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Submission #932433

# Submission time Handle Problem Language Result Execution time Memory
932433 2024-02-23T11:05:42 Z LucaIlie Star Trek (CEOI20_startrek) C++17
78 / 100
 96 ms 17720 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;
    dp[0] = l;
    for ( int i = 1; i < d; i++ )
        dp[i] = (l * lgPut( n, 2 * i ) + c * dp[i - 1]) % MOD;
    int dpd = dp[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 2 ms 6748 KB Output is correct
2 Correct 2 ms 6748 KB Output is correct
3 Runtime error 66 ms 13396 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 2 ms 6744 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 6748 KB Output is correct
6 Correct 2 ms 6748 KB Output is correct

Subtask #4
15.0 / 15.0

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

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 6744 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 6748 KB Output is correct
6 Correct 2 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 1 ms 6748 KB Output is correct
12 Correct 73 ms 13476 KB Output is correct
13 Correct 85 ms 17488 KB Output is correct
14 Correct 51 ms 10184 KB Output is correct
15 Correct 83 ms 10252 KB Output is correct
16 Correct 65 ms 10368 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 6744 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 6748 KB Output is correct
6 Correct 2 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 1 ms 6748 KB Output is correct
12 Correct 1 ms 6748 KB Output is correct
13 Correct 2 ms 6800 KB Output is correct
14 Correct 1 ms 6744 KB Output is correct
15 Correct 2 ms 6748 KB Output is correct
16 Correct 1 ms 6760 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 6748 KB Output is correct
20 Correct 1 ms 6748 KB Output is correct
21 Correct 2 ms 7000 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 6748 KB Output is correct
25 Correct 2 ms 7000 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 6748 KB Output is correct
29 Correct 10 ms 6748 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 2 ms 6744 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 6748 KB Output is correct
6 Correct 2 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 1 ms 6748 KB Output is correct
12 Correct 73 ms 13476 KB Output is correct
13 Correct 85 ms 17488 KB Output is correct
14 Correct 51 ms 10184 KB Output is correct
15 Correct 83 ms 10252 KB Output is correct
16 Correct 65 ms 10368 KB Output is correct
17 Correct 1 ms 6748 KB Output is correct
18 Correct 2 ms 6800 KB Output is correct
19 Correct 1 ms 6744 KB Output is correct
20 Correct 2 ms 6748 KB Output is correct
21 Correct 1 ms 6760 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 6748 KB Output is correct
25 Correct 1 ms 6748 KB Output is correct
26 Correct 2 ms 7000 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 6748 KB Output is correct
30 Correct 2 ms 7000 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 6748 KB Output is correct
34 Correct 10 ms 6748 KB Output is correct
35 Correct 8 ms 6748 KB Output is correct
36 Correct 73 ms 13404 KB Output is correct
37 Correct 80 ms 17720 KB Output is correct
38 Correct 52 ms 10308 KB Output is correct
39 Correct 65 ms 10240 KB Output is correct
40 Correct 81 ms 10248 KB Output is correct
41 Correct 96 ms 15728 KB Output is correct
42 Correct 86 ms 16764 KB Output is correct
43 Correct 54 ms 9672 KB Output is correct
44 Correct 68 ms 10180 KB Output is correct
45 Correct 76 ms 10064 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 2 ms 6748 KB Output is correct
4 Correct 2 ms 6748 KB Output is correct
5 Runtime error 66 ms 13396 KB Execution killed with signal 11
6 Halted 0 ms 0 KB -