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Submission #932420

# Submission time Handle Problem Language Result Execution time Memory
932420 2024-02-23T10:20:40 Z LucaIlie Star Trek (CEOI20_startrek) C++17
43 / 100
 1000 ms 15012 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], reach[MAX_N + 1], critical[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]);
    }
}


bool influence( int u, int p ) {
    if ( p == 0 )
        return false;

    if ( canWin[u] ) {
        if ( canWin[p] )
            return false;
        return true;
    }

    if ( countChildrenLosers[p] >= 2 )
        return false;
    return true;
}

void dfsCritical( int u, int p ) {
    critical[u] = (!canWin[u]);
    for ( int v: adj[u] ) {
        if ( v == p )
            continue;
        dfsCritical( v, u );
        if ( influence( v, u ) )
            critical[u] += critical[v];
    }
}

int losers = 0, c = 0;
void reroot( int u, int p ) {
    losers += !canWin[u];
    c += (canWin[u] ? 1 : -1) * critical[u];
    /*for ( int v = 1; v <= 4; v++ )
        printf( "%d ", critical[v] );
    printf( "\n" );*/

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

        if ( influence( v, u ) )
            critical[u] -= critical[v];
        //printf( "ch %d %d\n", critical[u], critical[v] );
        critical[v] -= (!canWin[v]);
        critical[u] -= (!canWin[u]);
        countChildrenLosers[u] -= (!canWin[v]);
        canWin[u] = (countChildrenLosers[u] > 0);
        countChildrenLosers[v] += (!canWin[u]);
        canWin[v] = (countChildrenLosers[v] > 0);
        critical[v] += (!canWin[v]);
        critical[u] += (!canWin[u]);
        if ( influence( u, v ) )
            critical[v] += critical[u];

        reroot( v, u );

        if ( influence( u, v ) )
            critical[v] -= critical[u];
        critical[v] -= (!canWin[v]);
        critical[u] -= (!canWin[u]);
        countChildrenLosers[v] -= (!canWin[u]);
        canWin[v] = (countChildrenLosers[v] > 0);
        countChildrenLosers[u] += (!canWin[v]);
        canWin[u] = (countChildrenLosers[u] > 0);
        critical[v] += (!canWin[v]);
        critical[u] += (!canWin[u]);
        if ( influence( v, u ) )
            critical[u] += critical[v];
    }
}

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;
}

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 );
    reroot( 1, 0 );

   // cout << "C: " << c << "\n";

    c = 0;
    for ( int r = 1; r <= n; r++ ) {
        dfsGame( r, 0 );
        dfsCritical( r, 0 );
        //cout << r << " " << critical[r] << "\n";
        c += (canWin[r] ? 1 : -1) * critical[r];
    }
    //cout << "C: " << c << "\n";

    while ( c < 0 )
        c += MOD;
    dp[0] = losers;
    for ( int i = 1; i < d; i++ )
        dp[i] = (losers * lgPut( n, 2 * i ) + c * dp[i - 1]) % MOD;

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

    return 0;
}

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4700 KB Output is correct
2 Correct 15 ms 4764 KB Output is correct

Subtask #2
0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4700 KB Output is correct
2 Correct 2 ms 4700 KB Output is correct
3 Runtime error 53 ms 11716 KB Execution killed with signal 11
4 Halted 0 ms 0 KB -

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4696 KB Output is correct
2 Correct 1 ms 4700 KB Output is correct
3 Correct 1 ms 4700 KB Output is correct
4 Correct 1 ms 4700 KB Output is correct
5 Correct 1 ms 4700 KB Output is correct
6 Correct 1 ms 4700 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4696 KB Output is correct
2 Correct 1 ms 4700 KB Output is correct
3 Correct 1 ms 4700 KB Output is correct
4 Correct 1 ms 4700 KB Output is correct
5 Correct 1 ms 4700 KB Output is correct
6 Correct 1 ms 4700 KB Output is correct
7 Correct 21 ms 4700 KB Output is correct
8 Correct 24 ms 4700 KB Output is correct
9 Correct 14 ms 4700 KB Output is correct
10 Correct 18 ms 4768 KB Output is correct
11 Correct 17 ms 4700 KB Output is correct

Subtask #5
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4696 KB Output is correct
2 Correct 1 ms 4700 KB Output is correct
3 Correct 1 ms 4700 KB Output is correct
4 Correct 1 ms 4700 KB Output is correct
5 Correct 1 ms 4700 KB Output is correct
6 Correct 1 ms 4700 KB Output is correct
7 Correct 21 ms 4700 KB Output is correct
8 Correct 24 ms 4700 KB Output is correct
9 Correct 14 ms 4700 KB Output is correct
10 Correct 18 ms 4768 KB Output is correct
11 Correct 17 ms 4700 KB Output is correct
12 Execution timed out 1074 ms 15012 KB Time limit exceeded
13 Halted 0 ms 0 KB -

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4696 KB Output is correct
2 Correct 1 ms 4700 KB Output is correct
3 Correct 1 ms 4700 KB Output is correct
4 Correct 1 ms 4700 KB Output is correct
5 Correct 1 ms 4700 KB Output is correct
6 Correct 1 ms 4700 KB Output is correct
7 Correct 21 ms 4700 KB Output is correct
8 Correct 24 ms 4700 KB Output is correct
9 Correct 14 ms 4700 KB Output is correct
10 Correct 18 ms 4768 KB Output is correct
11 Correct 17 ms 4700 KB Output is correct
12 Correct 1 ms 4700 KB Output is correct
13 Correct 18 ms 4700 KB Output is correct
14 Correct 1 ms 4700 KB Output is correct
15 Correct 2 ms 4700 KB Output is correct
16 Correct 1 ms 4700 KB Output is correct
17 Correct 2 ms 4696 KB Output is correct
18 Correct 1 ms 4700 KB Output is correct
19 Correct 1 ms 4700 KB Output is correct
20 Correct 1 ms 4696 KB Output is correct
21 Correct 22 ms 4788 KB Output is correct
22 Correct 23 ms 4696 KB Output is correct
23 Correct 14 ms 4700 KB Output is correct
24 Correct 17 ms 4764 KB Output is correct
25 Correct 17 ms 4700 KB Output is correct
26 Correct 26 ms 4700 KB Output is correct
27 Correct 38 ms 4700 KB Output is correct
28 Correct 19 ms 4700 KB Output is correct
29 Correct 25 ms 4700 KB Output is correct
30 Correct 24 ms 4700 KB Output is correct

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4696 KB Output is correct
2 Correct 1 ms 4700 KB Output is correct
3 Correct 1 ms 4700 KB Output is correct
4 Correct 1 ms 4700 KB Output is correct
5 Correct 1 ms 4700 KB Output is correct
6 Correct 1 ms 4700 KB Output is correct
7 Correct 21 ms 4700 KB Output is correct
8 Correct 24 ms 4700 KB Output is correct
9 Correct 14 ms 4700 KB Output is correct
10 Correct 18 ms 4768 KB Output is correct
11 Correct 17 ms 4700 KB Output is correct
12 Execution timed out 1074 ms 15012 KB Time limit exceeded
13 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4700 KB Output is correct
2 Correct 15 ms 4764 KB Output is correct
3 Correct 1 ms 4700 KB Output is correct
4 Correct 2 ms 4700 KB Output is correct
5 Runtime error 53 ms 11716 KB Execution killed with signal 11
6 Halted 0 ms 0 KB -