oj.uz

Submission #1066512

# Submission time Handle Problem Language Result Execution time Memory
1066512 2024-08-19T23:17:53 Z myst6 Ancient Machine 2 (JOI23_ancient2) C++17
89 / 100
 35 ms 944 KB 
#include "ancient2.h"

#include <bits/stdc++.h>

using namespace std;

const int MAX_BITS = 1000;

#define bs bitset<MAX_BITS>

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);
}

const int BOUND = 79;

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 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});
    }; 
    for (int j : P) {
        if (info.size() == N) break;
        if (j > BOUND) continue;
        int p = j;
        // 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);
}

Compilation message

ancient2.cpp: In function 'std::string Solve(int)':
ancient2.cpp:114:25: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  114 |         if (info.size() == N) break;
      |             ~~~~~~~~~~~~^~~~
ancient2.cpp:119:29: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  119 |             if (info.size() == N) break;
      |                 ~~~~~~~~~~~~^~~~
ancient2.cpp:116:13: warning: unused variable 'p' [-Wunused-variable]
  116 |         int p = j;
      |             ^
ancient2.cpp:124:25: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  124 |         if (info.size() == N) break;
      |             ~~~~~~~~~~~~^~~~
ancient2.cpp:126:29: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  126 |             if (info.size() == N) break;
      |                 ~~~~~~~~~~~~^~~~
ancient2.cpp:131:33: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  131 |                 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:139:24: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  139 |     assert(info.size() >= N);
      |            ~~~~~~~~~~~~^~~~

Subtask #1
89.0 / 100.0

# Verdict Execution time Memory Grader output
1 Partially correct 29 ms 856 KB Output is partially correct
2 Partially correct 35 ms 464 KB Output is partially correct
3 Partially correct 23 ms 620 KB Output is partially correct
4 Partially correct 22 ms 484 KB Output is partially correct
5 Partially correct 22 ms 592 KB Output is partially correct
6 Partially correct 23 ms 588 KB Output is partially correct
7 Partially correct 30 ms 448 KB Output is partially correct
8 Partially correct 22 ms 592 KB Output is partially correct
9 Partially correct 22 ms 344 KB Output is partially correct
10 Partially correct 21 ms 596 KB Output is partially correct
11 Partially correct 21 ms 600 KB Output is partially correct
12 Partially correct 22 ms 600 KB Output is partially correct
13 Partially correct 22 ms 596 KB Output is partially correct
14 Partially correct 21 ms 592 KB Output is partially correct
15 Partially correct 31 ms 468 KB Output is partially correct
16 Partially correct 24 ms 712 KB Output is partially correct
17 Partially correct 22 ms 592 KB Output is partially correct
18 Partially correct 33 ms 704 KB Output is partially correct
19 Partially correct 25 ms 704 KB Output is partially correct
20 Partially correct 25 ms 700 KB Output is partially correct
21 Partially correct 22 ms 592 KB Output is partially correct
22 Partially correct 25 ms 468 KB Output is partially correct
23 Partially correct 22 ms 344 KB Output is partially correct
24 Partially correct 28 ms 600 KB Output is partially correct
25 Partially correct 31 ms 452 KB Output is partially correct
26 Partially correct 22 ms 484 KB Output is partially correct
27 Partially correct 26 ms 704 KB Output is partially correct
28 Partially correct 22 ms 600 KB Output is partially correct
29 Partially correct 28 ms 852 KB Output is partially correct
30 Partially correct 22 ms 592 KB Output is partially correct
31 Partially correct 24 ms 592 KB Output is partially correct
32 Partially correct 35 ms 708 KB Output is partially correct
33 Partially correct 22 ms 592 KB Output is partially correct
34 Partially correct 31 ms 600 KB Output is partially correct
35 Partially correct 22 ms 592 KB Output is partially correct
36 Partially correct 22 ms 704 KB Output is partially correct
37 Partially correct 30 ms 876 KB Output is partially correct
38 Partially correct 34 ms 592 KB Output is partially correct
39 Partially correct 24 ms 944 KB Output is partially correct
40 Partially correct 28 ms 684 KB Output is partially correct
41 Partially correct 23 ms 460 KB Output is partially correct
42 Partially correct 23 ms 592 KB Output is partially correct
43 Partially correct 31 ms 600 KB Output is partially correct
44 Partially correct 31 ms 476 KB Output is partially correct
45 Partially correct 28 ms 476 KB Output is partially correct
46 Partially correct 29 ms 456 KB Output is partially correct
47 Partially correct 23 ms 592 KB Output is partially correct
48 Partially correct 27 ms 864 KB Output is partially correct
49 Partially correct 23 ms 600 KB Output is partially correct
50 Partially correct 23 ms 600 KB Output is partially correct
51 Partially correct 24 ms 704 KB Output is partially correct
52 Partially correct 23 ms 592 KB Output is partially correct
53 Partially correct 25 ms 708 KB Output is partially correct
54 Partially correct 24 ms 852 KB Output is partially correct
55 Partially correct 27 ms 616 KB Output is partially correct
56 Partially correct 24 ms 612 KB Output is partially correct
57 Partially correct 25 ms 460 KB Output is partially correct
58 Partially correct 24 ms 452 KB Output is partially correct
59 Partially correct 22 ms 600 KB Output is partially correct
60 Partially correct 26 ms 480 KB Output is partially correct
61 Partially correct 31 ms 344 KB Output is partially correct
62 Partially correct 23 ms 592 KB Output is partially correct
63 Partially correct 22 ms 600 KB Output is partially correct