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Submission #581597

# Submission time Handle Problem Language Result Execution time Memory
581597 2022-06-22T20:14:15 Z penguinhacker Semafor (COI20_semafor) C++17
100 / 100
 207 ms 632 KB 
#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define ar array

const int M=1e9+7;

ll bin_pow(ll b, ll p=M-2) {
	ll r=1;
	for (; p; p/=2, b=b*b%M)
		if (p%2)
			r=r*b%M;
	return r;
}

struct Mat {
	int n, m;
	vector<vector<int>> a;
	Mat() {}
	Mat(int n, int m) : n(n), m(m) {a.assign(n, vector<int>(m));}
	vector<int>& operator[](int i) {return a[i];}
	const vector<int>& operator[](int i) const {return a[i];}
	Mat operator*(const Mat& b) const {
		assert(m==b.n); Mat r(n, b.m);
		for (int i=0; i<n; ++i) for (int j=0; j<m; ++j) for (int k=0; k<b.m; ++k) r[i][k]=(r[i][k]+(ll)a[i][j]*b[j][k])%M;
		return r;
	};
};

Mat mat_pow(Mat b, ll p) {
	assert(b.n==b.m);
	int n=b.n;
	Mat r(n, n);
	for (int i=0; i<n; ++i)
		r[i][i]=1;
	for (; p; p/=2, b=b*b)
		if (p%2)
			r=r*b;
	return r;
}

int m, x, mask1[10], mask2[100];
ll n, k, C[11][11];

void init() {
	mask1[0]=1<<1|1<<3;
	mask1[1]=1<<1;
	mask1[2]=1<<0|1<<3;
	mask1[3]=1<<0|1<<1|1<<2;
	mask1[4]=1<<1|1<<4;
	mask1[5]=1<<0|1<<2|1<<4;
	mask1[6]=1<<2|1<<3;
	mask1[7]=1<<0|1<<1;
	mask1[8]=1<<0|1<<2|1<<3|1<<4;
	mask1[9]=1<<0|1<<1|1<<2|1<<4;
	for (int i=0; i<100; ++i)
		mask2[i]=(mask1[i/10]<<5)|mask1[i%10];
	C[0][0]=1;
	for (int i=1; i<=10; ++i)
		for (int j=0; j<=i; ++j)
			C[i][j]=((j?C[i-1][j-1]:0)+C[i-1][j])%M;
}

vector<int> get_changes(ll d) {
	Mat a(1, 5*m+1), t(5*m+1, 5*m+1);
	a[0][0]=1;
	for (int i=0; i<=5*m; ++i) {
		if (i)
			t[i][i-1]=i;
		if (i+1<=5*m)
			t[i][i+1]=5*m-i;
	}
	a=a*mat_pow(t, d);
	return a[0];
}

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	init();
	cin >> m >> n >> k >> x;
	int dim=m==1?10:100;
	Mat a(1, dim), t(dim, dim);
	a[0][x]=1;
	vector<int> block_changes=get_changes(k);
	for (int i=0; i<dim; ++i)
		for (int j=0; j<dim; ++j) {
			int num1=m==1?mask1[i]:mask2[i];
			int num2=m==1?mask1[j]:mask2[j];
			int dif=__builtin_popcount(num1^num2);
			t[i][j]=(ll)block_changes[dif]*bin_pow(C[5*m][dif])%M;
		}
	a=a*mat_pow(t, n/k);
	vector<int> final_changes=get_changes(n%k);
	vector<ll> ans(dim);
	for (int i=0; i<dim; ++i)
		for (int j=0; j<dim; ++j) {
			int num1=m==1?mask1[i]:mask2[i];
			int num2=m==1?mask1[j]:mask2[j];
			int dif=__builtin_popcount(num1^num2);
			ans[j]=(ans[j]+(ll)a[0][i]*final_changes[dif]%M*bin_pow(C[5*m][dif]))%M;
		}
	for (int i=0; i<dim; ++i)
		cout << ans[i] << "\n";
	return 0;
}

Subtask #1
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 280 KB Output is correct
2 Correct 1 ms 328 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 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 1 ms 280 KB Output is correct
2 Correct 1 ms 328 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 212 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 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 332 KB Output is correct
18 Correct 1 ms 328 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 1 ms 332 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 10 ms 500 KB Output is correct
2 Correct 9 ms 468 KB Output is correct
3 Correct 10 ms 500 KB Output is correct
4 Correct 9 ms 456 KB Output is correct
5 Correct 10 ms 504 KB Output is correct
6 Correct 8 ms 452 KB Output is correct
7 Correct 8 ms 468 KB Output is correct
8 Correct 8 ms 456 KB Output is correct
9 Correct 8 ms 468 KB Output is correct

Subtask #4
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 34 ms 460 KB Output is correct
2 Correct 89 ms 488 KB Output is correct
3 Correct 136 ms 500 KB Output is correct
4 Correct 207 ms 492 KB Output is correct
5 Correct 166 ms 480 KB Output is correct
6 Correct 153 ms 484 KB Output is correct
7 Correct 176 ms 488 KB Output is correct
8 Correct 193 ms 468 KB Output is correct
9 Correct 157 ms 492 KB Output is correct
10 Correct 158 ms 484 KB Output is correct
11 Correct 23 ms 484 KB Output is correct
12 Correct 11 ms 468 KB Output is correct
13 Correct 166 ms 484 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 34 ms 460 KB Output is correct
2 Correct 89 ms 488 KB Output is correct
3 Correct 136 ms 500 KB Output is correct
4 Correct 207 ms 492 KB Output is correct
5 Correct 166 ms 480 KB Output is correct
6 Correct 153 ms 484 KB Output is correct
7 Correct 176 ms 488 KB Output is correct
8 Correct 193 ms 468 KB Output is correct
9 Correct 157 ms 492 KB Output is correct
10 Correct 158 ms 484 KB Output is correct
11 Correct 23 ms 484 KB Output is correct
12 Correct 11 ms 468 KB Output is correct
13 Correct 166 ms 484 KB Output is correct
14 Correct 19 ms 504 KB Output is correct
15 Correct 73 ms 480 KB Output is correct
16 Correct 107 ms 480 KB Output is correct
17 Correct 143 ms 468 KB Output is correct
18 Correct 135 ms 468 KB Output is correct
19 Correct 131 ms 500 KB Output is correct
20 Correct 139 ms 480 KB Output is correct
21 Correct 200 ms 480 KB Output is correct
22 Correct 154 ms 468 KB Output is correct
23 Correct 139 ms 484 KB Output is correct
24 Correct 137 ms 488 KB Output is correct
25 Correct 155 ms 500 KB Output is correct
26 Correct 12 ms 468 KB Output is correct
27 Correct 21 ms 468 KB Output is correct
28 Correct 101 ms 484 KB Output is correct

Subtask #6
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 500 KB Output is correct
2 Correct 9 ms 468 KB Output is correct
3 Correct 10 ms 500 KB Output is correct
4 Correct 9 ms 456 KB Output is correct
5 Correct 10 ms 504 KB Output is correct
6 Correct 8 ms 452 KB Output is correct
7 Correct 8 ms 468 KB Output is correct
8 Correct 8 ms 456 KB Output is correct
9 Correct 8 ms 468 KB Output is correct
10 Correct 34 ms 460 KB Output is correct
11 Correct 89 ms 488 KB Output is correct
12 Correct 136 ms 500 KB Output is correct
13 Correct 207 ms 492 KB Output is correct
14 Correct 166 ms 480 KB Output is correct
15 Correct 153 ms 484 KB Output is correct
16 Correct 176 ms 488 KB Output is correct
17 Correct 193 ms 468 KB Output is correct
18 Correct 157 ms 492 KB Output is correct
19 Correct 158 ms 484 KB Output is correct
20 Correct 23 ms 484 KB Output is correct
21 Correct 11 ms 468 KB Output is correct
22 Correct 166 ms 484 KB Output is correct
23 Correct 19 ms 504 KB Output is correct
24 Correct 73 ms 480 KB Output is correct
25 Correct 107 ms 480 KB Output is correct
26 Correct 143 ms 468 KB Output is correct
27 Correct 135 ms 468 KB Output is correct
28 Correct 131 ms 500 KB Output is correct
29 Correct 139 ms 480 KB Output is correct
30 Correct 200 ms 480 KB Output is correct
31 Correct 154 ms 468 KB Output is correct
32 Correct 139 ms 484 KB Output is correct
33 Correct 137 ms 488 KB Output is correct
34 Correct 155 ms 500 KB Output is correct
35 Correct 12 ms 468 KB Output is correct
36 Correct 21 ms 468 KB Output is correct
37 Correct 101 ms 484 KB Output is correct
38 Correct 10 ms 468 KB Output is correct
39 Correct 8 ms 468 KB Output is correct
40 Correct 8 ms 468 KB Output is correct
41 Correct 9 ms 468 KB Output is correct
42 Correct 9 ms 452 KB Output is correct
43 Correct 9 ms 632 KB Output is correct
44 Correct 11 ms 468 KB Output is correct
45 Correct 166 ms 468 KB Output is correct
46 Correct 160 ms 496 KB Output is correct
47 Correct 11 ms 500 KB Output is correct
48 Correct 8 ms 500 KB Output is correct
49 Correct 9 ms 468 KB Output is correct
50 Correct 8 ms 468 KB Output is correct
51 Correct 8 ms 468 KB Output is correct
52 Correct 54 ms 488 KB Output is correct