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답안 #797970

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
797970 2023-07-30T08:08:57 Z finn__ L-triominoes (CEOI21_ltriominoes) C++17
63 / 100
 3273 ms 360 KB 
#include <bits/stdc++.h>
using namespace std;

constexpr size_t W = 13, K = 250, C = 12;

size_t w;
pair<size_t, size_t> p[K];
bitset<1 << W> state[2];
size_t r, s;

void find_transitions(uint32_t i, uint32_t j, bitset<1 << W> &next_state, size_t l = 0)
{
    if (i == (1 << w) - 1)
    {
        next_state[j] = 1;
        return;
    }

    for (size_t h = l; h < w; ++h)
        if (!(i & (1 << h)))
        {
            if (h && !(j & (1 << h)) && !(j & (1 << (h - 1))))
                find_transitions(i ^ (1 << h), j ^ (1 << h) ^ (1 << (h - 1)), next_state, h + 1);
            if (h + 1 < w && !(j & (1 << h)) && !(j & (1 << (h + 1))))
                find_transitions(i ^ (1 << h), j ^ (1 << h) ^ (1 << (h + 1)), next_state, h + 1);
            if (h + 1 < w && !(i & (1 << (h + 1))) && !(j & (1 << h)))
                find_transitions(i ^ (1 << h) ^ (1 << (h + 1)), j ^ (1 << h), next_state, h + 2);
            if (h + 1 < w && !(i & (1 << (h + 1))) && !(j & (1 << (h + 1))))
                find_transitions(i ^ (1 << h) ^ (1 << (h + 1)), j ^ (1 << (h + 1)), next_state, h + 2);
            break;
        }
}

void advance_state(size_t l)
{
    if (l <= C)
    {
        while (l--)
        {
            state[1].reset();
            for (size_t i = 0; i < 1 << w; ++i)
                if (state[0][i])
                    find_transitions(i, 0, state[1]);
            swap(state[0], state[1]);
        }
    }
    else
    {
        bitset<3> curr_components;
        for (size_t i = 0; i < 1 << w; ++i)
            if ((!(w & 1) || i != s) && state[0][i])
                curr_components[__builtin_popcount(i) % 3] = 1;

        state[0].reset();

        size_t d = (l * w) % 3;
        for (size_t i = 0; i < 1 << w; ++i)
            if ((!(w & 1) || i != r) && curr_components[(__builtin_popcount(i) + d) % 3])
                state[0][i] = 1;
    }
};

namespace matmul
{
    constexpr size_t W = 6, K = 250;

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

        bmatrix operator*(bmatrix const &y) const
        {
            bmatrix res;

            for (size_t i = 0; i < 1U << W; ++i)
                for (size_t j = 0; j < 1U << W; ++j)
                    if (mat[i][j])
                        res.mat[i] |= y.mat[j];

            return res;
        }

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

            while (n)
            {
                if (n & 1)
                {
                    v = pow2[i].mul_vec(v);
                }
                n >>= 1;
                ++i;
            }

            return v;
        }

        bool operator==(bmatrix const &y) const
        {
            for (size_t i = 0; i < 1 << W; ++i)
                if (mat[i] != y.mat[i])
                    return 0;
            return 1;
        }

        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;

    void run(size_t w, size_t h, size_t k)
    {
        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);
                        }
                    }
            }
        }

        pow2[1] = transitions;
        for (size_t i = 2; i < 31; ++i)
            pow2[i] = pow2[i - 1] * pow2[i - 1];

        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)
        {
            state = bmatrix::pow(state, pow2, p[i].second - pos);
            pos = p[i].second;
            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;
        }

        if (pos != h - 1)
        {
            state = bmatrix::pow(state, pow2, h - 1 - pos);
        }

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

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

    size_t h, k;
    cin >> w >> h >> k;

    if (w <= 6)
    {
        matmul::run(w, h, k);
        return 0;
    }

    for (size_t i = 0; i < w; i += 2)
        r |= 1 << i;
    for (size_t i = 1; i < w; i += 2)
        s |= 1 << i;

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

    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 (i < k && !p[i].second)
            x |= 1ULL << p[i].first, ++i;
        state[0][x] = 1;
    }
    else
        state[0][0] = 1;

    while (i < k)
    {
        advance_state(p[i].second - pos);
        pos = p[i].second;

        size_t x = 0;
        size_t j = i;
        while (j < k && p[j].second == p[i].second)
            x |= 1ULL << p[j].first, ++j;
        i = j;

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

    advance_state(h - 1 - pos);

    cout << (state[0][(1 << w) - 1] ? "YES" : "NO") << '\n';
}

Compilation message

ltrominoes.cpp: In function 'void find_transitions(uint32_t, uint32_t, std::bitset<8192>&, size_t)':
ltrominoes.cpp:13:11: warning: comparison of integer expressions of different signedness: 'uint32_t' {aka 'unsigned int'} and 'int' [-Wsign-compare]
   13 |     if (i == (1 << w) - 1)
      |         ~~^~~~~~~~~~~~~~~
ltrominoes.cpp: In function 'void advance_state(size_t)':
ltrominoes.cpp:41:34: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   41 |             for (size_t i = 0; i < 1 << w; ++i)
      |                                ~~^~~~~~~~
ltrominoes.cpp:50:30: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   50 |         for (size_t i = 0; i < 1 << w; ++i)
      |                            ~~^~~~~~~~
ltrominoes.cpp:57:30: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   57 |         for (size_t i = 0; i < 1 << w; ++i)
      |                            ~~^~~~~~~~
ltrominoes.cpp: In function 'void matmul::run(size_t, size_t, size_t)':
ltrominoes.cpp:126:30: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  126 |         for (size_t y = 0; y < 1 << w; ++y)
      |                            ~~^~~~~~~~
ltrominoes.cpp:138:23: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  138 |                 if (i == (1 << w) - 1)
      |                     ~~^~~~~~~~~~~~~~~
ltrominoes.cpp:199:34: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  199 |             for (size_t i = 0; i < 1 << w; ++i)
      |                                ~~^~~~~~~~
ltrominoes.cpp: In function 'int main()':
ltrominoes.cpp:261:30: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  261 |         for (size_t i = 0; i < 1 << w; ++i)
      |                            ~~^~~~~~~~

Subtask #1
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 340 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 2 ms 212 KB Output is correct
16 Correct 969 ms 308 KB Output is correct
17 Correct 11 ms 212 KB Output is correct
18 Correct 335 ms 304 KB Output is correct
19 Correct 3 ms 212 KB Output is correct
20 Correct 578 ms 308 KB Output is correct
21 Correct 236 ms 212 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 2 ms 212 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 106 ms 212 KB Output is correct
26 Correct 458 ms 304 KB Output is correct
27 Correct 1 ms 212 KB Output is correct

Subtask #2
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 340 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 0 ms 340 KB Output is correct
18 Correct 0 ms 212 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 0 ms 212 KB Output is correct
21 Correct 0 ms 340 KB Output is correct
22 Correct 0 ms 212 KB Output is correct
23 Correct 0 ms 212 KB Output is correct
24 Correct 0 ms 212 KB Output is correct

Subtask #3
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 0 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 0 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 ms 340 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 0 ms 340 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 0 ms 212 KB Output is correct
22 Correct 0 ms 212 KB Output is correct
23 Correct 0 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 0 ms 340 KB Output is correct
26 Correct 1 ms 212 KB Output is correct
27 Correct 0 ms 212 KB Output is correct
28 Correct 0 ms 340 KB Output is correct
29 Correct 0 ms 212 KB Output is correct
30 Correct 1 ms 340 KB Output is correct
31 Correct 1 ms 340 KB Output is correct
32 Correct 0 ms 340 KB Output is correct
33 Correct 1 ms 340 KB Output is correct
34 Correct 1 ms 340 KB Output is correct
35 Correct 1 ms 340 KB Output is correct
36 Correct 1 ms 340 KB Output is correct
37 Correct 1 ms 340 KB Output is correct
38 Correct 1 ms 340 KB Output is correct
39 Correct 1 ms 340 KB Output is correct
40 Correct 1 ms 340 KB Output is correct
41 Correct 1 ms 340 KB Output is correct
42 Correct 0 ms 340 KB Output is correct
43 Correct 0 ms 340 KB Output is correct
44 Correct 0 ms 340 KB Output is correct
45 Correct 1 ms 340 KB Output is correct
46 Correct 0 ms 340 KB Output is correct
47 Correct 1 ms 340 KB Output is correct
48 Correct 1 ms 360 KB Output is correct
49 Correct 1 ms 340 KB Output is correct

Subtask #4
0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 0 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Incorrect 1 ms 340 KB Output isn't correct
5 Halted 0 ms 0 KB -

Subtask #5
35.0 / 35.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 4 ms 212 KB Output is correct
5 Correct 4 ms 240 KB Output is correct
6 Correct 4 ms 212 KB Output is correct
7 Correct 2 ms 212 KB Output is correct
8 Correct 3 ms 212 KB Output is correct
9 Correct 5 ms 212 KB Output is correct
10 Correct 7 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 2 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 2 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 2 ms 212 KB Output is correct
18 Correct 2 ms 212 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 6 ms 328 KB Output is correct
21 Correct 3 ms 332 KB Output is correct
22 Correct 1 ms 212 KB Output is correct
23 Correct 1 ms 212 KB Output is correct
24 Correct 15 ms 328 KB Output is correct
25 Correct 8 ms 328 KB Output is correct
26 Correct 15 ms 332 KB Output is correct
27 Correct 15 ms 212 KB Output is correct
28 Correct 36 ms 212 KB Output is correct
29 Correct 29 ms 212 KB Output is correct
30 Correct 261 ms 212 KB Output is correct
31 Correct 10 ms 212 KB Output is correct
32 Correct 29 ms 332 KB Output is correct
33 Correct 5 ms 212 KB Output is correct
34 Correct 10 ms 212 KB Output is correct
35 Correct 15 ms 328 KB Output is correct
36 Correct 15 ms 212 KB Output is correct
37 Correct 10 ms 340 KB Output is correct
38 Correct 29 ms 336 KB Output is correct
39 Correct 4 ms 328 KB Output is correct
40 Correct 18 ms 332 KB Output is correct
41 Correct 13 ms 212 KB Output is correct
42 Correct 12 ms 332 KB Output is correct
43 Correct 230 ms 308 KB Output is correct
44 Correct 18 ms 332 KB Output is correct
45 Correct 11 ms 328 KB Output is correct
46 Correct 12 ms 212 KB Output is correct
47 Correct 3273 ms 308 KB Output is correct
48 Correct 2615 ms 316 KB Output is correct
49 Correct 712 ms 312 KB Output is correct
50 Correct 188 ms 308 KB Output is correct

Subtask #6
0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 340 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 2 ms 212 KB Output is correct
16 Correct 969 ms 308 KB Output is correct
17 Correct 11 ms 212 KB Output is correct
18 Correct 335 ms 304 KB Output is correct
19 Correct 3 ms 212 KB Output is correct
20 Correct 578 ms 308 KB Output is correct
21 Correct 236 ms 212 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 2 ms 212 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 106 ms 212 KB Output is correct
26 Correct 458 ms 304 KB Output is correct
27 Correct 1 ms 212 KB Output is correct
28 Correct 0 ms 212 KB Output is correct
29 Correct 0 ms 340 KB Output is correct
30 Correct 0 ms 340 KB Output is correct
31 Correct 0 ms 340 KB Output is correct
32 Correct 0 ms 212 KB Output is correct
33 Correct 0 ms 212 KB Output is correct
34 Correct 0 ms 212 KB Output is correct
35 Correct 0 ms 212 KB Output is correct
36 Correct 0 ms 340 KB Output is correct
37 Correct 1 ms 340 KB Output is correct
38 Correct 0 ms 340 KB Output is correct
39 Correct 0 ms 212 KB Output is correct
40 Correct 0 ms 340 KB Output is correct
41 Correct 0 ms 340 KB Output is correct
42 Correct 1 ms 340 KB Output is correct
43 Correct 0 ms 212 KB Output is correct
44 Correct 0 ms 340 KB Output is correct
45 Correct 0 ms 212 KB Output is correct
46 Correct 0 ms 212 KB Output is correct
47 Correct 0 ms 212 KB Output is correct
48 Correct 0 ms 340 KB Output is correct
49 Correct 0 ms 212 KB Output is correct
50 Correct 0 ms 212 KB Output is correct
51 Correct 0 ms 212 KB Output is correct
52 Correct 1 ms 340 KB Output is correct
53 Correct 0 ms 340 KB Output is correct
54 Correct 0 ms 340 KB Output is correct
55 Correct 0 ms 340 KB Output is correct
56 Correct 0 ms 340 KB Output is correct
57 Correct 1 ms 340 KB Output is correct
58 Correct 0 ms 340 KB Output is correct
59 Correct 0 ms 212 KB Output is correct
60 Correct 1 ms 340 KB Output is correct
61 Correct 0 ms 340 KB Output is correct
62 Correct 0 ms 340 KB Output is correct
63 Correct 0 ms 340 KB Output is correct
64 Correct 1 ms 340 KB Output is correct
65 Correct 0 ms 340 KB Output is correct
66 Correct 0 ms 340 KB Output is correct
67 Correct 0 ms 212 KB Output is correct
68 Correct 1 ms 340 KB Output is correct
69 Correct 0 ms 340 KB Output is correct
70 Correct 0 ms 212 KB Output is correct
71 Correct 1 ms 340 KB Output is correct
72 Correct 0 ms 212 KB Output is correct
73 Correct 0 ms 212 KB Output is correct
74 Correct 0 ms 340 KB Output is correct
75 Correct 1 ms 340 KB Output is correct
76 Correct 0 ms 340 KB Output is correct
77 Correct 1 ms 212 KB Output is correct
78 Correct 0 ms 212 KB Output is correct
79 Correct 0 ms 340 KB Output is correct
80 Correct 0 ms 212 KB Output is correct
81 Correct 1 ms 340 KB Output is correct
82 Correct 1 ms 340 KB Output is correct
83 Correct 0 ms 340 KB Output is correct
84 Correct 1 ms 340 KB Output is correct
85 Correct 1 ms 340 KB Output is correct
86 Correct 1 ms 340 KB Output is correct
87 Correct 1 ms 340 KB Output is correct
88 Correct 1 ms 340 KB Output is correct
89 Correct 1 ms 340 KB Output is correct
90 Correct 1 ms 340 KB Output is correct
91 Correct 1 ms 340 KB Output is correct
92 Correct 1 ms 340 KB Output is correct
93 Correct 0 ms 340 KB Output is correct
94 Correct 0 ms 340 KB Output is correct
95 Correct 0 ms 340 KB Output is correct
96 Correct 1 ms 340 KB Output is correct
97 Correct 0 ms 340 KB Output is correct
98 Correct 1 ms 340 KB Output is correct
99 Correct 1 ms 360 KB Output is correct
100 Correct 1 ms 340 KB Output is correct
101 Correct 1 ms 340 KB Output is correct
102 Correct 0 ms 340 KB Output is correct
103 Correct 1 ms 340 KB Output is correct
104 Incorrect 1 ms 340 KB Output isn't correct
105 Halted 0 ms 0 KB -