oj.uz

Submission #562912

# Submission time Handle Problem Language Result Execution time Memory
562912 2022-05-15T15:26:13 Z Redhood Semafor (COI20_semafor) C++14
100 / 100
 123 ms 616 KB 
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>

#define fi first
#define se second
#define sz(x) (int)(x).size()
#define pb push_back
#define mkp make_pair
#define all(x) (x).begin(), (x).end()

using namespace std;
using namespace __gnu_cxx;
using namespace __gnu_pbds;






typedef long long ll;
typedef long double ld;

#define int long long
int Cnk[11][11];
const int mod = (int)1e9 + 7;
const ll mod2 = 1ll * mod * mod;
template<typename T>
void md(T &a){
    if(a >= mod)
        a-=mod;
}
template<typename T>
void md2(T &a){
    if(a >= mod2)
        a-=mod2;
}
int B;
struct mat{
    vector<vector<int>>a;
    int n , m;
    mat(){
        n = m = B;
        a.resize(n , vector < int > (m));
        for(int i=0;i<n;++i)
            for(int j=0;j<m;++j)
                a[i][j]=0;
    }
    mat(int _n, int _m){
        n = _n , m = _m;
        a.resize(n , vector < int > (m));
        for(int i=0;i<n;++i)
            for(int j=0;j<m;++j){
                a[i][j] = 0;
            }
    }
};

mat operator*(const mat&a , const mat&b){
    mat c(a.n, b.m);
    assert(a.m == b.n);
    for(int i = 0; i < a.n; ++i){
        for(int j = 0; j < b.m;++j){
            ll f = 0;
            for(int k = 0; k < a.m; ++k){
                f += (1ll * a.a[i][k] * b.a[k][j]);
                md2(f);
            }
            c.a[i][j] = f % mod;
        }
    }
    return c;
}
mat one(int f){
    mat c(f , f);
    for(int i = 0; i < f; ++i)
        c.a[i][i] = 1;
    return c;
}
mat binpow(const mat &a , ll b){
    if(b == 0){
        return one(a.n);
    }
    mat ans = binpow(a , b / 2);
    ans = ans * ans;
    if(b & 1)
        ans = ans * a;
    return ans;
}
int binpow_num(int a , int b){
    if(b == 0)
        return 1;
    int ans = binpow_num(a , b / 2);
    ans = (1ll * ans * ans) % mod;
    if(b & 1)
        ans = (1ll * ans * a) % mod;
    return ans;
}
int INV(int x){
    return binpow_num(x , mod - 2);
}



signed main(){
    ios_base::sync_with_stdio(0) , cin.tie(0) , cout.tie(0);

    /// n a b c d e
    /// 0 0 1 0 1 0
    /// 1 0 1 0 0 0
    /// 2 1 0 0 1 0
    /// 3 1 1 1 0 0
    /// 4 0 1 0 0 1
    /// 5 1 0 1 0 1
    /// 6 0 0 1 1 0
    /// 7 1 1 0 0 0
    /// 8 1 0 1 1 1
    /// 9 1 1 1 0 1

    string st[10];
    st[0] ="01010";
    st[1] ="01000";
    st[2]="10010";
    st[3]= "11100";
    st[4]= "01001";
    st[5]= "10101";
    st[6]= "00110";
    st[7]= "11000";
    st[8]= "10111";
    st[9]= "11101";



    vector<int> id(10), f;
    for(int i = 0; i < 10; ++i){
        id[i] = 0;
        for(int j = 0; j < 5; ++j){
            if(st[i][j] == '1')
                id[i] += (1 << j);
        }
    }
    f = id;
    sort(all(f));
    f.erase(unique(all(f)), f.end());
    assert(sz(f) == 10);




    int m, x;
    ll n ,k ;
    cin >> m >> n >> k >> x;
    B = m * 5 + 1;


    auto get_msk = [&](int ff){
        int msk = 0;
        if(m == 1){
            msk = id[ff];
        }else{
            msk = ((id[ff / 10])<<5)|(id[ff%10]);
        }
        return msk;
    };



    vector < int > get(100);
    vector < int > cnt(10);

    for(int i = 0; i < 11; ++i){
        Cnk[i][0]=1;
        for(int j = 1; j <= i; ++j){
            Cnk[i][j] = Cnk[i - 1][j] + Cnk[i - 1][j - 1];
            md(Cnk[i][j]);
        }
    }

    mat trans(B,B);
    for(int i = 0; i < B; ++i){
        for(int j = 0; j < B; ++j){

            if(abs(i - j) > 1)
                continue;
            if(i == j)
                continue;
            if(i + 1 == j)
                trans.a[i][j] = 1ll * (B-1 - i)% mod;
            else
                trans.a[i][j] = 1ll * i % mod;
        }
    }

    mat trans1 = trans;
    trans = binpow(trans1 , k);




    int states = 10;
    if(m == 2)states *= 10;


    mat ST(states , states);


    mat init(1 , B);
    init.a[0][0] = 1;
    trans = init * trans;
    for(int i = 0; i < states; ++i) {
        for(int j = 0 ; j < states; ++j){
            int t = __builtin_popcount(get_msk(i) ^ get_msk(j));

            assert(t < B);
        //            if(t >= B){
//                cout << "FUKK " << i << ' ' << j << endl;
//                cout << get_msk(i) << ' ' << get_msk(j) << endl;
//                exit(0);
//            }

            ST.a[i][j] = (1ll * trans.a[0][t] * INV(Cnk[B-1][t])) % mod;
        }
    }

//
//    for(int i = 0; i < states; ++i){
//        for(int j = 0;  j < states; ++j){
//            cout << ST.a[i][j] << ' ';
//        }
//        cout << '\n';
//    }


    mat INIT(1 , states);


    INIT.a[0][x] = 1;

    ST = INIT * binpow(ST , n / k);

    trans =trans1;
    trans = binpow(trans , n % k);

//
//    for(int i = 0; i < 10; ++i)
//        cout << ST.a[0][i] << ' ';
//    cout << endl;

    vector < int > ans(states);


//    cerr << states << endl;
    for(int i = 0; i < states; ++i) {
        for(int j = 0 ; j < states; ++j){
            int t = __builtin_popcount(get_msk(i) ^ get_msk(j));
            assert(t < B);
            ans[j] += 1ll * ST.a[0][i] * 1ll * trans.a[0][t] % mod * INV(Cnk[B-1][t]) % mod;
            md(ans[j]);
        }
    }

    for(int i = 0; i < states; ++i){
        cout << ans[i] << '\n';
    }


    return 0;
}

Subtask #1
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 320 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 320 KB Output is correct
6 Correct 1 ms 316 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 324 KB Output is correct
9 Correct 1 ms 324 KB Output is correct
10 Correct 1 ms 212 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 320 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 320 KB Output is correct
6 Correct 1 ms 316 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 324 KB Output is correct
9 Correct 1 ms 324 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 1 ms 316 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 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 1 ms 320 KB Output is correct
18 Correct 1 ms 320 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 212 KB Output is correct
22 Correct 1 ms 212 KB Output is correct

Subtask #3
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 468 KB Output is correct
2 Correct 8 ms 572 KB Output is correct
3 Correct 8 ms 572 KB Output is correct
4 Correct 8 ms 572 KB Output is correct
5 Correct 8 ms 456 KB Output is correct
6 Correct 8 ms 468 KB Output is correct
7 Correct 8 ms 468 KB Output is correct
8 Correct 8 ms 468 KB Output is correct
9 Correct 9 ms 616 KB Output is correct

Subtask #4
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 29 ms 548 KB Output is correct
2 Correct 66 ms 572 KB Output is correct
3 Correct 95 ms 572 KB Output is correct
4 Correct 121 ms 560 KB Output is correct
5 Correct 115 ms 468 KB Output is correct
6 Correct 112 ms 468 KB Output is correct
7 Correct 120 ms 560 KB Output is correct
8 Correct 109 ms 556 KB Output is correct
9 Correct 110 ms 560 KB Output is correct
10 Correct 115 ms 560 KB Output is correct
11 Correct 17 ms 572 KB Output is correct
12 Correct 10 ms 568 KB Output is correct
13 Correct 123 ms 560 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 29 ms 548 KB Output is correct
2 Correct 66 ms 572 KB Output is correct
3 Correct 95 ms 572 KB Output is correct
4 Correct 121 ms 560 KB Output is correct
5 Correct 115 ms 468 KB Output is correct
6 Correct 112 ms 468 KB Output is correct
7 Correct 120 ms 560 KB Output is correct
8 Correct 109 ms 556 KB Output is correct
9 Correct 110 ms 560 KB Output is correct
10 Correct 115 ms 560 KB Output is correct
11 Correct 17 ms 572 KB Output is correct
12 Correct 10 ms 568 KB Output is correct
13 Correct 123 ms 560 KB Output is correct
14 Correct 16 ms 468 KB Output is correct
15 Correct 47 ms 548 KB Output is correct
16 Correct 73 ms 468 KB Output is correct
17 Correct 99 ms 468 KB Output is correct
18 Correct 107 ms 468 KB Output is correct
19 Correct 84 ms 468 KB Output is correct
20 Correct 102 ms 556 KB Output is correct
21 Correct 108 ms 564 KB Output is correct
22 Correct 119 ms 576 KB Output is correct
23 Correct 97 ms 468 KB Output is correct
24 Correct 102 ms 468 KB Output is correct
25 Correct 94 ms 560 KB Output is correct
26 Correct 12 ms 448 KB Output is correct
27 Correct 14 ms 448 KB Output is correct
28 Correct 82 ms 560 KB Output is correct

Subtask #6
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 468 KB Output is correct
2 Correct 8 ms 572 KB Output is correct
3 Correct 8 ms 572 KB Output is correct
4 Correct 8 ms 572 KB Output is correct
5 Correct 8 ms 456 KB Output is correct
6 Correct 8 ms 468 KB Output is correct
7 Correct 8 ms 468 KB Output is correct
8 Correct 8 ms 468 KB Output is correct
9 Correct 9 ms 616 KB Output is correct
10 Correct 29 ms 548 KB Output is correct
11 Correct 66 ms 572 KB Output is correct
12 Correct 95 ms 572 KB Output is correct
13 Correct 121 ms 560 KB Output is correct
14 Correct 115 ms 468 KB Output is correct
15 Correct 112 ms 468 KB Output is correct
16 Correct 120 ms 560 KB Output is correct
17 Correct 109 ms 556 KB Output is correct
18 Correct 110 ms 560 KB Output is correct
19 Correct 115 ms 560 KB Output is correct
20 Correct 17 ms 572 KB Output is correct
21 Correct 10 ms 568 KB Output is correct
22 Correct 123 ms 560 KB Output is correct
23 Correct 16 ms 468 KB Output is correct
24 Correct 47 ms 548 KB Output is correct
25 Correct 73 ms 468 KB Output is correct
26 Correct 99 ms 468 KB Output is correct
27 Correct 107 ms 468 KB Output is correct
28 Correct 84 ms 468 KB Output is correct
29 Correct 102 ms 556 KB Output is correct
30 Correct 108 ms 564 KB Output is correct
31 Correct 119 ms 576 KB Output is correct
32 Correct 97 ms 468 KB Output is correct
33 Correct 102 ms 468 KB Output is correct
34 Correct 94 ms 560 KB Output is correct
35 Correct 12 ms 448 KB Output is correct
36 Correct 14 ms 448 KB Output is correct
37 Correct 82 ms 560 KB Output is correct
38 Correct 11 ms 572 KB Output is correct
39 Correct 9 ms 576 KB Output is correct
40 Correct 9 ms 580 KB Output is correct
41 Correct 9 ms 576 KB Output is correct
42 Correct 9 ms 468 KB Output is correct
43 Correct 9 ms 576 KB Output is correct
44 Correct 9 ms 580 KB Output is correct
45 Correct 115 ms 468 KB Output is correct
46 Correct 113 ms 560 KB Output is correct
47 Correct 11 ms 468 KB Output is correct
48 Correct 9 ms 468 KB Output is correct
49 Correct 9 ms 580 KB Output is correct
50 Correct 8 ms 468 KB Output is correct
51 Correct 8 ms 572 KB Output is correct
52 Correct 37 ms 560 KB Output is correct