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Submission #932439

# Submission time Handle Problem Language Result Execution time Memory
932439 2024-02-23T11:23:45 Z LucaIlie Star Trek (CEOI20_startrek) C++17
85 / 100
 1000 ms 137652 KB 
#include <bits/stdc++.h>

#define int long long

using namespace std;

const int MAX_N = 1e5;
const int MAX_D = 1e5;
const int MOD = 1e9 + 7;
bool canWin[MAX_N + 1];
int countChildrenLosers[MAX_N + 1], critical[MAX_N + 1], sumCriticalW[MAX_N + 1], sumCriticalL[MAX_N + 1], dp[MAX_D];
vector<int> adj[MAX_N + 1];

void dfsGame( int u, int p ) {
    canWin[u] = false;
    countChildrenLosers[u] = 0;
    for ( int v: adj[u] ) {
        if ( v == p )
            continue;
        dfsGame( v, u );
        canWin[u] |= !canWin[v];
        countChildrenLosers[u] += !canWin[v];
    }
}

void calcCritical( int u ) {
    if ( canWin[u] ) {
        if ( countChildrenLosers[u] >= 2 )
            critical[u] = 0;
        else
            critical[u] = sumCriticalL[u];
    } else
        critical[u] = sumCriticalW[u] + 1;
}

void dfsCritical( int u, int p ) {
    sumCriticalW[u] = sumCriticalL[u] = 0;
    for ( int v: adj[u] ) {
        if ( v == p )
            continue;
        dfsCritical( v, u );
        if ( canWin[v] )
            sumCriticalW[u] += critical[v];
        else
            sumCriticalL[u] += critical[v];
    }
    calcCritical( u );
}

void reroot( int u, int v ) {
    if ( canWin[v] )
        sumCriticalW[u] -= critical[v];
    else {
        sumCriticalL[u] -= critical[v];
        countChildrenLosers[u]--;
    }
    canWin[u] = (countChildrenLosers[u] > 0);
    calcCritical( u );

    if ( canWin[u] )
        sumCriticalW[v] += critical[u];
    else {
        sumCriticalL[v] += critical[u];
        countChildrenLosers[v]++;
    }
    canWin[v] = (countChildrenLosers[v] > 0);
    calcCritical( v );
}

int l = 0, c = 0;
void dfs( int u, int p ) {
    l += !canWin[u];
    c += (canWin[u] ? 1 : -1) * critical[u];

    for ( int v: adj[u] ) {
        if ( v == p )
            continue;

        reroot( u, v );
        dfs( v, u );
        reroot( v, u );
    }
}

int lgPut( int x, int n ) {
    if ( n == 0 )
        return 1;

    int p = lgPut( x, n / 2 );
    p = (long long)p * p % MOD;
    if ( n % 2 == 1 )
        p = (long long)p * x % MOD;

    return p;
}

int calcDp( int n, int i ) {
    if ( i == 0 )
        return 1;
    return (lgPut( n, 2 * i ) + c * calcDp( n, i - 1 )) % MOD;
}

signed main() {
    int n, d;

    cin >> n >> d;

    for ( int i = 0; i < n - 1; i++ ) {
        int u, v;
        cin >> u >> v;
        adj[u].push_back( v );
        adj[v].push_back( u );
    }

    dfsGame( 1, 0 );
    dfsCritical( 1, 0 );
    dfs( 1, 0 );

    while ( c < 0 )
        c += MOD;
    int dpd = l * (n == 2 ? 0 : calcDp( n, d - 1 )) % MOD;

    dfsGame( 1, 0 );
    dfsCritical( 1, 0 );
    if ( canWin[1] )
        cout << (lgPut( n, 2 * d ) - dpd * critical[1] % MOD + MOD) % MOD;
    else
        cout << dpd * critical[1] % MOD << "\n";

    return 0;
}

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6744 KB Output is correct
2 Correct 2 ms 6748 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6748 KB Output is correct
2 Correct 1 ms 6748 KB Output is correct
3 Correct 1 ms 6748 KB Output is correct
4 Correct 1 ms 6744 KB Output is correct
5 Correct 1 ms 6748 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6748 KB Output is correct
2 Correct 1 ms 6748 KB Output is correct
3 Correct 2 ms 6748 KB Output is correct
4 Correct 1 ms 6748 KB Output is correct
5 Correct 1 ms 6744 KB Output is correct
6 Correct 1 ms 6744 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6748 KB Output is correct
2 Correct 1 ms 6748 KB Output is correct
3 Correct 2 ms 6748 KB Output is correct
4 Correct 1 ms 6748 KB Output is correct
5 Correct 1 ms 6744 KB Output is correct
6 Correct 1 ms 6744 KB Output is correct
7 Correct 2 ms 6748 KB Output is correct
8 Correct 2 ms 6748 KB Output is correct
9 Correct 2 ms 6748 KB Output is correct
10 Correct 2 ms 6748 KB Output is correct
11 Correct 2 ms 6744 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6748 KB Output is correct
2 Correct 1 ms 6748 KB Output is correct
3 Correct 2 ms 6748 KB Output is correct
4 Correct 1 ms 6748 KB Output is correct
5 Correct 1 ms 6744 KB Output is correct
6 Correct 1 ms 6744 KB Output is correct
7 Correct 2 ms 6748 KB Output is correct
8 Correct 2 ms 6748 KB Output is correct
9 Correct 2 ms 6748 KB Output is correct
10 Correct 2 ms 6748 KB Output is correct
11 Correct 2 ms 6744 KB Output is correct
12 Correct 81 ms 13580 KB Output is correct
13 Correct 130 ms 17488 KB Output is correct
14 Correct 52 ms 10192 KB Output is correct
15 Correct 66 ms 10064 KB Output is correct
16 Correct 67 ms 10368 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6748 KB Output is correct
2 Correct 1 ms 6748 KB Output is correct
3 Correct 2 ms 6748 KB Output is correct
4 Correct 1 ms 6748 KB Output is correct
5 Correct 1 ms 6744 KB Output is correct
6 Correct 1 ms 6744 KB Output is correct
7 Correct 2 ms 6748 KB Output is correct
8 Correct 2 ms 6748 KB Output is correct
9 Correct 2 ms 6748 KB Output is correct
10 Correct 2 ms 6748 KB Output is correct
11 Correct 2 ms 6744 KB Output is correct
12 Correct 1 ms 6744 KB Output is correct
13 Correct 2 ms 6748 KB Output is correct
14 Correct 1 ms 6748 KB Output is correct
15 Correct 1 ms 6748 KB Output is correct
16 Correct 1 ms 6772 KB Output is correct
17 Correct 1 ms 6748 KB Output is correct
18 Correct 1 ms 6748 KB Output is correct
19 Correct 1 ms 6748 KB Output is correct
20 Correct 1 ms 6744 KB Output is correct
21 Correct 2 ms 6744 KB Output is correct
22 Correct 1 ms 6744 KB Output is correct
23 Correct 1 ms 6748 KB Output is correct
24 Correct 2 ms 6748 KB Output is correct
25 Correct 2 ms 6748 KB Output is correct
26 Correct 13 ms 9304 KB Output is correct
27 Correct 13 ms 9564 KB Output is correct
28 Correct 13 ms 9820 KB Output is correct
29 Correct 11 ms 9396 KB Output is correct
30 Correct 9 ms 8420 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6748 KB Output is correct
2 Correct 1 ms 6748 KB Output is correct
3 Correct 2 ms 6748 KB Output is correct
4 Correct 1 ms 6748 KB Output is correct
5 Correct 1 ms 6744 KB Output is correct
6 Correct 1 ms 6744 KB Output is correct
7 Correct 2 ms 6748 KB Output is correct
8 Correct 2 ms 6748 KB Output is correct
9 Correct 2 ms 6748 KB Output is correct
10 Correct 2 ms 6748 KB Output is correct
11 Correct 2 ms 6744 KB Output is correct
12 Correct 81 ms 13580 KB Output is correct
13 Correct 130 ms 17488 KB Output is correct
14 Correct 52 ms 10192 KB Output is correct
15 Correct 66 ms 10064 KB Output is correct
16 Correct 67 ms 10368 KB Output is correct
17 Correct 1 ms 6744 KB Output is correct
18 Correct 2 ms 6748 KB Output is correct
19 Correct 1 ms 6748 KB Output is correct
20 Correct 1 ms 6748 KB Output is correct
21 Correct 1 ms 6772 KB Output is correct
22 Correct 1 ms 6748 KB Output is correct
23 Correct 1 ms 6748 KB Output is correct
24 Correct 1 ms 6748 KB Output is correct
25 Correct 1 ms 6744 KB Output is correct
26 Correct 2 ms 6744 KB Output is correct
27 Correct 1 ms 6744 KB Output is correct
28 Correct 1 ms 6748 KB Output is correct
29 Correct 2 ms 6748 KB Output is correct
30 Correct 2 ms 6748 KB Output is correct
31 Correct 13 ms 9304 KB Output is correct
32 Correct 13 ms 9564 KB Output is correct
33 Correct 13 ms 9820 KB Output is correct
34 Correct 11 ms 9396 KB Output is correct
35 Correct 9 ms 8420 KB Output is correct
36 Correct 75 ms 13392 KB Output is correct
37 Correct 104 ms 17488 KB Output is correct
38 Correct 54 ms 10308 KB Output is correct
39 Correct 64 ms 10256 KB Output is correct
40 Correct 70 ms 10320 KB Output is correct
41 Correct 99 ms 15696 KB Output is correct
42 Correct 97 ms 16728 KB Output is correct
43 Correct 58 ms 12488 KB Output is correct
44 Correct 71 ms 10872 KB Output is correct
45 Correct 104 ms 13008 KB Output is correct

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6744 KB Output is correct
2 Correct 2 ms 6748 KB Output is correct
3 Correct 1 ms 6748 KB Output is correct
4 Correct 1 ms 6748 KB Output is correct
5 Correct 1 ms 6748 KB Output is correct
6 Correct 1 ms 6744 KB Output is correct
7 Correct 1 ms 6748 KB Output is correct
8 Correct 1 ms 6748 KB Output is correct
9 Correct 1 ms 6748 KB Output is correct
10 Correct 2 ms 6748 KB Output is correct
11 Correct 1 ms 6748 KB Output is correct
12 Correct 1 ms 6744 KB Output is correct
13 Correct 1 ms 6744 KB Output is correct
14 Correct 2 ms 6748 KB Output is correct
15 Correct 2 ms 6748 KB Output is correct
16 Correct 2 ms 6748 KB Output is correct
17 Correct 2 ms 6748 KB Output is correct
18 Correct 2 ms 6744 KB Output is correct
19 Correct 81 ms 13580 KB Output is correct
20 Correct 130 ms 17488 KB Output is correct
21 Correct 52 ms 10192 KB Output is correct
22 Correct 66 ms 10064 KB Output is correct
23 Correct 67 ms 10368 KB Output is correct
24 Correct 1 ms 6744 KB Output is correct
25 Correct 2 ms 6748 KB Output is correct
26 Correct 1 ms 6748 KB Output is correct
27 Correct 1 ms 6748 KB Output is correct
28 Correct 1 ms 6772 KB Output is correct
29 Correct 1 ms 6748 KB Output is correct
30 Correct 1 ms 6748 KB Output is correct
31 Correct 1 ms 6748 KB Output is correct
32 Correct 1 ms 6744 KB Output is correct
33 Correct 2 ms 6744 KB Output is correct
34 Correct 1 ms 6744 KB Output is correct
35 Correct 1 ms 6748 KB Output is correct
36 Correct 2 ms 6748 KB Output is correct
37 Correct 2 ms 6748 KB Output is correct
38 Correct 13 ms 9304 KB Output is correct
39 Correct 13 ms 9564 KB Output is correct
40 Correct 13 ms 9820 KB Output is correct
41 Correct 11 ms 9396 KB Output is correct
42 Correct 9 ms 8420 KB Output is correct
43 Correct 75 ms 13392 KB Output is correct
44 Correct 104 ms 17488 KB Output is correct
45 Correct 54 ms 10308 KB Output is correct
46 Correct 64 ms 10256 KB Output is correct
47 Correct 70 ms 10320 KB Output is correct
48 Correct 99 ms 15696 KB Output is correct
49 Correct 97 ms 16728 KB Output is correct
50 Correct 58 ms 12488 KB Output is correct
51 Correct 71 ms 10872 KB Output is correct
52 Correct 104 ms 13008 KB Output is correct
53 Execution timed out 1077 ms 137652 KB Time limit exceeded
54 Halted 0 ms 0 KB -