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Submission #879582

# Submission time Handle Problem Language Result Execution time Memory
879582 2023-11-27T16:36:05 Z Shayan86 Star Trek (CEOI20_startrek) C++17
100 / 100
 68 ms 18772 KB 
#include <bits/stdc++.h>
using namespace std;

#pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
// Ofast, O0, O1, O2, O3, unroll-loops, fast-math, trapv

typedef long long ll;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;

#define Mp          make_pair
#define sep         ' '
#define endl        '\n'
#define F	        first
#define S	        second
#define pb          push_back
#define all(x)      (x).begin(),(x).end()
#define kill(res)	cout << res << '\n', exit(0);
#define set_dec(x)	cout << fixed << setprecision(x);
#define fast_io     ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define file_io     freopen("input.txt", "r", stdin) ; freopen("output.txt", "w", stdout);

const ll MT = 2;
const ll N = 1e5 + 50;
const ll Mod = 1e9 + 7;

ll n, d;

struct shet{
    int col = 0, s0 = 0, s1 = 0, t0 = 0, cnt = 1;
};

ll calcute(shet a){
    if(a.t0 >= 2) return 0;
    if(a.t0 == 1) return a.s0;
    return a.s1 + 1;
}

shet add(shet a, shet b){
    if(b.col){
        a.s1 += b.cnt; a.cnt = calcute(a);
    }
    else{
        a.t0++; a.s0 += b.cnt; a.col |= 1; a.cnt = calcute(a);
    }
    return a;
}

shet del(shet a, shet b){
    if(b.col){
        a.s1 -= b.cnt; a.cnt = calcute(a);
    }
    else{
        a.t0--; a.s0 -= b.cnt; a.cnt = calcute(a);
        if(!a.t0) a.col = 0;
    }
    return a;
}

shet val[N], rval[N];

vector<int> adj[N];

ll mod(ll a, ll b = Mod){
    return (a%b+b)%b;
}

struct matrix{
    ll n, m, a[MT][MT];
    matrix(int n_, int m_, int x = 0){
        n = n_; m = m_;
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                a[i][j] = x;
    }
    matrix operator * (const matrix &t){
        matrix r = matrix(n, t.m);
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                for(int k = 0; k < t.m; k++)
                    r.a[i][k] = mod(r.a[i][k] + mod(a[i][j] * t.a[j][k]));
        return r;
    }
};

matrix Pow(matrix a, ll b){
    matrix ans = matrix(a.n, a.m);
    for(int i = 0; i < MT; i++) ans.a[i][i] = 1;

	for(; b; b /= 2, a = a * a){
        if(b % 2) ans = ans * a;
	}
	return ans;
}

ll power(ll a, ll b, ll md = Mod){
    ll ans = 1;
    for(; b; b /= 2, a = a * a % md){
        if(b % 2) ans = ans * a % md;
    }
    return ans;
}

void dfs(int v, int p = 0){
    for(int u: adj[v]){
        if(u == p) continue;
        dfs(u, v);
        val[v] = add(val[v], val[u]);
    }
}

void cal(int v, int p = 0){
    rval[v] = val[v];
    for(int u: adj[v]){
        if(u == p) continue;
        val[v] = del(val[v], val[u]);
        val[u] = add(val[u], val[v]);
        cal(u, v);
        val[u] = del(val[u], val[v]);
        val[v] = add(val[v], val[u]);
    }
}

int main(){
    fast_io;

    cin >> n >> d; d++;

    int u, v;
    for(int i = 1; i < n; i++){
        cin >> u >> v;
        adj[u].pb(v);
        adj[v].pb(u);
    }

    dfs(1); cal(1);

    //for(int i = 1; i <= n; i++) cout << rval[i].col << sep << rval[i].cnt << sep << rval[i].t0 << endl;

    ll sum0 = 0, sum1 = 0, cnt0 = 0;
    for(int i = 1; i <= n; i++){
        if(rval[i].col) sum1 = mod(sum1 + rval[i].cnt);
        else sum0 = mod(sum0 + rval[i].cnt);
        if(!rval[i].col) cnt0++;
    }

    matrix m = matrix(2, 2);
    m.a[0][0] = mod(sum1 - sum0); m.a[0][1] = cnt0;
    m.a[1][0] = 0; m.a[1][1] = n*n%Mod;

    matrix ans = matrix(2, 1);
    ans.a[0][0] = 0; ans.a[1][0] = 1;

    ans = Pow(m, d-1) * ans;

    ll res = mod(rval[1].cnt * ans.a[0][0]);

    if(!rval[1].col) kill(res);
    res = mod(power(n*n%Mod, d-1) - res);
    kill(res);

}

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB Output is correct
2 Correct 2 ms 2652 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2652 KB Output is correct
2 Correct 1 ms 2652 KB Output is correct
3 Correct 1 ms 2652 KB Output is correct
4 Correct 2 ms 2800 KB Output is correct
5 Correct 2 ms 2908 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB Output is correct
2 Correct 1 ms 2808 KB Output is correct
3 Correct 1 ms 2652 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 2 ms 2652 KB Output is correct
6 Correct 2 ms 2816 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB Output is correct
2 Correct 1 ms 2808 KB Output is correct
3 Correct 1 ms 2652 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 2 ms 2652 KB Output is correct
6 Correct 2 ms 2816 KB Output is correct
7 Correct 2 ms 2816 KB Output is correct
8 Correct 2 ms 2908 KB Output is correct
9 Correct 1 ms 2648 KB Output is correct
10 Correct 2 ms 2732 KB Output is correct
11 Correct 2 ms 2828 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB Output is correct
2 Correct 1 ms 2808 KB Output is correct
3 Correct 1 ms 2652 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 2 ms 2652 KB Output is correct
6 Correct 2 ms 2816 KB Output is correct
7 Correct 2 ms 2816 KB Output is correct
8 Correct 2 ms 2908 KB Output is correct
9 Correct 1 ms 2648 KB Output is correct
10 Correct 2 ms 2732 KB Output is correct
11 Correct 2 ms 2828 KB Output is correct
12 Correct 62 ms 14380 KB Output is correct
13 Correct 55 ms 18576 KB Output is correct
14 Correct 48 ms 11012 KB Output is correct
15 Correct 63 ms 10956 KB Output is correct
16 Correct 51 ms 11044 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB Output is correct
2 Correct 1 ms 2808 KB Output is correct
3 Correct 1 ms 2652 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 2 ms 2652 KB Output is correct
6 Correct 2 ms 2816 KB Output is correct
7 Correct 2 ms 2816 KB Output is correct
8 Correct 2 ms 2908 KB Output is correct
9 Correct 1 ms 2648 KB Output is correct
10 Correct 2 ms 2732 KB Output is correct
11 Correct 2 ms 2828 KB Output is correct
12 Correct 2 ms 2660 KB Output is correct
13 Correct 2 ms 2652 KB Output is correct
14 Correct 1 ms 2652 KB Output is correct
15 Correct 1 ms 2812 KB Output is correct
16 Correct 2 ms 2908 KB Output is correct
17 Correct 2 ms 2652 KB Output is correct
18 Correct 2 ms 2652 KB Output is correct
19 Correct 1 ms 2812 KB Output is correct
20 Correct 1 ms 2624 KB Output is correct
21 Correct 2 ms 2904 KB Output is correct
22 Correct 2 ms 2908 KB Output is correct
23 Correct 2 ms 2652 KB Output is correct
24 Correct 2 ms 2652 KB Output is correct
25 Correct 2 ms 2652 KB Output is correct
26 Correct 2 ms 2908 KB Output is correct
27 Correct 2 ms 2908 KB Output is correct
28 Correct 2 ms 2652 KB Output is correct
29 Correct 2 ms 2652 KB Output is correct
30 Correct 2 ms 2652 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB Output is correct
2 Correct 1 ms 2808 KB Output is correct
3 Correct 1 ms 2652 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 2 ms 2652 KB Output is correct
6 Correct 2 ms 2816 KB Output is correct
7 Correct 2 ms 2816 KB Output is correct
8 Correct 2 ms 2908 KB Output is correct
9 Correct 1 ms 2648 KB Output is correct
10 Correct 2 ms 2732 KB Output is correct
11 Correct 2 ms 2828 KB Output is correct
12 Correct 62 ms 14380 KB Output is correct
13 Correct 55 ms 18576 KB Output is correct
14 Correct 48 ms 11012 KB Output is correct
15 Correct 63 ms 10956 KB Output is correct
16 Correct 51 ms 11044 KB Output is correct
17 Correct 2 ms 2660 KB Output is correct
18 Correct 2 ms 2652 KB Output is correct
19 Correct 1 ms 2652 KB Output is correct
20 Correct 1 ms 2812 KB Output is correct
21 Correct 2 ms 2908 KB Output is correct
22 Correct 2 ms 2652 KB Output is correct
23 Correct 2 ms 2652 KB Output is correct
24 Correct 1 ms 2812 KB Output is correct
25 Correct 1 ms 2624 KB Output is correct
26 Correct 2 ms 2904 KB Output is correct
27 Correct 2 ms 2908 KB Output is correct
28 Correct 2 ms 2652 KB Output is correct
29 Correct 2 ms 2652 KB Output is correct
30 Correct 2 ms 2652 KB Output is correct
31 Correct 2 ms 2908 KB Output is correct
32 Correct 2 ms 2908 KB Output is correct
33 Correct 2 ms 2652 KB Output is correct
34 Correct 2 ms 2652 KB Output is correct
35 Correct 2 ms 2652 KB Output is correct
36 Correct 46 ms 14468 KB Output is correct
37 Correct 56 ms 18772 KB Output is correct
38 Correct 43 ms 10848 KB Output is correct
39 Correct 58 ms 11032 KB Output is correct
40 Correct 33 ms 11020 KB Output is correct
41 Correct 56 ms 16556 KB Output is correct
42 Correct 45 ms 17236 KB Output is correct
43 Correct 23 ms 9972 KB Output is correct
44 Correct 43 ms 11044 KB Output is correct
45 Correct 55 ms 10896 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB Output is correct
2 Correct 2 ms 2652 KB Output is correct
3 Correct 2 ms 2652 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 1 ms 2652 KB Output is correct
6 Correct 2 ms 2800 KB Output is correct
7 Correct 2 ms 2908 KB Output is correct
8 Correct 1 ms 2652 KB Output is correct
9 Correct 1 ms 2808 KB Output is correct
10 Correct 1 ms 2652 KB Output is correct
11 Correct 1 ms 2652 KB Output is correct
12 Correct 2 ms 2652 KB Output is correct
13 Correct 2 ms 2816 KB Output is correct
14 Correct 2 ms 2816 KB Output is correct
15 Correct 2 ms 2908 KB Output is correct
16 Correct 1 ms 2648 KB Output is correct
17 Correct 2 ms 2732 KB Output is correct
18 Correct 2 ms 2828 KB Output is correct
19 Correct 62 ms 14380 KB Output is correct
20 Correct 55 ms 18576 KB Output is correct
21 Correct 48 ms 11012 KB Output is correct
22 Correct 63 ms 10956 KB Output is correct
23 Correct 51 ms 11044 KB Output is correct
24 Correct 2 ms 2660 KB Output is correct
25 Correct 2 ms 2652 KB Output is correct
26 Correct 1 ms 2652 KB Output is correct
27 Correct 1 ms 2812 KB Output is correct
28 Correct 2 ms 2908 KB Output is correct
29 Correct 2 ms 2652 KB Output is correct
30 Correct 2 ms 2652 KB Output is correct
31 Correct 1 ms 2812 KB Output is correct
32 Correct 1 ms 2624 KB Output is correct
33 Correct 2 ms 2904 KB Output is correct
34 Correct 2 ms 2908 KB Output is correct
35 Correct 2 ms 2652 KB Output is correct
36 Correct 2 ms 2652 KB Output is correct
37 Correct 2 ms 2652 KB Output is correct
38 Correct 2 ms 2908 KB Output is correct
39 Correct 2 ms 2908 KB Output is correct
40 Correct 2 ms 2652 KB Output is correct
41 Correct 2 ms 2652 KB Output is correct
42 Correct 2 ms 2652 KB Output is correct
43 Correct 46 ms 14468 KB Output is correct
44 Correct 56 ms 18772 KB Output is correct
45 Correct 43 ms 10848 KB Output is correct
46 Correct 58 ms 11032 KB Output is correct
47 Correct 33 ms 11020 KB Output is correct
48 Correct 56 ms 16556 KB Output is correct
49 Correct 45 ms 17236 KB Output is correct
50 Correct 23 ms 9972 KB Output is correct
51 Correct 43 ms 11044 KB Output is correct
52 Correct 55 ms 10896 KB Output is correct
53 Correct 68 ms 18668 KB Output is correct
54 Correct 51 ms 16984 KB Output is correct
55 Correct 32 ms 9144 KB Output is correct
56 Correct 55 ms 14428 KB Output is correct
57 Correct 50 ms 11104 KB Output is correct
58 Correct 34 ms 11136 KB Output is correct
59 Correct 34 ms 10836 KB Output is correct
60 Correct 34 ms 10844 KB Output is correct