MAX_BITS = 1000;
const int BOUND = 100;

#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];
                }
            }
        }
    }
}

// info[m][r] => index === r (mod m)
string solve(int N, vector<array<int,3>> &info) {
    // Clear old stuff
    vector<bs> A(N);
    bs S, b;

    // Populate the matrix A and vector b with parity information
    int equation_index = 0;
    for (auto [i, j, parity] : info) {
        for (int k = i; k < N; k += j) {
            A[equation_index][k] = 1;
        }
        // cerr << i << "," << j << "," << parity << "\n";
        b[equation_index] = parity /* Your parity information for p_{i,j} */;
        equation_index++;
        if (equation_index == N) break;
    }

    // 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);
}

vector<int> P = {
    2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
    67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149,
    151, 157, 163
};

string Solve1(int N) {
    vector<array<int,3>> info;
    function<void(int,int)> add = [&](int i, int j) -> void {
        int m = 2 * j;
        vector<int> a(m), b(m);
        // nodes r=0..j-1 is even parity modulo r
        // nodes r=j..2j-1 is odd parity modulo r
        for (int r=0; r<j; r++) {
            // both transition to next node in chain
            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 one, transition to opposite node in chain
        b[i] = j + ((i + 1) % j);
        b[i + j] = (i + 1) % j;
        info.push_back({i, j, Query(m, a, b) / j});
    }; 
    for (int j : P) {
        if (info.size() == N) break;
        if (j > BOUND) continue;
        // while (j * p <= BOUND) j *= p;
        for (int i=0; i<j-1; i++) {
            if (info.size() == N) break;
            add(i, j);
        }
    }
    for (int p : P) {
        if (info.size() == N) break;
        for (int q : P) {
            if (info.size() == N) break;
            if (p >= q) continue;
            int j = p * q;
            if (j > BOUND) continue;
            for (int i=0; i<j-q; i++) {
                if (info.size() == N) break;
                if (i > q) {
                    add(i, j);
                }
            }
        }
    }
    // cout << info.size() << "\n";
    assert(info.size() >= N);
    // cout << solve(N, info) << "\n";
    return solve(N, info);
}

string Solve(int N) {
    vector<array<int,3>> info;
    function<void(int,int)> add = [&](int i, int j) -> void {
        int m = 2 * j;
        vector<int> a(m), b(m);
        // nodes r=0..j-1 is even parity modulo r
        // nodes r=j..2j-1 is odd parity modulo r
        for (int r=0; r<j; r++) {
            // both transition to next node in chain
            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 one, transition to opposite node in chain
        b[i] = j + ((i + 1) % j);
        b[i + j] = (i + 1) % j;
        info.push_back({i, j, Query(m, a, b) / j});
    }; 
    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});
        }
    }
    int A = all.size();
    vector<bs> mis = MIS(all);
    int M = mis.size();
    // cout << M << "\n";
    // for (bs &HELP : mis) {
    //     cout << HELP.to_string() << "\n";
    // }
    // random_shuffle(mis.begin(), mis.end());
    for (bs &HELP : mis) {
        if (info.size() == N) break;
        bool found = false;
        for (int i=0; i<A; i++) {
            if (HELP == all[i]) {
                add(ij[i][0], ij[i][1]);
                found = true;
            }
        }
        assert(found);
    }
    // cout << solve(N, info) << "\n";
    return solve(N, info);
}

Compilation message

ancient2.cpp: In function 'std::string Solve1(int)':
ancient2.cpp:138:25: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  138 |         if (info.size() == N) break;
      |             ~~~~~~~~~~~~^~~~
ancient2.cpp:142:29: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  142 |             if (info.size() == N) break;
      |                 ~~~~~~~~~~~~^~~~
ancient2.cpp:147:25: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  147 |         if (info.size() == N) break;
      |             ~~~~~~~~~~~~^~~~
ancient2.cpp:149:29: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  149 |             if (info.size() == N) break;
      |                 ~~~~~~~~~~~~^~~~
ancient2.cpp:154:33: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  154 |                 if (info.size() == N) break;
      |                     ~~~~~~~~~~~~^~~~
In file included from /usr/include/c++/10/cassert:44,
                 from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:33,
                 from ancient2.cpp:3:
ancient2.cpp:162:24: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  162 |     assert(info.size() >= N);
      |            ~~~~~~~~~~~~^~~~
ancient2.cpp: In function 'std::string Solve(int)':
ancient2.cpp:207:25: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  207 |         if (info.size() == N) break;
      |             ~~~~~~~~~~~~^~~~
ancient2.cpp:200:9: warning: unused variable 'M' [-Wunused-variable]
  200 |     int M = mis.size();
      |         ^

Subtask #1
97.0 / 100.0

# Verdict Execution time Memory Grader output
1 Partially correct 108 ms 1488 KB Output is partially correct
2 Partially correct 114 ms 1788 KB Output is partially correct
3 Partially correct 109 ms 1596 KB Output is partially correct
4 Partially correct 113 ms 1592 KB Output is partially correct
5 Partially correct 108 ms 1584 KB Output is partially correct
6 Partially correct 102 ms 1488 KB Output is partially correct
7 Partially correct 110 ms 1488 KB Output is partially correct
8 Partially correct 112 ms 1488 KB Output is partially correct
9 Partially correct 109 ms 1596 KB Output is partially correct
10 Partially correct 107 ms 1488 KB Output is partially correct
11 Partially correct 110 ms 1592 KB Output is partially correct
12 Partially correct 105 ms 1488 KB Output is partially correct
13 Partially correct 106 ms 1488 KB Output is partially correct
14 Partially correct 106 ms 1488 KB Output is partially correct
15 Partially correct 106 ms 1488 KB Output is partially correct
16 Partially correct 107 ms 1488 KB Output is partially correct
17 Partially correct 107 ms 1740 KB Output is partially correct
18 Partially correct 105 ms 1616 KB Output is partially correct
19 Partially correct 106 ms 1488 KB Output is partially correct
20 Partially correct 113 ms 1488 KB Output is partially correct
21 Partially correct 106 ms 1488 KB Output is partially correct
22 Partially correct 109 ms 1488 KB Output is partially correct
23 Partially correct 107 ms 1488 KB Output is partially correct
24 Partially correct 115 ms 1488 KB Output is partially correct
25 Partially correct 106 ms 1488 KB Output is partially correct
26 Partially correct 106 ms 1488 KB Output is partially correct
27 Partially correct 105 ms 1488 KB Output is partially correct
28 Partially correct 123 ms 1588 KB Output is partially correct
29 Partially correct 110 ms 1592 KB Output is partially correct
30 Partially correct 108 ms 1488 KB Output is partially correct
31 Partially correct 109 ms 1488 KB Output is partially correct
32 Partially correct 106 ms 1488 KB Output is partially correct
33 Partially correct 113 ms 1488 KB Output is partially correct
34 Partially correct 107 ms 1584 KB Output is partially correct
35 Partially correct 107 ms 1592 KB Output is partially correct
36 Partially correct 108 ms 1488 KB Output is partially correct
37 Partially correct 115 ms 1488 KB Output is partially correct
38 Partially correct 109 ms 1616 KB Output is partially correct
39 Partially correct 112 ms 1488 KB Output is partially correct
40 Partially correct 108 ms 1488 KB Output is partially correct
41 Partially correct 109 ms 1488 KB Output is partially correct
42 Partially correct 113 ms 1488 KB Output is partially correct
43 Partially correct 107 ms 1588 KB Output is partially correct
44 Partially correct 108 ms 1608 KB Output is partially correct
45 Partially correct 107 ms 1488 KB Output is partially correct
46 Partially correct 112 ms 1592 KB Output is partially correct
47 Partially correct 108 ms 1488 KB Output is partially correct
48 Partially correct 107 ms 1596 KB Output is partially correct
49 Partially correct 113 ms 1488 KB Output is partially correct
50 Partially correct 109 ms 1592 KB Output is partially correct
51 Partially correct 109 ms 1592 KB Output is partially correct
52 Partially correct 107 ms 1488 KB Output is partially correct
53 Partially correct 109 ms 1488 KB Output is partially correct
54 Partially correct 126 ms 1592 KB Output is partially correct
55 Partially correct 116 ms 1484 KB Output is partially correct
56 Partially correct 115 ms 1488 KB Output is partially correct
57 Partially correct 117 ms 1488 KB Output is partially correct
58 Partially correct 108 ms 1488 KB Output is partially correct
59 Partially correct 106 ms 1488 KB Output is partially correct
60 Partially correct 119 ms 1600 KB Output is partially correct
61 Partially correct 129 ms 1488 KB Output is partially correct
62 Partially correct 108 ms 1596 KB Output is partially correct
63 Partially correct 113 ms 1488 KB Output is partially correct