Submission #412837

#	Time	Username	Problem	Language	Result	Execution time	Memory
412837		couplefire	Semafor (COI20_semafor)	C++17	100 / 100	258 ms	836 KiB

semafor

#include <bits/stdc++.h>
using namespace std;
#define int long long

const int MOD = 1000000007;

inline int add(int a, int b){return (a+b>=MOD)?a+b-MOD:a+b;}
inline void inc(int& a, int b){a = add(a, b);}
inline int sub(int a, int b){return (a-b<0)?a-b+MOD:a-b;}
inline void dec(int &a, int b){a = sub(a, b);}
inline int mul(int a, int b){return 1ll*a*b%MOD;}
inline void grow(int &a, int b){a = mul(a, b);}

int bpow(int a, int b){
    int res = 1;
    while(b > 0){
        if(b&1) grow(res, a);
        grow(a, a);
        b >>= 1;
    }
    return res;
}

int inv(int a){return bpow(a, MOD-2);}

struct Matrix{
    int n, m;
    vector<vector<int>> mat;
    Matrix(){}
    Matrix(int _n, int _m){
        n = _n, m = _m;
        mat.assign(n, vector<int>(m, 0));
    }
    void setID(){
        assert(n == m);
        for(int i = 0; i<n; i++)
            mat[i][i] = 1;
    }
    Matrix operator * (const Matrix &o) const{
        Matrix res(n, o.m);
        for(int i = 0; i<n; i++)
            for(int j = 0; j<o.m; j++)
                for(int k = 0; k<m; k++)
                    inc(res.mat[i][j], mul(mat[i][k], o.mat[k][j]));
        return res; 
    }
};

Matrix matpow(Matrix a, int b){
    assert(a.n == a.m);
    Matrix res(a.n, a.n); res.setID();
    while(b > 0){
        if(b&1) res = res*a;
        a = a*a;
        b >>= 1;
    }
    return res;
}

int n_mask[10] = {10, 2, 9, 7, 18, 21, 12, 3, 29, 23};

int m, n, k, x;
Matrix help, g, tmp_help;
int comb[15][15];
Matrix trans, ans, tmp_trans;

void solveHelp(int siz){
    help = Matrix(1, siz+1);
    help.mat[0][0] = 1;
    g = Matrix(siz+1, siz+1);
    for(int i = 0; i<siz; i++)
        g.mat[i][i+1] = mul(mul(comb[siz][i], siz-i), inv(comb[siz][i+1])),
        g.mat[i+1][i] = mul(mul(comb[siz][i+1], i+1), inv(comb[siz][i]));
    tmp_help = help*matpow(g, n%k);
    help = help*matpow(g, k);
}

signed main(){
    // freopen("a.in", "r", stdin);
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cin >> m >> n >> k >> x;
    comb[0][0] = 1;
    for(int i = 1; i<=10; i++){
        comb[i][0] = comb[i][i] = 1;
        for(int j = 1; j<i; j++)
            comb[i][j] = add(comb[i-1][j-1], comb[i-1][j]);
    }
    solveHelp(m*5);
    if(m == 1){
        trans = Matrix(10, 10);
        tmp_trans = Matrix(10, 10);
        ans = Matrix(1, 10);
        for(int i = 0; i<10; i++)
            for(int j = 0; j<10; j++)
                trans.mat[i][j] = help.mat[0][__builtin_popcount(n_mask[i]^n_mask[j])],
                tmp_trans.mat[i][j] = tmp_help.mat[0][__builtin_popcount(n_mask[i]^n_mask[j])];
        ans.mat[0][x] = 1;
        ans = ans*matpow(trans, n/k);
        ans = ans*tmp_trans;
        for(int i = 0; i<10; i++)
            cout << ans.mat[0][i] << '\n';
    } else{
        trans = Matrix(100, 100);
        tmp_trans = Matrix(100, 100);
        ans = Matrix(1, 100);
        for(int a = 0; a<10; a++)
            for(int b = 0; b<10; b++)
                for(int c = 0; c<10; c++)
                    for(int d = 0; d<10; d++)
                        trans.mat[a+10*b][c+10*d] = 
                        help.mat[0][__builtin_popcount(n_mask[a]^n_mask[c])+__builtin_popcount(n_mask[b]^n_mask[d])],
                        tmp_trans.mat[a+10*b][c+10*d] = 
                        tmp_help.mat[0][__builtin_popcount(n_mask[a]^n_mask[c])+__builtin_popcount(n_mask[b]^n_mask[d])];
        ans.mat[0][x] = 1;
        ans = ans*matpow(trans, n/k);
        ans = ans*tmp_trans;
        for(int i = 0; i<100; i++)
            cout << ans.mat[0][i] << '\n';
    }
}

• Subtask 1: 6 / 6
• Subtask 2: 15 / 15
• Subtask 3: 12 / 12
• Subtask 4: 12 / 12
• Subtask 5: 15 / 15
• Subtask 6: 40 / 40