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Submission #932435

# Submission time Handle Problem Language Result Execution time Memory
932435 2024-02-23T11:07:28 Z LucaIlie Star Trek (CEOI20_startrek) C++17
78 / 100
 121 ms 17724 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 = calcDp( n, d - 1 );
  	if ( dpd != dp[d - 1] )
      exit( 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 6748 KB Output is correct
2 Correct 3 ms 7004 KB Output is correct
3 Runtime error 69 ms 13416 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 6748 KB Output is correct
2 Correct 2 ms 6748 KB Output is correct
3 Correct 1 ms 6748 KB Output is correct
4 Correct 5 ms 7000 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 2 ms 6748 KB Output is correct
2 Correct 2 ms 6748 KB Output is correct
3 Correct 1 ms 6748 KB Output is correct
4 Correct 5 ms 7000 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 6748 KB Output is correct

Subtask #5
15.0 / 15.0

# 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 Correct 1 ms 6748 KB Output is correct
4 Correct 5 ms 7000 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 6748 KB Output is correct
12 Correct 78 ms 13396 KB Output is correct
13 Correct 83 ms 17492 KB Output is correct
14 Correct 53 ms 10292 KB Output is correct
15 Correct 67 ms 10268 KB Output is correct
16 Correct 67 ms 10324 KB Output is correct

Subtask #6
20.0 / 20.0

# 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 Correct 1 ms 6748 KB Output is correct
4 Correct 5 ms 7000 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 6748 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 3 ms 7004 KB Output is correct
16 Correct 1 ms 6748 KB Output is correct
17 Correct 2 ms 6560 KB Output is correct
18 Correct 1 ms 7000 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 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 19 ms 9308 KB Output is correct
27 Correct 21 ms 9564 KB Output is correct
28 Correct 26 ms 9860 KB Output is correct
29 Correct 19 ms 9300 KB Output is correct
30 Correct 14 ms 8536 KB Output is correct

Subtask #7
20.0 / 20.0

# 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 Correct 1 ms 6748 KB Output is correct
4 Correct 5 ms 7000 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 6748 KB Output is correct
12 Correct 78 ms 13396 KB Output is correct
13 Correct 83 ms 17492 KB Output is correct
14 Correct 53 ms 10292 KB Output is correct
15 Correct 67 ms 10268 KB Output is correct
16 Correct 67 ms 10324 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 3 ms 7004 KB Output is correct
21 Correct 1 ms 6748 KB Output is correct
22 Correct 2 ms 6560 KB Output is correct
23 Correct 1 ms 7000 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 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 19 ms 9308 KB Output is correct
32 Correct 21 ms 9564 KB Output is correct
33 Correct 26 ms 9860 KB Output is correct
34 Correct 19 ms 9300 KB Output is correct
35 Correct 14 ms 8536 KB Output is correct
36 Correct 77 ms 13396 KB Output is correct
37 Correct 83 ms 17724 KB Output is correct
38 Correct 55 ms 10184 KB Output is correct
39 Correct 71 ms 10048 KB Output is correct
40 Correct 69 ms 10320 KB Output is correct
41 Correct 121 ms 15840 KB Output is correct
42 Correct 91 ms 16720 KB Output is correct
43 Correct 84 ms 12492 KB Output is correct
44 Correct 74 ms 10832 KB Output is correct
45 Correct 89 ms 13024 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 6748 KB Output is correct
4 Correct 3 ms 7004 KB Output is correct
5 Runtime error 69 ms 13416 KB Execution killed with signal 11
6 Halted 0 ms 0 KB -