oj.uz

Submission #562913

# Submission time Handle Problem Language Result Execution time Memory
562913 2022-05-15T15:26:43 Z Redhood Semafor (COI20_semafor) C++14
100 / 100
 144 ms 556 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 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 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 212 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 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 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 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 ms 212 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 212 KB Output is correct
18 Correct 1 ms 212 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 1 ms 212 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 340 KB Output is correct
2 Correct 9 ms 468 KB Output is correct
3 Correct 8 ms 340 KB Output is correct
4 Correct 9 ms 444 KB Output is correct
5 Correct 10 ms 452 KB Output is correct
6 Correct 9 ms 340 KB Output is correct
7 Correct 9 ms 340 KB Output is correct
8 Correct 9 ms 340 KB Output is correct
9 Correct 9 ms 340 KB Output is correct

Subtask #4
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 28 ms 340 KB Output is correct
2 Correct 66 ms 428 KB Output is correct
3 Correct 98 ms 340 KB Output is correct
4 Correct 144 ms 440 KB Output is correct
5 Correct 120 ms 436 KB Output is correct
6 Correct 112 ms 428 KB Output is correct
7 Correct 126 ms 436 KB Output is correct
8 Correct 130 ms 432 KB Output is correct
9 Correct 117 ms 436 KB Output is correct
10 Correct 116 ms 432 KB Output is correct
11 Correct 22 ms 440 KB Output is correct
12 Correct 10 ms 364 KB Output is correct
13 Correct 123 ms 432 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 28 ms 340 KB Output is correct
2 Correct 66 ms 428 KB Output is correct
3 Correct 98 ms 340 KB Output is correct
4 Correct 144 ms 440 KB Output is correct
5 Correct 120 ms 436 KB Output is correct
6 Correct 112 ms 428 KB Output is correct
7 Correct 126 ms 436 KB Output is correct
8 Correct 130 ms 432 KB Output is correct
9 Correct 117 ms 436 KB Output is correct
10 Correct 116 ms 432 KB Output is correct
11 Correct 22 ms 440 KB Output is correct
12 Correct 10 ms 364 KB Output is correct
13 Correct 123 ms 432 KB Output is correct
14 Correct 17 ms 448 KB Output is correct
15 Correct 49 ms 428 KB Output is correct
16 Correct 74 ms 428 KB Output is correct
17 Correct 118 ms 340 KB Output is correct
18 Correct 107 ms 340 KB Output is correct
19 Correct 92 ms 340 KB Output is correct
20 Correct 102 ms 432 KB Output is correct
21 Correct 121 ms 436 KB Output is correct
22 Correct 124 ms 432 KB Output is correct
23 Correct 94 ms 432 KB Output is correct
24 Correct 98 ms 432 KB Output is correct
25 Correct 98 ms 452 KB Output is correct
26 Correct 13 ms 556 KB Output is correct
27 Correct 18 ms 360 KB Output is correct
28 Correct 78 ms 432 KB Output is correct

Subtask #6
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 340 KB Output is correct
2 Correct 9 ms 468 KB Output is correct
3 Correct 8 ms 340 KB Output is correct
4 Correct 9 ms 444 KB Output is correct
5 Correct 10 ms 452 KB Output is correct
6 Correct 9 ms 340 KB Output is correct
7 Correct 9 ms 340 KB Output is correct
8 Correct 9 ms 340 KB Output is correct
9 Correct 9 ms 340 KB Output is correct
10 Correct 28 ms 340 KB Output is correct
11 Correct 66 ms 428 KB Output is correct
12 Correct 98 ms 340 KB Output is correct
13 Correct 144 ms 440 KB Output is correct
14 Correct 120 ms 436 KB Output is correct
15 Correct 112 ms 428 KB Output is correct
16 Correct 126 ms 436 KB Output is correct
17 Correct 130 ms 432 KB Output is correct
18 Correct 117 ms 436 KB Output is correct
19 Correct 116 ms 432 KB Output is correct
20 Correct 22 ms 440 KB Output is correct
21 Correct 10 ms 364 KB Output is correct
22 Correct 123 ms 432 KB Output is correct
23 Correct 17 ms 448 KB Output is correct
24 Correct 49 ms 428 KB Output is correct
25 Correct 74 ms 428 KB Output is correct
26 Correct 118 ms 340 KB Output is correct
27 Correct 107 ms 340 KB Output is correct
28 Correct 92 ms 340 KB Output is correct
29 Correct 102 ms 432 KB Output is correct
30 Correct 121 ms 436 KB Output is correct
31 Correct 124 ms 432 KB Output is correct
32 Correct 94 ms 432 KB Output is correct
33 Correct 98 ms 432 KB Output is correct
34 Correct 98 ms 452 KB Output is correct
35 Correct 13 ms 556 KB Output is correct
36 Correct 18 ms 360 KB Output is correct
37 Correct 78 ms 432 KB Output is correct
38 Correct 10 ms 340 KB Output is correct
39 Correct 9 ms 340 KB Output is correct
40 Correct 9 ms 372 KB Output is correct
41 Correct 9 ms 340 KB Output is correct
42 Correct 9 ms 460 KB Output is correct
43 Correct 10 ms 340 KB Output is correct
44 Correct 11 ms 340 KB Output is correct
45 Correct 137 ms 436 KB Output is correct
46 Correct 115 ms 432 KB Output is correct
47 Correct 10 ms 340 KB Output is correct
48 Correct 9 ms 368 KB Output is correct
49 Correct 8 ms 452 KB Output is correct
50 Correct 9 ms 444 KB Output is correct
51 Correct 10 ms 340 KB Output is correct
52 Correct 44 ms 428 KB Output is correct