Submission #1066421

#	Time	Username	Problem	Language	Result	Execution time	Memory
1066421		myst6	Ancient Machine 2 (JOI23_ancient2)	C++17	0 / 100	13 ms	600 KiB

ancient2

#include "ancient2.h"

#include <bits/stdc++.h>

using namespace std;

const int MAX_BITS = 1000;
const int MAX_J = 45;
const int NUM_EQUATIONS = MAX_J * (MAX_J + 1) / 2;

vector<bitset<MAX_BITS>> A(NUM_EQUATIONS);
bitset<MAX_BITS> S;
bitset<NUM_EQUATIONS> b;

void gaussian_elimination() {
    int row = 0;

    for (int col = 0; col < MAX_BITS; ++col) {
        // Find pivot row
        int pivot = -1;
        for (int i = row; i < NUM_EQUATIONS; ++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 < NUM_EQUATIONS; ++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 < MAX_BITS; ++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(vector<vector<int>> &info) {
    // Populate the matrix A and vector b with parity information
    int equation_index = 0;
    for (int j = 1; j <= 45; ++j) {
        for (int i = 0; i < j; ++i) {
            for (int k = i; k < MAX_BITS; k += j) {
                A[equation_index][k] = 1;
            }
            b[equation_index] = info[j][i] /* Your parity information for p_{i,j} */;
            equation_index++;
        }
    }
    assert(equation_index == NUM_EQUATIONS);

    // Perform Gaussian elimination
    gaussian_elimination();

    // Output the reconstructed binary string
    return S.to_string();
}

string Solve(int N) {
    vector<vector<int>> info(MAX_J + 1);
    for (int j=1; j<=MAX_J; j++) {
        for (int i=0; i<j; i++) {
            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[j].push_back(Query(m, a, b));
        }
    }

    return solve(info);
}

• Subtask 1: 0 / 100