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Submission #932428

# Submission time Handle Problem Language Result Execution time Memory
932428 2024-02-23T10:57:33 Z LucaIlie Star Trek (CEOI20_startrek) C++17
78 / 100
 101 ms 18768 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 losers = 0, c = 0;
void dfs( int u, int p ) {
    losers += !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;
}

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;
    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 2 ms 6748 KB Output is correct
2 Correct 2 ms 6744 KB Output is correct

Subtask #2
0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6748 KB Output is correct
2 Correct 2 ms 6748 KB Output is correct
3 Runtime error 70 ms 13420 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 6744 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 6748 KB Output is correct
5 Correct 1 ms 6748 KB Output is correct
6 Correct 1 ms 6748 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6744 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 6748 KB Output is correct
5 Correct 1 ms 6748 KB Output is correct
6 Correct 1 ms 6748 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 7000 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6744 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 6748 KB Output is correct
5 Correct 1 ms 6748 KB Output is correct
6 Correct 1 ms 6748 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 7000 KB Output is correct
12 Correct 92 ms 13396 KB Output is correct
13 Correct 84 ms 17540 KB Output is correct
14 Correct 93 ms 10216 KB Output is correct
15 Correct 75 ms 10320 KB Output is correct
16 Correct 85 ms 10280 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6744 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 6748 KB Output is correct
5 Correct 1 ms 6748 KB Output is correct
6 Correct 1 ms 6748 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 7000 KB Output is correct
12 Correct 1 ms 6748 KB Output is correct
13 Correct 2 ms 6748 KB Output is correct
14 Correct 1 ms 6748 KB Output is correct
15 Correct 2 ms 6748 KB Output is correct
16 Correct 1 ms 6748 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 6748 KB Output is correct
21 Correct 2 ms 6748 KB Output is correct
22 Correct 2 ms 6748 KB Output is correct
23 Correct 2 ms 6744 KB Output is correct
24 Correct 2 ms 6744 KB Output is correct
25 Correct 2 ms 6744 KB Output is correct
26 Correct 10 ms 6748 KB Output is correct
27 Correct 11 ms 6748 KB Output is correct
28 Correct 12 ms 6804 KB Output is correct
29 Correct 10 ms 6744 KB Output is correct
30 Correct 8 ms 6748 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6744 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 6748 KB Output is correct
5 Correct 1 ms 6748 KB Output is correct
6 Correct 1 ms 6748 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 7000 KB Output is correct
12 Correct 92 ms 13396 KB Output is correct
13 Correct 84 ms 17540 KB Output is correct
14 Correct 93 ms 10216 KB Output is correct
15 Correct 75 ms 10320 KB Output is correct
16 Correct 85 ms 10280 KB Output is correct
17 Correct 1 ms 6748 KB Output is correct
18 Correct 2 ms 6748 KB Output is correct
19 Correct 1 ms 6748 KB Output is correct
20 Correct 2 ms 6748 KB Output is correct
21 Correct 1 ms 6748 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 6748 KB Output is correct
26 Correct 2 ms 6748 KB Output is correct
27 Correct 2 ms 6748 KB Output is correct
28 Correct 2 ms 6744 KB Output is correct
29 Correct 2 ms 6744 KB Output is correct
30 Correct 2 ms 6744 KB Output is correct
31 Correct 10 ms 6748 KB Output is correct
32 Correct 11 ms 6748 KB Output is correct
33 Correct 12 ms 6804 KB Output is correct
34 Correct 10 ms 6744 KB Output is correct
35 Correct 8 ms 6748 KB Output is correct
36 Correct 87 ms 14672 KB Output is correct
37 Correct 80 ms 18768 KB Output is correct
38 Correct 53 ms 11260 KB Output is correct
39 Correct 81 ms 11272 KB Output is correct
40 Correct 77 ms 11344 KB Output is correct
41 Correct 89 ms 16976 KB Output is correct
42 Correct 85 ms 17812 KB Output is correct
43 Correct 55 ms 10708 KB Output is correct
44 Correct 101 ms 11516 KB Output is correct
45 Correct 79 ms 11344 KB Output is correct

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 6748 KB Output is correct
2 Correct 2 ms 6744 KB Output is correct
3 Correct 1 ms 6748 KB Output is correct
4 Correct 2 ms 6748 KB Output is correct
5 Runtime error 70 ms 13420 KB Execution killed with signal 11
6 Halted 0 ms 0 KB -