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Submission #289501

# Submission time Handle Problem Language Result Execution time Memory
289501 2020-09-02T17:18:10 Z model_code Star Trek (CEOI20_startrek) C++17
100 / 100
 117 ms 13880 KB 
#include <iostream>
#include <vector>

using namespace std;

/*
Note that this is an O(N+logD) solution

Made for you by Mate Busa
*/

const long long mod = 1000000007;
long long N, D, a, b, L, W, LC, WC, sL, sW, sLC, sWC;
vector<int> neighbour[100000];
bool lose[100000];
bool visited[100000];
long long c[100000];
long long oW[100000];
long long oL[100000];
long long h[100000];

//calculate the state for all roots
void dfs(int x){
    visited[x] = true; lose[x] = true;
    for(int i:neighbour[x]){
        if(!visited[i]){
            dfs(i);
            if(lose[i]) h[x]++;
        }
    }
    if(h[x]!=0) lose[x] = false;
}
void critical(int x){
    if(lose[x]){
        c[x] = oW[x] + 1;
    } else {
        if(h[x]==1){
            c[x] = oL[x];
        } else {
            c[x] = 0;
        }
    }
}
//calculate critical states
void dfs2(int x){
    visited[x] = true;
    for(int i:neighbour[x]){
        if(!visited[i]){
            dfs2(i);
            if(lose[i]){
                oL[x] += c[i];
            } else {
                oW[x] += c[i];
            }
        }
    }
    critical(x);
}
//reroot the tree in a neighbour
void reroot(int x, int y){
    if(lose[y]){
        h[x]--; oL[x] -= c[y];
    } else {
        oW[x] -= c[y];
    }
    if(h[x]==0) lose[x] = true;
    critical(x);
    if(lose[x]){
        h[y]++; oL[y] += c[x];
    } else {
        oW[y] += c[x];
    }
    if(h[y]!=0) lose[y] = false;
    critical(y);
}
void evaluate(int x){
    visited[x] = true;
    if(lose[x]){
        L++; LC = (LC+c[x])%mod;
    } else {
        W++; WC = (WC+c[x])%mod;
    }
    for(int i:neighbour[x]){
        if(!visited[i]){
            reroot(x,i);
            evaluate(i);
            reroot(i,x);
        }
    }
}

//a bonus dimension
void step(long long pl, long long plc, long long pw, long long pwc){
    sL = ((((pl * N) % mod) * W) % mod + (pwc * L) % mod + ((((pl * N)%mod - plc + mod)%mod) * L)%mod) % mod;
    sLC = (plc * WC + pwc * LC) % mod;
    sW = ((((pw * N) % mod) * W) % mod + (plc * L) % mod + ((((pw * N)%mod - pwc + mod)%mod) * L)%mod) % mod;
    sWC = (pwc * WC + plc * LC) % mod;
}
//double up the number of dimensions
void step2(long long pl, long long plc, long long pw, long long pwc){
    L = ((((pl * N) % mod) * pw) % mod + (pwc * pl) % mod + ((((pl * N)%mod - plc + mod)%mod) * pl)%mod) % mod;
    LC = (plc * pwc + pwc * plc) % mod;
    W = ((((pw * N) % mod) * pw) % mod + (plc * pl) % mod + ((((pw * N)%mod - pwc + mod)%mod) * pl)%mod) % mod;
    WC = (pwc * pwc + plc * plc) % mod;
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);

    cin >> N >> D;
    for(int i=0; i<N-1; i++){
        cin >> a >> b;
        neighbour[a-1].push_back(b-1);
        neighbour[b-1].push_back(a-1);
    }

    dfs(0);
    for(int i=0; i<N; i++) visited[i] = false;
    dfs2(0);
    for(int i=0; i<N; i++) visited[i] = false;
    evaluate(0);

    if(lose[0]){
        sL = 1; sLC = c[0];
    } else {
        sW = 1; sWC = c[0];
    }

    //use binary representation of D
    while(D>0){
        if(D%2==1) step(sL, sLC, sW, sWC);
        step2(L,LC,W,WC); D /= 2;
    }

    cout << sW << '\n';

    return 0;
}

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2816 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2688 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2688 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2688 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2688 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct
6 Correct 2 ms 2688 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2688 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2688 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct
6 Correct 2 ms 2688 KB Output is correct
7 Correct 2 ms 2816 KB Output is correct
8 Correct 2 ms 2816 KB Output is correct
9 Correct 2 ms 2816 KB Output is correct
10 Correct 3 ms 2816 KB Output is correct
11 Correct 2 ms 2816 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2688 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2688 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct
6 Correct 2 ms 2688 KB Output is correct
7 Correct 2 ms 2816 KB Output is correct
8 Correct 2 ms 2816 KB Output is correct
9 Correct 2 ms 2816 KB Output is correct
10 Correct 3 ms 2816 KB Output is correct
11 Correct 2 ms 2816 KB Output is correct
12 Correct 94 ms 11352 KB Output is correct
13 Correct 100 ms 13880 KB Output is correct
14 Correct 78 ms 9332 KB Output is correct
15 Correct 111 ms 9208 KB Output is correct
16 Correct 106 ms 9208 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2688 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2688 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct
6 Correct 2 ms 2688 KB Output is correct
7 Correct 2 ms 2816 KB Output is correct
8 Correct 2 ms 2816 KB Output is correct
9 Correct 2 ms 2816 KB Output is correct
10 Correct 3 ms 2816 KB Output is correct
11 Correct 2 ms 2816 KB Output is correct
12 Correct 2 ms 2688 KB Output is correct
13 Correct 2 ms 2816 KB Output is correct
14 Correct 2 ms 2688 KB Output is correct
15 Correct 2 ms 2688 KB Output is correct
16 Correct 2 ms 2688 KB Output is correct
17 Correct 2 ms 2688 KB Output is correct
18 Correct 2 ms 2688 KB Output is correct
19 Correct 2 ms 2688 KB Output is correct
20 Correct 2 ms 2688 KB Output is correct
21 Correct 2 ms 2816 KB Output is correct
22 Correct 3 ms 2816 KB Output is correct
23 Correct 2 ms 2816 KB Output is correct
24 Correct 2 ms 2816 KB Output is correct
25 Correct 2 ms 2816 KB Output is correct
26 Correct 2 ms 2816 KB Output is correct
27 Correct 2 ms 2816 KB Output is correct
28 Correct 2 ms 2816 KB Output is correct
29 Correct 2 ms 2816 KB Output is correct
30 Correct 2 ms 2816 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2688 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2688 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct
6 Correct 2 ms 2688 KB Output is correct
7 Correct 2 ms 2816 KB Output is correct
8 Correct 2 ms 2816 KB Output is correct
9 Correct 2 ms 2816 KB Output is correct
10 Correct 3 ms 2816 KB Output is correct
11 Correct 2 ms 2816 KB Output is correct
12 Correct 94 ms 11352 KB Output is correct
13 Correct 100 ms 13880 KB Output is correct
14 Correct 78 ms 9332 KB Output is correct
15 Correct 111 ms 9208 KB Output is correct
16 Correct 106 ms 9208 KB Output is correct
17 Correct 2 ms 2688 KB Output is correct
18 Correct 2 ms 2816 KB Output is correct
19 Correct 2 ms 2688 KB Output is correct
20 Correct 2 ms 2688 KB Output is correct
21 Correct 2 ms 2688 KB Output is correct
22 Correct 2 ms 2688 KB Output is correct
23 Correct 2 ms 2688 KB Output is correct
24 Correct 2 ms 2688 KB Output is correct
25 Correct 2 ms 2688 KB Output is correct
26 Correct 2 ms 2816 KB Output is correct
27 Correct 3 ms 2816 KB Output is correct
28 Correct 2 ms 2816 KB Output is correct
29 Correct 2 ms 2816 KB Output is correct
30 Correct 2 ms 2816 KB Output is correct
31 Correct 2 ms 2816 KB Output is correct
32 Correct 2 ms 2816 KB Output is correct
33 Correct 2 ms 2816 KB Output is correct
34 Correct 2 ms 2816 KB Output is correct
35 Correct 2 ms 2816 KB Output is correct
36 Correct 99 ms 11324 KB Output is correct
37 Correct 105 ms 13816 KB Output is correct
38 Correct 71 ms 9332 KB Output is correct
39 Correct 92 ms 9208 KB Output is correct
40 Correct 112 ms 9208 KB Output is correct
41 Correct 101 ms 12664 KB Output is correct
42 Correct 114 ms 13048 KB Output is correct
43 Correct 65 ms 8564 KB Output is correct
44 Correct 108 ms 9336 KB Output is correct
45 Correct 96 ms 9208 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2816 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2688 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct
6 Correct 2 ms 2688 KB Output is correct
7 Correct 2 ms 2688 KB Output is correct
8 Correct 2 ms 2688 KB Output is correct
9 Correct 2 ms 2688 KB Output is correct
10 Correct 2 ms 2688 KB Output is correct
11 Correct 2 ms 2688 KB Output is correct
12 Correct 2 ms 2688 KB Output is correct
13 Correct 2 ms 2688 KB Output is correct
14 Correct 2 ms 2816 KB Output is correct
15 Correct 2 ms 2816 KB Output is correct
16 Correct 2 ms 2816 KB Output is correct
17 Correct 3 ms 2816 KB Output is correct
18 Correct 2 ms 2816 KB Output is correct
19 Correct 94 ms 11352 KB Output is correct
20 Correct 100 ms 13880 KB Output is correct
21 Correct 78 ms 9332 KB Output is correct
22 Correct 111 ms 9208 KB Output is correct
23 Correct 106 ms 9208 KB Output is correct
24 Correct 2 ms 2688 KB Output is correct
25 Correct 2 ms 2816 KB Output is correct
26 Correct 2 ms 2688 KB Output is correct
27 Correct 2 ms 2688 KB Output is correct
28 Correct 2 ms 2688 KB Output is correct
29 Correct 2 ms 2688 KB Output is correct
30 Correct 2 ms 2688 KB Output is correct
31 Correct 2 ms 2688 KB Output is correct
32 Correct 2 ms 2688 KB Output is correct
33 Correct 2 ms 2816 KB Output is correct
34 Correct 3 ms 2816 KB Output is correct
35 Correct 2 ms 2816 KB Output is correct
36 Correct 2 ms 2816 KB Output is correct
37 Correct 2 ms 2816 KB Output is correct
38 Correct 2 ms 2816 KB Output is correct
39 Correct 2 ms 2816 KB Output is correct
40 Correct 2 ms 2816 KB Output is correct
41 Correct 2 ms 2816 KB Output is correct
42 Correct 2 ms 2816 KB Output is correct
43 Correct 99 ms 11324 KB Output is correct
44 Correct 105 ms 13816 KB Output is correct
45 Correct 71 ms 9332 KB Output is correct
46 Correct 92 ms 9208 KB Output is correct
47 Correct 112 ms 9208 KB Output is correct
48 Correct 101 ms 12664 KB Output is correct
49 Correct 114 ms 13048 KB Output is correct
50 Correct 65 ms 8564 KB Output is correct
51 Correct 108 ms 9336 KB Output is correct
52 Correct 96 ms 9208 KB Output is correct
53 Correct 109 ms 13876 KB Output is correct
54 Correct 117 ms 13048 KB Output is correct
55 Correct 54 ms 8052 KB Output is correct
56 Correct 93 ms 11384 KB Output is correct
57 Correct 89 ms 9208 KB Output is correct
58 Correct 87 ms 9208 KB Output is correct
59 Correct 93 ms 9208 KB Output is correct
60 Correct 90 ms 9208 KB Output is correct