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답안 #381605

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
381605 2021-03-25T10:53:34 Z VEGAnn Semafor (COI20_semafor) C++14
21 / 100
 538 ms 1004 KB 
#include <bits/stdc++.h>
#define i2 array<int,2>
#define sz(x) ((int)x.size())
using namespace std;
typedef long long ll;
const int PW = 5;
const int M = (1 << PW);
const int N = 100;
const int ML = 11;
const int SN = ML * ML;
const int md = int(1e9) + 7;
int digs[10];
bool mrk[M];
ll m, n, k, x;

struct matrix{
    int a[M][M];
};

matrix base, base_k, base_nw;

int sum(int x, int y){
    x += y;
    if (x >= md)
        x -= md;
    return x;
}

void SUM(int &x, int y){
    x += y;
    if (x >= md)
        x -= md;
}

int mult(int x, int y) { return (1ll * x * y) % md; }

matrix mat_mult(matrix a, matrix b){
    matrix res;

    for (int i = 0; i < M; i++)
    for (int j = 0; j < M; j++) {
        int nw = 0;

        for (int k = 0; k < M; k++)
            nw = sum(nw, mult(a.a[i][k], b.a[k][j]));

        res.a[i][j] = nw;
    }

    return res;
}

matrix binpow(matrix a, ll po){
    matrix res;
    bool was = 0;

    while (po > 0){
        if (po & 1){
            if (!was)
                res = a;
            else res = mat_mult(res, a);

            was = 1;
        }

        a = mat_mult(a, a);
        po >>= 1;
    }

    return res;
}

struct matrix_sml{
    int a[SN][SN];
};

struct matrix_big{
    int a[N][N];
};

int cnt_ways[ML];

matrix_sml mat_mult_sml(matrix_sml a, matrix_sml b){
    matrix_sml res;

    for (int i = 0; i < SN; i++)
    for (int j = 0; j < SN; j++) {
        int nw = 0;

        for (int k = 0; k < SN; k++)
            nw = sum(nw, mult(a.a[i][k], b.a[k][j]));

        res.a[i][j] = nw;
    }

    return res;
}

matrix_sml binpow_sml(matrix_sml a, ll po){
    matrix_sml res;
    bool was = 0;

    while (po > 0){
        if (po & 1){
            if (!was)
                res = a;
            else res = mat_mult_sml(res, a);

            was = 1;
        }

        a = mat_mult_sml(a, a);
        po >>= 1;
    }

    return res;
}

int get_mask(int x){
    return (digs[x / 10] << PW) + digs[x % 10];
}

//int P(ll n, ll k){
//    int res = 1;
//
//    for (ll x = 0; x < k; x++)
//        res = mult(res, (n - x) % md);
//
//    return res;
//}

matrix_big mat_mult_big(matrix_big a, matrix_big b){
    matrix_big res;

    for (int i = 0; i < N; i++)
    for (int j = 0; j < N; j++) {
        int nw = 0;

        for (int k = 0; k < N; k++)
            nw = sum(nw, mult(a.a[i][k], b.a[k][j]));

        res.a[i][j] = nw;
    }

    return res;
}

matrix_big binpow_big(matrix_big a, ll po){
    matrix_big res;
    bool was = 0;

    while (po > 0){
        if (po & 1){
            if (!was)
                res = a;
            else res = mat_mult_big(res, a);

            was = 1;
        }

        a = mat_mult_big(a, a);
        po >>= 1;
    }

    return res;
}

int get_id(int x, int y){
    return x * ML + y;
}

void calc_cnt_ways(ll k){
    for (int dif = 0; dif < ML; dif++){
        if (dif > k){
            cnt_ways[dif] = 0;
            continue;
        }

        matrix_sml base;

        for (int i = 0; i < SN; i++){
            for (int j = 0; j < SN; j++)
                base.a[i][j] = 0;
        }

        int inv = 10 - dif;

        for (int i = 0; i < SN; i++){
            int x = i / ML, y = i % ML;

            if (x > dif) continue;

            if (y > 0)
                base.a[i][get_id(x, y - 1)] = y;

            if (y + 1 < inv)
                base.a[i][get_id(x, y + 1)] = (inv - y);

            if (x > 0)
                base.a[i][get_id(x - 1, y)] = x;

            if (x < dif)
                base.a[i][get_id(x + 1, y)] = (dif - x);
        }

        base = binpow_sml(base, k);

        cnt_ways[dif] = base.a[0][get_id(dif, 0)];
    }
}

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

#ifdef _LOCAL
    freopen("in.txt","r",stdin);
#endif // _LOCAL

    cin >> m >> n >> k >> x;

    digs[1] = 8;
    digs[2] = 18;
    digs[3] = 28;
    digs[4] = 9;
    digs[5] = 21;
    digs[6] = 6;
    digs[7] = 24;
    digs[8] = 23;
    digs[9] = 29;
    digs[0] = 10;

    if (m == 1){
        for (int i = 0; i < 10; i++)
            mrk[digs[i]] = 1;

        for (int i = 0; i < M; i++){
            for (int j = 0; j < PW; j++)
                base.a[i][(i ^ (1 << j))] = 1;
        }

        base_k = binpow(base, k);

        /// in base_k you need transitions only between digits

        for (int i = 0; i < M; i++)
        for (int j = 0; j < M; j++)
            if (!mrk[i] || !mrk[j])
                base_k.a[i][j] = 0;

        base_k = binpow(base_k, n / k);

        if (n % k > 0){
            /// calc one more matirix pls

            base_nw = binpow(base, n % k);

            for (int i = 0; i < M; i++)
            for (int j = 0; j < M; j++)
                if (!mrk[i] || !mrk[j])
                    base_nw.a[i][j] = 0;

            base_k = mat_mult(base_k, base_nw);
        }

        for (int i = 0; i < 10; i++)
            cout << base_k.a[digs[x]][digs[i]] << '\n';

        return 0;
    }

    calc_cnt_ways(k);

    matrix_big base;

    /// calc base (big)

    for (int i = 0; i < 100; i++)
    for (int j = 0; j < 100; j++){
        int fi_msk = get_mask(i);
        int se_msk = get_mask(j);

        int dif = __builtin_popcount(fi_msk ^ se_msk);

        if (dif > k){
            base.a[i][j] = 0;
            continue;
        }

        base.a[i][j] = cnt_ways[dif];
    }

    matrix_big base_n = binpow_big(base, n / k);

    if (n % k > 0){
        calc_cnt_ways(n % k);

        matrix_big base_nw;

        for (int i = 0; i < 100; i++)
        for (int j = 0; j < 100; j++){
            int fi_msk = get_mask(i);
            int se_msk = get_mask(j);

            int dif = __builtin_popcount(fi_msk ^ se_msk);

            if (dif > k){
                base_nw.a[i][j] = 0;
                continue;
            }

            base_nw.a[i][j] = cnt_ways[dif];
        }

        base_n = mat_mult_big(base_n, base_nw);
    }

    for (int i = 0; i < 100; i++)
        cout << base_n.a[x][i] << '\n';

    return 0;
}

Subtask #1
6.0 / 6.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 364 KB Output is correct
2 Correct 1 ms 364 KB Output is correct
3 Correct 2 ms 364 KB Output is correct
4 Correct 1 ms 364 KB Output is correct
5 Correct 2 ms 364 KB Output is correct
6 Correct 1 ms 364 KB Output is correct
7 Correct 2 ms 384 KB Output is correct
8 Correct 2 ms 364 KB Output is correct
9 Correct 2 ms 364 KB Output is correct
10 Correct 2 ms 364 KB Output is correct

Subtask #2
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 364 KB Output is correct
2 Correct 1 ms 364 KB Output is correct
3 Correct 2 ms 364 KB Output is correct
4 Correct 1 ms 364 KB Output is correct
5 Correct 2 ms 364 KB Output is correct
6 Correct 1 ms 364 KB Output is correct
7 Correct 2 ms 384 KB Output is correct
8 Correct 2 ms 364 KB Output is correct
9 Correct 2 ms 364 KB Output is correct
10 Correct 2 ms 364 KB Output is correct
11 Correct 7 ms 364 KB Output is correct
12 Correct 8 ms 364 KB Output is correct
13 Correct 12 ms 364 KB Output is correct
14 Correct 16 ms 364 KB Output is correct
15 Correct 15 ms 364 KB Output is correct
16 Correct 16 ms 364 KB Output is correct
17 Correct 14 ms 364 KB Output is correct
18 Correct 8 ms 364 KB Output is correct
19 Correct 9 ms 364 KB Output is correct
20 Correct 15 ms 364 KB Output is correct
21 Correct 11 ms 364 KB Output is correct
22 Correct 11 ms 364 KB Output is correct

Subtask #3
0 / 12.0

# 결과 실행 시간 메모리 Grader output
1 Correct 298 ms 748 KB Output is correct
2 Incorrect 538 ms 748 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #4
0 / 12.0

# 결과 실행 시간 메모리 Grader output
1 Incorrect 418 ms 1004 KB Output isn't correct
2 Halted 0 ms 0 KB -

Subtask #5
0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Incorrect 418 ms 1004 KB Output isn't correct
2 Halted 0 ms 0 KB -

Subtask #6
0 / 40.0

# 결과 실행 시간 메모리 Grader output
1 Correct 298 ms 748 KB Output is correct
2 Incorrect 538 ms 748 KB Output isn't correct
3 Halted 0 ms 0 KB -