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Submission #987369

# Submission time Handle Problem Language Result Execution time Memory
987369 2024-05-22T16:26:43 Z alexdd Semafor (COI20_semafor) C++17
100 / 100
 292 ms 1880 KB 
#include<iostream>
#include<map>
using namespace std;
#define int long long
const long long MOD = 1e9+7;
int DIM;
struct matrix
{
    int v[105][105];
};
matrix inm(matrix x, matrix y)
{
    matrix aux;
    for(int i=0;i<DIM;i++)
    {
        for(int j=0;j<DIM;j++)
        {
            aux.v[i][j]=0;
            for(int k=0;k<DIM;k++)
            {
                aux.v[i][j] += 1LL*x.v[i][k] * y.v[k][j]%MOD;
                aux.v[i][j]%=MOD;
            }
        }
    }
    return aux;
}
matrix unu;
matrix put(matrix a, int exp)
{
    matrix aux=unu;
    while(exp>0)
    {
        if(exp%2==1) aux = inm(aux,a);
        a = inm(a,a);
        exp/=2;
    }
    return aux;
}
int m;
map<pair<int,int>,pair<int,bool>> mp;
long long put_nr(long long a, int exp)
{
    if(exp==0)
        return 1;
    if(exp%2==0)
        return put_nr(a*a%MOD,exp/2);
    else
        return put_nr(a*a%MOD,exp/2)*a%MOD;
}
long long fact[3005],invf[3005];
long long comb(int x, int y)
{
    if(x<y)
        return 0;
    return ((((fact[x]*invf[y])%MOD)*invf[x-y])%MOD);
}
matrix dp;
int calc(int cnt1, int k)
{
    if(k%2!=cnt1%2)
        return 0;
    DIM=11;
    for(int i=0;i<11;i++)
        for(int j=0;j<11;j++)
            dp.v[i][j]=0;
    for(int cur=0;cur<=m*5;cur++)
    {
        if(cur>0) dp.v[cur][cur-1] = m*5-(cur-1);
        if(cur<10) dp.v[cur][cur+1] = cur+1;
    }
    dp = put(dp,k);
    DIM=100;
    return dp.v[cnt1][0] * put_nr(comb(m*5,cnt1),MOD-2)%MOD;
}
int getmp(int config, int k)
{
    int cnt1=0;
    for(int i=0;i<10;i++)
        if(((1<<i)&config))
            cnt1++;
    if(mp[{cnt1,k}].second==0)
    {
        mp[{cnt1,k}]={calc(cnt1,k),1};
    }
    return mp[{cnt1,k}].first;
}
int mask[100];
matrix calc_matrix(int k)
{
    matrix aux;
    for(int i=0;i<100;i++)
    {
        for(int j=0;j<100;j++)
        {
            if(m==1 && (i>9 || j>9)) aux.v[i][j]=0;
            else aux.v[i][j] = getmp((mask[i]^mask[j]),k);
        }
    }
    return aux;
}
void calc_mask()
{
    mask[0] = (1<<1) + (1<<3);
    mask[1] = (1<<1);
    mask[2] = (1<<0) + (1<<3);
    mask[3] = (1<<0) + (1<<1) + (1<<2);
    mask[4] = (1<<1) + (1<<4);
    mask[5] = (1<<0) + (1<<2) + (1<<4);
    mask[6] = (1<<2) + (1<<3);
    mask[7] = (1<<0) + (1<<1);
    mask[8] = (1<<0) + (1<<2) + (1<<3) + (1<<4);
    mask[9] = (1<<0) + (1<<1) + (1<<2) + (1<<4);
    for(int i=10;i<100;i++)
    {
        mask[i] = (mask[i/10]<<5) + mask[i%10];
    }
    for(int i=9;i>=0;i--)
        mask[i] += (mask[0]<<5);
}
signed main()
{
    DIM=100;
    for(int i=0;i<100;i++)
        for(int j=0;j<100;j++)
            unu.v[i][j]=0;
    for(int i=0;i<100;i++)
        unu.v[i][i]=1;

    fact[0]=1;
    for(int i=1;i<=3000;i++)
        fact[i]=fact[i-1]*i%MOD;
    invf[3000]=put_nr(fact[3000],MOD-2);
    for(int i=2999;i>=0;i--)
        invf[i]=invf[i+1]*(i+1)%MOD;

    int n,k,x;
    cin>>m>>n>>k>>x;
    calc_mask();
    matrix km = calc_matrix(k);
    matrix rm = calc_matrix(n%k);
    matrix rez=unu;
    if(n/k > 0) rez = inm(rez,put(km,n/k));
    if(n%k > 0) rez = inm(rez,rm);

    for(int i=0;i<100;i++)
    {
        if(m==1 && i>9)
            break;
        cout<<rez.v[x][i]<<"\n";
    }
    return 0;
}

Subtask #1
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 1624 KB Output is correct
2 Correct 21 ms 1624 KB Output is correct
3 Correct 17 ms 1688 KB Output is correct
4 Correct 13 ms 1692 KB Output is correct
5 Correct 17 ms 1628 KB Output is correct
6 Correct 13 ms 1880 KB Output is correct
7 Correct 24 ms 1688 KB Output is correct
8 Correct 28 ms 1624 KB Output is correct
9 Correct 16 ms 1628 KB Output is correct
10 Correct 24 ms 1624 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 1624 KB Output is correct
2 Correct 21 ms 1624 KB Output is correct
3 Correct 17 ms 1688 KB Output is correct
4 Correct 13 ms 1692 KB Output is correct
5 Correct 17 ms 1628 KB Output is correct
6 Correct 13 ms 1880 KB Output is correct
7 Correct 24 ms 1688 KB Output is correct
8 Correct 28 ms 1624 KB Output is correct
9 Correct 16 ms 1628 KB Output is correct
10 Correct 24 ms 1624 KB Output is correct
11 Correct 21 ms 1628 KB Output is correct
12 Correct 45 ms 1628 KB Output is correct
13 Correct 27 ms 1628 KB Output is correct
14 Correct 25 ms 1628 KB Output is correct
15 Correct 21 ms 1628 KB Output is correct
16 Correct 28 ms 1624 KB Output is correct
17 Correct 24 ms 1624 KB Output is correct
18 Correct 267 ms 1624 KB Output is correct
19 Correct 272 ms 1624 KB Output is correct
20 Correct 21 ms 1628 KB Output is correct
21 Correct 19 ms 1624 KB Output is correct
22 Correct 15 ms 1692 KB Output is correct

Subtask #3
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 1712 KB Output is correct
2 Correct 14 ms 1628 KB Output is correct
3 Correct 14 ms 1624 KB Output is correct
4 Correct 14 ms 1628 KB Output is correct
5 Correct 14 ms 1684 KB Output is correct
6 Correct 14 ms 1628 KB Output is correct
7 Correct 14 ms 1628 KB Output is correct
8 Correct 14 ms 1624 KB Output is correct
9 Correct 14 ms 1628 KB Output is correct

Subtask #4
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 65 ms 1664 KB Output is correct
2 Correct 148 ms 1664 KB Output is correct
3 Correct 228 ms 1684 KB Output is correct
4 Correct 292 ms 1668 KB Output is correct
5 Correct 277 ms 1872 KB Output is correct
6 Correct 264 ms 1628 KB Output is correct
7 Correct 284 ms 1628 KB Output is correct
8 Correct 267 ms 1624 KB Output is correct
9 Correct 267 ms 1628 KB Output is correct
10 Correct 270 ms 1672 KB Output is correct
11 Correct 36 ms 1628 KB Output is correct
12 Correct 17 ms 1700 KB Output is correct
13 Correct 278 ms 1628 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 65 ms 1664 KB Output is correct
2 Correct 148 ms 1664 KB Output is correct
3 Correct 228 ms 1684 KB Output is correct
4 Correct 292 ms 1668 KB Output is correct
5 Correct 277 ms 1872 KB Output is correct
6 Correct 264 ms 1628 KB Output is correct
7 Correct 284 ms 1628 KB Output is correct
8 Correct 267 ms 1624 KB Output is correct
9 Correct 267 ms 1628 KB Output is correct
10 Correct 270 ms 1672 KB Output is correct
11 Correct 36 ms 1628 KB Output is correct
12 Correct 17 ms 1700 KB Output is correct
13 Correct 278 ms 1628 KB Output is correct
14 Correct 37 ms 1624 KB Output is correct
15 Correct 116 ms 1672 KB Output is correct
16 Correct 172 ms 1668 KB Output is correct
17 Correct 224 ms 1628 KB Output is correct
18 Correct 243 ms 1664 KB Output is correct
19 Correct 210 ms 1672 KB Output is correct
20 Correct 244 ms 1684 KB Output is correct
21 Correct 267 ms 1624 KB Output is correct
22 Correct 274 ms 1624 KB Output is correct
23 Correct 223 ms 1664 KB Output is correct
24 Correct 234 ms 1668 KB Output is correct
25 Correct 232 ms 1872 KB Output is correct
26 Correct 25 ms 1824 KB Output is correct
27 Correct 32 ms 1628 KB Output is correct
28 Correct 175 ms 1624 KB Output is correct

Subtask #6
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 14 ms 1712 KB Output is correct
2 Correct 14 ms 1628 KB Output is correct
3 Correct 14 ms 1624 KB Output is correct
4 Correct 14 ms 1628 KB Output is correct
5 Correct 14 ms 1684 KB Output is correct
6 Correct 14 ms 1628 KB Output is correct
7 Correct 14 ms 1628 KB Output is correct
8 Correct 14 ms 1624 KB Output is correct
9 Correct 14 ms 1628 KB Output is correct
10 Correct 65 ms 1664 KB Output is correct
11 Correct 148 ms 1664 KB Output is correct
12 Correct 228 ms 1684 KB Output is correct
13 Correct 292 ms 1668 KB Output is correct
14 Correct 277 ms 1872 KB Output is correct
15 Correct 264 ms 1628 KB Output is correct
16 Correct 284 ms 1628 KB Output is correct
17 Correct 267 ms 1624 KB Output is correct
18 Correct 267 ms 1628 KB Output is correct
19 Correct 270 ms 1672 KB Output is correct
20 Correct 36 ms 1628 KB Output is correct
21 Correct 17 ms 1700 KB Output is correct
22 Correct 278 ms 1628 KB Output is correct
23 Correct 37 ms 1624 KB Output is correct
24 Correct 116 ms 1672 KB Output is correct
25 Correct 172 ms 1668 KB Output is correct
26 Correct 224 ms 1628 KB Output is correct
27 Correct 243 ms 1664 KB Output is correct
28 Correct 210 ms 1672 KB Output is correct
29 Correct 244 ms 1684 KB Output is correct
30 Correct 267 ms 1624 KB Output is correct
31 Correct 274 ms 1624 KB Output is correct
32 Correct 223 ms 1664 KB Output is correct
33 Correct 234 ms 1668 KB Output is correct
34 Correct 232 ms 1872 KB Output is correct
35 Correct 25 ms 1824 KB Output is correct
36 Correct 32 ms 1628 KB Output is correct
37 Correct 175 ms 1624 KB Output is correct
38 Correct 23 ms 1628 KB Output is correct
39 Correct 23 ms 1624 KB Output is correct
40 Correct 24 ms 1628 KB Output is correct
41 Correct 24 ms 1624 KB Output is correct
42 Correct 25 ms 1624 KB Output is correct
43 Correct 26 ms 1516 KB Output is correct
44 Correct 25 ms 1880 KB Output is correct
45 Correct 266 ms 1624 KB Output is correct
46 Correct 260 ms 1628 KB Output is correct
47 Correct 28 ms 1628 KB Output is correct
48 Correct 24 ms 1628 KB Output is correct
49 Correct 17 ms 1628 KB Output is correct
50 Correct 14 ms 1628 KB Output is correct
51 Correct 18 ms 1628 KB Output is correct
52 Correct 95 ms 1672 KB Output is correct