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Submission #932436

# Submission time Handle Problem Language Result Execution time Memory
932436 2024-02-23T11:07:51 Z LucaIlie Star Trek (CEOI20_startrek) C++17
78 / 100
 1000 ms 110900 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 l;
    return (l * 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 = calcDp( n, d - 1 );

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

Subtask #2
0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6744 KB Output is correct
2 Correct 2 ms 7004 KB Output is correct
3 Execution timed out 1096 ms 110900 KB Time limit exceeded
4 Halted 0 ms 0 KB -

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 1 ms 6748 KB Output is correct
4 Correct 2 ms 6748 KB Output is correct
5 Correct 1 ms 6748 KB Output is correct
6 Correct 1 ms 6904 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 1 ms 6748 KB Output is correct
4 Correct 2 ms 6748 KB Output is correct
5 Correct 1 ms 6748 KB Output is correct
6 Correct 1 ms 6904 KB Output is correct
7 Correct 2 ms 6748 KB Output is correct
8 Correct 2 ms 6756 KB Output is correct
9 Correct 2 ms 6744 KB Output is correct
10 Correct 2 ms 6748 KB Output is correct
11 Correct 2 ms 6748 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 1 ms 6748 KB Output is correct
4 Correct 2 ms 6748 KB Output is correct
5 Correct 1 ms 6748 KB Output is correct
6 Correct 1 ms 6904 KB Output is correct
7 Correct 2 ms 6748 KB Output is correct
8 Correct 2 ms 6756 KB Output is correct
9 Correct 2 ms 6744 KB Output is correct
10 Correct 2 ms 6748 KB Output is correct
11 Correct 2 ms 6748 KB Output is correct
12 Correct 79 ms 13396 KB Output is correct
13 Correct 84 ms 17492 KB Output is correct
14 Correct 56 ms 10184 KB Output is correct
15 Correct 67 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 1 ms 6748 KB Output is correct
4 Correct 2 ms 6748 KB Output is correct
5 Correct 1 ms 6748 KB Output is correct
6 Correct 1 ms 6904 KB Output is correct
7 Correct 2 ms 6748 KB Output is correct
8 Correct 2 ms 6756 KB Output is correct
9 Correct 2 ms 6744 KB Output is correct
10 Correct 2 ms 6748 KB Output is correct
11 Correct 2 ms 6748 KB Output is correct
12 Correct 1 ms 6748 KB Output is correct
13 Correct 2 ms 6748 KB Output is correct
14 Correct 2 ms 6748 KB Output is correct
15 Correct 2 ms 7004 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 2 ms 6744 KB Output is correct
20 Correct 1 ms 6748 KB Output is correct
21 Correct 2 ms 6744 KB Output is correct
22 Correct 2 ms 6748 KB Output is correct
23 Correct 2 ms 6748 KB Output is correct
24 Correct 2 ms 6744 KB Output is correct
25 Correct 2 ms 6744 KB Output is correct
26 Correct 11 ms 9308 KB Output is correct
27 Correct 12 ms 9564 KB Output is correct
28 Correct 13 ms 9832 KB Output is correct
29 Correct 14 ms 9308 KB Output is correct
30 Correct 8 ms 8540 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 1 ms 6748 KB Output is correct
4 Correct 2 ms 6748 KB Output is correct
5 Correct 1 ms 6748 KB Output is correct
6 Correct 1 ms 6904 KB Output is correct
7 Correct 2 ms 6748 KB Output is correct
8 Correct 2 ms 6756 KB Output is correct
9 Correct 2 ms 6744 KB Output is correct
10 Correct 2 ms 6748 KB Output is correct
11 Correct 2 ms 6748 KB Output is correct
12 Correct 79 ms 13396 KB Output is correct
13 Correct 84 ms 17492 KB Output is correct
14 Correct 56 ms 10184 KB Output is correct
15 Correct 67 ms 10064 KB Output is correct
16 Correct 67 ms 10368 KB Output is correct
17 Correct 1 ms 6748 KB Output is correct
18 Correct 2 ms 6748 KB Output is correct
19 Correct 2 ms 6748 KB Output is correct
20 Correct 2 ms 7004 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 2 ms 6744 KB Output is correct
25 Correct 1 ms 6748 KB Output is correct
26 Correct 2 ms 6744 KB Output is correct
27 Correct 2 ms 6748 KB Output is correct
28 Correct 2 ms 6748 KB Output is correct
29 Correct 2 ms 6744 KB Output is correct
30 Correct 2 ms 6744 KB Output is correct
31 Correct 11 ms 9308 KB Output is correct
32 Correct 12 ms 9564 KB Output is correct
33 Correct 13 ms 9832 KB Output is correct
34 Correct 14 ms 9308 KB Output is correct
35 Correct 8 ms 8540 KB Output is correct
36 Correct 73 ms 13472 KB Output is correct
37 Correct 84 ms 17636 KB Output is correct
38 Correct 55 ms 10184 KB Output is correct
39 Correct 67 ms 10252 KB Output is correct
40 Correct 86 ms 10608 KB Output is correct
41 Correct 88 ms 15812 KB Output is correct
42 Correct 83 ms 16760 KB Output is correct
43 Correct 59 ms 12620 KB Output is correct
44 Correct 69 ms 10836 KB Output is correct
45 Correct 79 ms 13140 KB Output is correct

Subtask #8
0 / 15.0

# 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 Correct 1 ms 6744 KB Output is correct
4 Correct 2 ms 7004 KB Output is correct
5 Execution timed out 1096 ms 110900 KB Time limit exceeded
6 Halted 0 ms 0 KB -