Submission #21415

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
21415	2017-04-13T19:25:53 Z	gs14004	비트 (kriii4_Q)	C++11	100 / 100	229 ms	2384 KB

Q

#include <bits/stdc++.h>
using namespace std;
typedef long long lint;
typedef pair<int, int> pi;
const int mod = 1e9 + 7;

lint ipow(lint x, lint p){
	lint ret = 1, piv = x % mod;
	while(p){
		if(p&1) ret *= piv;
		piv *= piv;
		ret %= mod;
		piv %= mod;
		p >>= 1;
	}
	return ret % mod;
}

const int MAXN = 105;
struct matrix{
	lint adj[MAXN][MAXN];
	int n;
	matrix(int _n, int c){
		n = _n;
		for(int i=0; i<n; i++){
			for(int j=0; j<n; j++){
				adj[i][j] = (i == j ? c : 0);
			}
		}
	}
	matrix operator*(const matrix &a)const{
		matrix c(n, 0);
		for(int i=0; i<n; i++){
			for(int j=0; j<n; j++){
				for(int k=0; k<n; k++){
					c.adj[j][k] += adj[j][i] * a.adj[i][k] % mod;
					c.adj[j][k] %= mod;
				}
			}
		}
		return c;
	}
};

int n, k;
vector<lint> basis[102];
lint sol[102];

void solve(){
	for(int i=n-1; i>=0; i--){
		assert(!basis[i].empty());
		for(int j=i+1; j<n; j++){
			sol[i] += mod - sol[j] * basis[i][j] % mod;
			sol[i] %= mod;
		}
		sol[i] *= ipow(basis[i][i], mod - 2);
		sol[i] %= mod;
	}
	for(int i=0; i<n; i++) printf("%lld\n", sol[i]);
}

void insert(vector<lint> v, int x){
	bool ok = 0;
	for(int i=0; i<n; i++){
		if(v[i]){
			if(basis[i].empty()){
				basis[i] = v;
				sol[i] = x;
				ok = 1;
				break;
			}
			else{
				lint w = ipow(basis[i][i], mod - 2) * v[i] % mod;
				for(int j=0; j<n; j++){
					v[j] += mod - w * basis[i][j] % mod;
					v[j] %= mod;
				}
				x += mod - w * sol[i] % mod;
				x %= mod;
			}
		}
	}
	assert(ok);
}

int main(){
	cin >> n >> k;
	matrix ret(n+1, 1), piv(n+1, 0);
	for(int i=0; i<=n; i++){
		if(i < n) piv.adj[i][i+1] = (n - i) * ipow(n, mod-2) % mod;
		if(i > 0) piv.adj[i][i-1] = i * ipow(n, mod-2) % mod;
	}
	for(; k; k>>=1){
		if(k&1) ret = ret * piv;
		piv = piv * piv;
	}
	for(int i=0; i<n; i++){
		vector<lint> rw(n);
		rw[i]++;
		for(int j=0; j<n; j++){
			rw[j] += mod - ret.adj[i+1][j+1];
			rw[j] %= mod;
		}
		insert(rw, 1);
	}
	solve();
}

Subtask #1

9.0 / 9.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	3 ms	2252 KB	Output is correct
2	Correct	6 ms	2380 KB	Output is correct
3	Correct	0 ms	2252 KB	Output is correct
4	Correct	0 ms	2252 KB	Output is correct
5	Correct	6 ms	2384 KB	Output is correct
6	Correct	0 ms	2248 KB	Output is correct
7	Correct	0 ms	2252 KB	Output is correct
8	Correct	3 ms	2380 KB	Output is correct
9	Correct	0 ms	2252 KB	Output is correct
10	Correct	0 ms	2248 KB	Output is correct
11	Correct	0 ms	2248 KB	Output is correct
12	Correct	6 ms	2380 KB	Output is correct
13	Correct	0 ms	2252 KB	Output is correct
14	Correct	6 ms	2252 KB	Output is correct
15	Correct	6 ms	2380 KB	Output is correct
16	Correct	0 ms	2248 KB	Output is correct
17	Correct	3 ms	2244 KB	Output is correct
18	Correct	6 ms	2248 KB	Output is correct
19	Correct	6 ms	2380 KB	Output is correct
20	Correct	0 ms	2248 KB	Output is correct

Subtask #2

91.0 / 91.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	19 ms	2248 KB	Output is correct
2	Correct	159 ms	2384 KB	Output is correct
3	Correct	3 ms	2252 KB	Output is correct
4	Correct	26 ms	2244 KB	Output is correct
5	Correct	119 ms	2380 KB	Output is correct
6	Correct	209 ms	2384 KB	Output is correct
7	Correct	6 ms	2248 KB	Output is correct
8	Correct	43 ms	2248 KB	Output is correct
9	Correct	106 ms	2380 KB	Output is correct
10	Correct	16 ms	2252 KB	Output is correct
11	Correct	66 ms	2244 KB	Output is correct
12	Correct	189 ms	2380 KB	Output is correct
13	Correct	3 ms	2252 KB	Output is correct
14	Correct	26 ms	2252 KB	Output is correct
15	Correct	86 ms	2380 KB	Output is correct
16	Correct	0 ms	2248 KB	Output is correct
17	Correct	9 ms	2252 KB	Output is correct
18	Correct	133 ms	2380 KB	Output is correct
19	Correct	0 ms	2248 KB	Output is correct
20	Correct	229 ms	2380 KB	Output is correct