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Submission #927891

# Submission time Handle Problem Language Result Execution time Memory
927891 2024-02-15T13:45:37 Z math_rabbit_1028 Chess Rush (CEOI20_chessrush) C++14
100 / 100
 590 ms 40576 KB 
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
const ll MOD = 1'000'000'007;

int R, C, Q;
ll inv[1010];

typedef vector<vector<ll>> matrix;
matrix A, E;
matrix prod(matrix A) {
    matrix B = vector<vector<ll>> (C+1, vector<ll>(C+1, 0));
    for (int i = 1; i <= C; i++) {
        for (int j = 1; j <= C; j++) {
            for (int k = -1; k <= 1; k++) {
                if (j+k < 1 || j+k > C) continue;
                B[i][j] += A[i][j+k];
                B[i][j] %= MOD;
            }
        }
    }
    return B;
}
matrix square(matrix A) {
    matrix B = vector<vector<ll>> (C+1, vector<ll>(C+1, 0));
    for (int i = 1; i <= C; i++) {
        for (int k = 1; k <= C; k++) {
            B[i][1] += A[i][k] * A[k][1];
            B[i][1] %= MOD;
        }
        B[1][i] = B[i][1];
    }
    for (int i = 2; i <= C; i++) {
        for (int j = 2; j <= C; j++) {
            if (i+j-1 <= C) {
                B[i][j] = B[i-1][j-1] + B[1][i+j-1];
                B[i][j] %= MOD;
            }
        }
    }
    for (int i = C; i >= 2; i--) {
        for (int j = C; j >= 2; j--) {
            if (i+j-1 >= C) B[i][j] = B[C+1-i][C+1-j];
        }
    }
    return B;
}
matrix myPow(int x) {
    if (x == 0) return E;
    matrix B = myPow(x/2);
    B = square(B);
    if (x % 2 == 0) return B;
    else return prod(B);
}
int myPow(int a, int x) {
    if (x == 0) return 1;
    ll b = myPow(a, x/2);
    b = b*b%MOD;
    if (x % 2 == 0) return b;
    else return b*a%MOD;
}
void init() {
    A = vector<vector<ll>> (C+1, vector<ll>(C+1, 0));
    E = vector<vector<ll>> (C+1, vector<ll>(C+1, 0));
    for (int i = 1; i <= C; i++) {
        for (int j = 1; j <= C; j++) {
            if (abs(i-j) <= 1) A[i][j] = 1;
            if (i == j) E[i][j] = 1;
        }
    }
    A = myPow(R-1);

    for (int i = 1; i <= C; i++) {
        inv[i] = myPow(i, MOD-2);
    }
}

pll PAWN(int a, int b) {
    if (a == b) return {R-1, 1};
    return {0, 0};
}
pll ROOK(int a, int b) {
    if (a == b) return {1, 1};
    return {2, 2};
}
pll QUEEN(int a, int b) {
    if (a == b || abs(a-b) == R-1) return {1, 1};
    vector<pll> st, ed;
    for (int j = 1; j <= C; j++) if (j != a) st.push_back({1, j});
    for (int i = 2; ; i++) {
        int j = a + i-1;
        if (j > C) break;
        st.push_back({i, j});
    }
    for (int i = 2; ; i++) {
        int j = a + 1-i;
        if (j < 1) break;
        st.push_back({i, j});
    }
    for (int j = 1; j <= C; j++) if (j != b) ed.push_back({R, j});
    for (int i = 2; ; i++) {
        int j = b + i-1;
        if (j > C) break;
        ed.push_back({R-i+1, j});
    }
    for (int i = 2; ; i++) {
        int j = b + 1-i;
        if (j < 1) break;
        ed.push_back({R-i+1, j});
    }

    int cnt = 0;
    for (auto &[x, y] : st) if (y == b) cnt++;
    for (auto &[x, y] : ed) if (y == a) cnt++;
    cnt += st.size() + ed.size();
    st.insert(st.end(), ed.begin(), ed.end());
    sort(st.begin(), st.end());
    st.erase(unique(st.begin(), st.end()), st.end());
    cnt -= st.size();
    return {2, cnt};
}

pll solve(int a, int b) {
    ll t1 = ceil((double)(R-a-b+1)/(2*C-2));
    ll t2 = ceil((double)(R-a-1+b)/(2*C-2));
    pll ans;
    if (t1 < t2) ans = {2*t1+2, 2*t1*(C-1) - (R-a-b+1)};
    else ans = {2*t2+1, 2*t2*(C-1) - (R-a-1+b)};
    ll cnt = 1;
    ans.second /= 2;
    for (int i = 1; i <= ans.second; i++) {
        cnt *= (ans.first-2+i);
        cnt %= MOD;
        cnt *= inv[i];
        cnt %= MOD;
    }
    return {ans.first, cnt};
}
pll BISHOP(int a, int b) {
    if ((1+a)%2 != (R+b)%2) return {0, 0};
    pll A = solve(a, b), B = solve(C+1-a, C+1-b);
    if (A.first == B.first) return {A.first, (A.second + B.second) % MOD};
    else if (A.first < B.first) return A;
    else return B;
}

pll KING(int a, int b) {
    return {R-1, A[a][b]};
}

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

    cin >> R >> C >> Q;

    init();

    while (Q--) {
        char T; int a, b; pll res;
        cin >> T >> a >> b;
        if (T == 'P') res = PAWN(a, b);
        else if (T == 'R') res = ROOK(a, b);
        else if (T == 'Q') res = QUEEN(a, b);
        else if (T == 'B') res = BISHOP(a, b);
        else if (T == 'K') res = KING(a, b);
        cout << res.first << " " << res.second << "\n";
    }

    return 0;
}

Compilation message

chessrush.cpp: In function 'pll QUEEN(int, int)':
chessrush.cpp:114:16: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
  114 |     for (auto &[x, y] : st) if (y == b) cnt++;
      |                ^
chessrush.cpp:115:16: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
  115 |     for (auto &[x, y] : ed) if (y == a) cnt++;
      |                ^

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 208 ms 25700 KB Output is correct

Subtask #2
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 2 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 42 ms 6892 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct

Subtask #4
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 199 ms 39848 KB Output is correct
6 Correct 82 ms 10368 KB Output is correct
7 Correct 2 ms 348 KB Output is correct
8 Correct 488 ms 39816 KB Output is correct
9 Correct 2 ms 348 KB Output is correct
10 Correct 5 ms 784 KB Output is correct

Subtask #5
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 1 ms 860 KB Output is correct
3 Correct 1 ms 604 KB Output is correct
4 Correct 1 ms 348 KB Output is correct

Subtask #6
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 1 ms 860 KB Output is correct
3 Correct 1 ms 604 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 2 ms 348 KB Output is correct
6 Correct 2 ms 600 KB Output is correct
7 Correct 3 ms 604 KB Output is correct
8 Correct 3 ms 860 KB Output is correct

Subtask #7
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 1 ms 860 KB Output is correct
3 Correct 1 ms 604 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 2 ms 348 KB Output is correct
6 Correct 2 ms 600 KB Output is correct
7 Correct 3 ms 604 KB Output is correct
8 Correct 3 ms 860 KB Output is correct
9 Correct 2 ms 348 KB Output is correct
10 Correct 2 ms 348 KB Output is correct
11 Correct 7 ms 884 KB Output is correct
12 Correct 8 ms 860 KB Output is correct
13 Correct 2 ms 520 KB Output is correct
14 Correct 1 ms 348 KB Output is correct

Subtask #8
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 1 ms 860 KB Output is correct
3 Correct 1 ms 604 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 2 ms 348 KB Output is correct
6 Correct 2 ms 600 KB Output is correct
7 Correct 3 ms 604 KB Output is correct
8 Correct 3 ms 860 KB Output is correct
9 Correct 2 ms 348 KB Output is correct
10 Correct 2 ms 348 KB Output is correct
11 Correct 7 ms 884 KB Output is correct
12 Correct 8 ms 860 KB Output is correct
13 Correct 2 ms 520 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 2 ms 348 KB Output is correct
16 Correct 2 ms 348 KB Output is correct
17 Correct 527 ms 39844 KB Output is correct
18 Correct 549 ms 39840 KB Output is correct
19 Correct 401 ms 37056 KB Output is correct
20 Correct 417 ms 39848 KB Output is correct

Subtask #9
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 208 ms 25700 KB Output is correct
3 Correct 1 ms 344 KB Output is correct
4 Correct 2 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 42 ms 6892 KB Output is correct
7 Correct 1 ms 344 KB Output is correct
8 Correct 1 ms 344 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 199 ms 39848 KB Output is correct
12 Correct 82 ms 10368 KB Output is correct
13 Correct 2 ms 348 KB Output is correct
14 Correct 488 ms 39816 KB Output is correct
15 Correct 2 ms 348 KB Output is correct
16 Correct 5 ms 784 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 1 ms 860 KB Output is correct
19 Correct 1 ms 604 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 2 ms 348 KB Output is correct
22 Correct 2 ms 600 KB Output is correct
23 Correct 3 ms 604 KB Output is correct
24 Correct 3 ms 860 KB Output is correct
25 Correct 2 ms 348 KB Output is correct
26 Correct 2 ms 348 KB Output is correct
27 Correct 7 ms 884 KB Output is correct
28 Correct 8 ms 860 KB Output is correct
29 Correct 2 ms 520 KB Output is correct
30 Correct 1 ms 348 KB Output is correct
31 Correct 2 ms 348 KB Output is correct
32 Correct 2 ms 348 KB Output is correct
33 Correct 527 ms 39844 KB Output is correct
34 Correct 549 ms 39840 KB Output is correct
35 Correct 401 ms 37056 KB Output is correct
36 Correct 417 ms 39848 KB Output is correct
37 Correct 478 ms 40164 KB Output is correct
38 Correct 590 ms 40576 KB Output is correct
39 Correct 539 ms 39956 KB Output is correct
40 Correct 2 ms 348 KB Output is correct
41 Correct 460 ms 39804 KB Output is correct
42 Correct 3 ms 344 KB Output is correct