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Submission #815742

# Submission time Handle Problem Language Result Execution time Memory
815742 2023-08-08T20:29:40 Z finn__ Chess Rush (CEOI20_chessrush) C++17
100 / 100
 306 ms 16048 KB 
#include <bits/stdc++.h>
using namespace std;

constexpr size_t N = 1000;
constexpr int64_t MOD = 1000000007;

template <size_t L>
struct Matrix
{
    int64_t m[L][L];

    void square(size_t n, Matrix &c) const
    {
        memset(c.m, 0, sizeof c.m);

        // Fill first row.
        for (size_t j = 0; j < n; ++j)
            for (size_t k = 0; k < n; ++k)
                c.m[0][j] = (c.m[0][j] + m[0][k] * m[k][j]) % MOD;

        // Use very obscure recurrence f_ij = f_i-1,j-1 + f_0,i+j to fill upper triangle.
        for (size_t i = 1; i < n; ++i)
            for (size_t j = i; i + j < n; ++j)
                c.m[i][j] = (c.m[i - 1][j - 1] + c.m[0][i + j]) % MOD;

        // Use symmetry to fill the rest
        for (size_t i = 1; i < n; ++i)
            for (size_t j = n - i; j < n; ++j)
                c.m[i][j] = c.m[n - j - 1][n - i - 1];

        for (size_t i = 1; i < n; ++i)
            for (size_t j = 0; j < i; ++j)
                c.m[i][j] = c.m[j][i];
    }

    void mul_tridiagonal(size_t n, Matrix &c) const
    {
        memset(c.m, 0, sizeof c.m);

        // For a 1 at (i, j), add j-th row of m to i-th row of c
        for (size_t i = 0; i < n; ++i)
            for (size_t j = i ? (i - 1) : 0; j < min(i + 2, n); ++j)
                for (size_t k = 0; k < n; ++k)
                    c.m[i][k] += m[j][k];

        for (size_t i = 0; i < n; ++i)
            for (size_t j = 0; j < n; ++j)
                c.m[i][j] %= MOD;
    }
};

template <typename T>
T binary_exp(T x, T y)
{
    T z = 1;

    while (y)
    {
        if (y & 1)
            z = (z * x) % MOD;
        x = (x * x) % MOD;
        y >>= 1;
    }

    return z;
}

template <typename T>
T modular_inverse(T x) { return binary_exp(x, MOD - 2); }

Matrix<N> kpow, tmp;

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

    int r, c, q;
    cin >> r >> c >> q;

    // Build matrix for king

    for (size_t i = 0; i < c; ++i)
        kpow.m[i][i] = 1;

    for (size_t i = 30; i <= 30; --i)
    {
        kpow.square(c, tmp);
        memcpy(kpow.m, tmp.m, sizeof tmp.m);
        if (((r - 1) >> i) & 1)
            kpow.mul_tridiagonal(c, tmp), memcpy(kpow.m, tmp.m, sizeof tmp.m);
    }

    while (q--)
    {
        char type;
        int start, finish;
        cin >> type >> start >> finish;

        switch (type)
        {
        case 'P':
        {
            if (start == finish)
                cout << r - 1 << " 1\n";
            else
                cout << "0 0\n";
            break;
        }
        case 'R':
        {
            if (start == finish)
                cout << "1 1\n";
            else
                cout << "2 2\n";
            break;
        }
        case 'Q':
        {
            if (start == finish || abs(start - finish) == (r - 1))
                cout << "1 1\n";
            else
            {
                int ans = 4 + (r == c) * ((start == 1 || start == c) + (finish == 1 || finish == c));
                if ((r - abs(start - finish)) & 1)
                {
                    int side_space = (r - 1 - abs(start - finish)) / 2;
                    ans += min(start, finish) - side_space >= 1;
                    ans += max(start, finish) + side_space <= c;
                }
                cout << "2 " << ans << '\n';
            }
            break;
        }
        case 'B':
        {
            if (!((r - abs(start - finish)) & 1))
            {
                cout << "0 0\n";
                break;
            }

            if (abs(start - finish) == r - 1)
            {
                cout << "1 1\n";
                break;
            }

            // Solve for the case when the first move is to the right, then just swap positions
            auto solve_bishop = [&]()
            {
                if (start == c)
                    return make_pair((int64_t)(1LL << 42), (int64_t)0);
                int64_t moves = 1 + (r - 1 - (c - start) + c - 2) / (c - 1),
                        t = (((r - 1 - (c - start) + c - 2) / (c - 1) - 1) & 1) ? 1 : c;
                bool last_dir = t == 1;
                t += (last_dir ? 1 : -1) * (r - 1 - (c - 1) * (moves - 2) - (c - start));
                if (t == finish)
                    return make_pair(moves, int64_t(1));

                int64_t f;
                if ((finish > t && last_dir) || (finish < t && !last_dir))
                {
                    f = abs(t - finish) / 2;
                }
                else
                {
                    ++moves;
                    if (last_dir)
                        f = c - (t + finish) / 2;
                    else
                        f = (t + finish) / 2 - 1;
                }

                int64_t num_ways = 1;
                for (int64_t i = 0; i < f; ++i)
                    num_ways = (num_ways * (moves - 1 + i)) % MOD;
                int64_t factorial = 1;
                for (int64_t i = 2; i <= f; ++i)
                    factorial = (factorial * i) % MOD;
                num_ways = (num_ways * modular_inverse(factorial)) % MOD;

                return make_pair(moves, num_ways);
            };

            auto [dis_right, ways_right] = solve_bishop();
            start = c - start + 1;
            finish = c - finish + 1;
            auto [dis_left, ways_left] = solve_bishop();

            int64_t dis = min(dis_left, dis_right);
            int64_t ways = 0;
            if (dis == dis_left)
                ways += ways_left;
            if (dis == dis_right)
                ways += ways_right;

            cout << dis << ' ' << ways % MOD << '\n';
            break;
        }
        case 'K':
        {
            cout << r - 1 << ' ' << kpow.m[start - 1][finish - 1] << '\n';
            break;
        }
        }
    }
}

Compilation message

chessrush.cpp: In function 'int main()':
chessrush.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 i = 0; i < c; ++i)
      |                        ~~^~~

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 27 ms 15956 KB Output is correct
2 Correct 166 ms 15972 KB Output is correct

Subtask #2
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 28 ms 15972 KB Output is correct
2 Correct 33 ms 15956 KB Output is correct
3 Correct 29 ms 15956 KB Output is correct
4 Correct 56 ms 15956 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 33 ms 15952 KB Output is correct
2 Correct 29 ms 15956 KB Output is correct
3 Correct 29 ms 15956 KB Output is correct
4 Correct 28 ms 15956 KB Output is correct

Subtask #4
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 33 ms 15952 KB Output is correct
2 Correct 29 ms 15956 KB Output is correct
3 Correct 29 ms 15956 KB Output is correct
4 Correct 28 ms 15956 KB Output is correct
5 Correct 237 ms 15880 KB Output is correct
6 Correct 90 ms 15968 KB Output is correct
7 Correct 37 ms 15956 KB Output is correct
8 Correct 286 ms 15956 KB Output is correct
9 Correct 43 ms 15964 KB Output is correct
10 Correct 38 ms 15956 KB Output is correct

Subtask #5
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 30 ms 15880 KB Output is correct
2 Correct 37 ms 15968 KB Output is correct
3 Correct 30 ms 15956 KB Output is correct
4 Correct 28 ms 15972 KB Output is correct

Subtask #6
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 30 ms 15880 KB Output is correct
2 Correct 37 ms 15968 KB Output is correct
3 Correct 30 ms 15956 KB Output is correct
4 Correct 28 ms 15972 KB Output is correct
5 Correct 29 ms 15984 KB Output is correct
6 Correct 31 ms 15972 KB Output is correct
7 Correct 35 ms 15972 KB Output is correct
8 Correct 32 ms 15976 KB Output is correct

Subtask #7
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 30 ms 15880 KB Output is correct
2 Correct 37 ms 15968 KB Output is correct
3 Correct 30 ms 15956 KB Output is correct
4 Correct 28 ms 15972 KB Output is correct
5 Correct 29 ms 15984 KB Output is correct
6 Correct 31 ms 15972 KB Output is correct
7 Correct 35 ms 15972 KB Output is correct
8 Correct 32 ms 15976 KB Output is correct
9 Correct 35 ms 15972 KB Output is correct
10 Correct 46 ms 15960 KB Output is correct
11 Correct 50 ms 15968 KB Output is correct
12 Correct 50 ms 15964 KB Output is correct
13 Correct 39 ms 15968 KB Output is correct
14 Correct 38 ms 15956 KB Output is correct

Subtask #8
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 30 ms 15880 KB Output is correct
2 Correct 37 ms 15968 KB Output is correct
3 Correct 30 ms 15956 KB Output is correct
4 Correct 28 ms 15972 KB Output is correct
5 Correct 29 ms 15984 KB Output is correct
6 Correct 31 ms 15972 KB Output is correct
7 Correct 35 ms 15972 KB Output is correct
8 Correct 32 ms 15976 KB Output is correct
9 Correct 35 ms 15972 KB Output is correct
10 Correct 46 ms 15960 KB Output is correct
11 Correct 50 ms 15968 KB Output is correct
12 Correct 50 ms 15964 KB Output is correct
13 Correct 39 ms 15968 KB Output is correct
14 Correct 38 ms 15956 KB Output is correct
15 Correct 38 ms 15956 KB Output is correct
16 Correct 39 ms 15972 KB Output is correct
17 Correct 279 ms 15968 KB Output is correct
18 Correct 306 ms 16048 KB Output is correct
19 Correct 239 ms 15956 KB Output is correct
20 Correct 259 ms 15964 KB Output is correct

Subtask #9
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 27 ms 15956 KB Output is correct
2 Correct 166 ms 15972 KB Output is correct
3 Correct 28 ms 15972 KB Output is correct
4 Correct 33 ms 15956 KB Output is correct
5 Correct 29 ms 15956 KB Output is correct
6 Correct 56 ms 15956 KB Output is correct
7 Correct 33 ms 15952 KB Output is correct
8 Correct 29 ms 15956 KB Output is correct
9 Correct 29 ms 15956 KB Output is correct
10 Correct 28 ms 15956 KB Output is correct
11 Correct 237 ms 15880 KB Output is correct
12 Correct 90 ms 15968 KB Output is correct
13 Correct 37 ms 15956 KB Output is correct
14 Correct 286 ms 15956 KB Output is correct
15 Correct 43 ms 15964 KB Output is correct
16 Correct 38 ms 15956 KB Output is correct
17 Correct 30 ms 15880 KB Output is correct
18 Correct 37 ms 15968 KB Output is correct
19 Correct 30 ms 15956 KB Output is correct
20 Correct 28 ms 15972 KB Output is correct
21 Correct 29 ms 15984 KB Output is correct
22 Correct 31 ms 15972 KB Output is correct
23 Correct 35 ms 15972 KB Output is correct
24 Correct 32 ms 15976 KB Output is correct
25 Correct 35 ms 15972 KB Output is correct
26 Correct 46 ms 15960 KB Output is correct
27 Correct 50 ms 15968 KB Output is correct
28 Correct 50 ms 15964 KB Output is correct
29 Correct 39 ms 15968 KB Output is correct
30 Correct 38 ms 15956 KB Output is correct
31 Correct 38 ms 15956 KB Output is correct
32 Correct 39 ms 15972 KB Output is correct
33 Correct 279 ms 15968 KB Output is correct
34 Correct 306 ms 16048 KB Output is correct
35 Correct 239 ms 15956 KB Output is correct
36 Correct 259 ms 15964 KB Output is correct
37 Correct 269 ms 15964 KB Output is correct
38 Correct 303 ms 15976 KB Output is correct
39 Correct 281 ms 15968 KB Output is correct
40 Correct 30 ms 15956 KB Output is correct
41 Correct 268 ms 15884 KB Output is correct
42 Correct 30 ms 15972 KB Output is correct