Submission #797411

#	Time	Username	Problem	Language	Result	Execution time	Memory
797411		finn__	L-triominoes (CEOI21_ltriominoes)	C++17	0 / 100	8007 ms	76544 KiB

ltrominoes

#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,sse4")

#include <bits/stdc++.h>
using namespace std;

constexpr size_t W = 13, K = 250;

struct bmatrix
{
    bitset<1 << W> mat[1 << W];

    bmatrix transpose() const
    {
        bmatrix res;
        for (size_t i = 0; i < 1U << W; ++i)
            for (size_t j = 0; j < 1U << W; ++j)
                res.mat[i][j] = mat[j][i];
        return res;
    }

    bmatrix operator*(bmatrix const &y) const
    {
        bmatrix x = y.transpose();
        bmatrix res;

        for (size_t i = 0; i < 1U << W; ++i)
            for (size_t j = 0; j < 1U << W; ++j)
                res.mat[i][j] = (mat[i] & x.mat[j]).any();

        return res;
    }

    static bitset<1 << W> pow(bitset<1 << W> v, bmatrix pow2[31], size_t &m, size_t n, size_t w)
    {
        size_t i = 1;

        while (n)
        {
            if (n & 1)
            {
                while (m < i)
                {
                    ++m;
                    pow2[m] = pow2[m - 1] * pow2[m - 1];
                }
                v = pow2[i].mul_vec(v);
                if (v.count() == 1 << w)
                    break;
            }
            n >>= 1;
            ++i;
        }

        return v;
    }

    bitset<1 << W> mul_vec(bitset<1 << W> const &v) const
    {
        bitset<1 << W> res;
        for (size_t i = 0; i < 1U << W; ++i)
            res[i] = (mat[i] & v).any();
        return res;
    }
};

pair<size_t, size_t> p[K];
bmatrix transitions, pow2[31];
bitset<1 << W> state, state2;

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    size_t w, h, k;
    cin >> w >> h >> k;
    assert(h <= 1000);

    for (size_t i = 0; i < k; ++i)
        cin >> p[i].first >> p[i].second, --p[i].first, --p[i].second;

    for (size_t y = 0; y < 1 << w; ++y)
    {
        queue<uint32_t> q;
        q.push(y << W);

        while (!q.empty())
        {
            uint32_t u = q.front();
            q.pop();

            size_t i = u >> W, j = u & ((1 << W) - 1);

            if (i == (1 << w) - 1)
            {
                transitions.mat[j][y] = 1;
                continue;
            }

            for (size_t h = 0; h < w; ++h)
                if (!(i & (1 << h)))
                {
                    if (h && !(j & (1 << h)) && !(j & (1 << (h - 1))))
                    {
                        size_t ni = i ^ (1 << h), nj = j ^ (1 << h) ^ (1 << (h - 1));
                        q.push((ni << W) | nj);
                    }
                    if (h + 1 < w && !(j & (1 << h)) && !(j & (1 << (h + 1))))
                    {
                        size_t ni = i ^ (1 << h), nj = j ^ (1 << h) ^ (1 << (h + 1));
                        q.push((ni << W) | nj);
                    }
                    if (h + 1 < w && !(i & (1 << (h + 1))) && !(j & (1 << h)))
                    {
                        size_t ni = i ^ (1 << h) ^ (1 << (h + 1)), nj = j ^ (1 << h);
                        q.push((ni << W) | nj);
                    }
                    if (h + 1 < w && !(i & (1 << (h + 1))) && !(j & (1 << (h + 1))))
                    {
                        size_t ni = i ^ (1 << h) ^ (1 << (h + 1)), nj = j ^ (1 << (h + 1));
                        q.push((ni << W) | nj);
                    }
                }
        }
    }

    sort(p, p + k, [](auto const &a, auto const &b)
         { return a.second < b.second; });
    size_t i = 0, pos = 0;
    if (k && !p[0].second)
    {
        size_t x = 0;
        while (!p[i].second)
            x |= 1 << p[i].first, ++i;
        state[x] = 1;
    }
    else
        state[0] = 1;

    while (i < k)
    {
        while (pos < p[i].second)
            state = transitions.mul_vec(state), ++pos;
        size_t x = 0;
        size_t j = i;
        while (j < k && p[j].second == p[i].second)
            x |= 1 << p[j].first, ++j;
        i = j;

        state2.reset();
        for (size_t i = 0; i < 1 << w; ++i)
            if (!(i & x) && state[i])
                state2[i ^ x] = 1;
        state = state2;
    }

    while (pos < h - 1)
        state = transitions.mul_vec(state), ++pos;

    cout << (state[(1 << w) - 1] ? "YES" : "NO") << '\n';
}

Compilation message (stderr)

ltrominoes.cpp: In static member function 'static std::bitset<8192> bmatrix::pow(std::bitset<8192>, bmatrix*, size_t&, size_t, size_t)':
ltrominoes.cpp:48:31: warning: comparison of integer expressions of different signedness: 'std::size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   48 |                 if (v.count() == 1 << w)
      |                     ~~~~~~~~~~^~~~~~~~~
ltrominoes.cpp: In function 'int main()':
ltrominoes.cpp:83:26: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   83 |     for (size_t y = 0; y < 1 << w; ++y)
      |                        ~~^~~~~~~~
ltrominoes.cpp:95:19: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   95 |             if (i == (1 << w) - 1)
      |                 ~~^~~~~~~~~~~~~~~
ltrominoes.cpp:152:30: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  152 |         for (size_t i = 0; i < 1 << w; ++i)
      |                            ~~^~~~~~~~

• Subtask 1: 0 / 10
• Subtask 2: 0 / 7
• Subtask 3: 0 / 11
• Subtask 4: 0 / 17
• Subtask 5: 0 / 35
• Subtask 6: 0 / 20