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Submission #932440

# Submission time Handle Problem Language Result Execution time Memory
932440 2024-02-23T11:26:59 Z LucaIlie Star Trek (CEOI20_startrek) C++17
78 / 100
 1000 ms 17936 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 1;
    return (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 = 0;
    for ( int i = 0; i <= d - 1; i++ )
        dpd = (dpd + lgPut( n * n % MOD, i ) * lgPut( c, d - 1 - i )) % MOD;
    dpd = dpd * l % MOD;

    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 3 ms 6748 KB Output is correct
3 Execution timed out 1082 ms 6748 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 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 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 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 6744 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 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 6744 KB Output is correct
12 Correct 80 ms 13444 KB Output is correct
13 Correct 95 ms 17936 KB Output is correct
14 Correct 52 ms 10360 KB Output is correct
15 Correct 70 ms 10100 KB Output is correct
16 Correct 66 ms 10140 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 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 6744 KB Output is correct
12 Correct 1 ms 7000 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 6744 KB Output is correct
16 Correct 2 ms 6988 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 6744 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 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 18 ms 6744 KB Output is correct
27 Correct 19 ms 6744 KB Output is correct
28 Correct 20 ms 6744 KB Output is correct
29 Correct 17 ms 6744 KB Output is correct
30 Correct 12 ms 6748 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 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 6744 KB Output is correct
12 Correct 80 ms 13444 KB Output is correct
13 Correct 95 ms 17936 KB Output is correct
14 Correct 52 ms 10360 KB Output is correct
15 Correct 70 ms 10100 KB Output is correct
16 Correct 66 ms 10140 KB Output is correct
17 Correct 1 ms 7000 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 6744 KB Output is correct
21 Correct 2 ms 6988 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 6744 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 6748 KB Output is correct
29 Correct 2 ms 6748 KB Output is correct
30 Correct 1 ms 6748 KB Output is correct
31 Correct 18 ms 6744 KB Output is correct
32 Correct 19 ms 6744 KB Output is correct
33 Correct 20 ms 6744 KB Output is correct
34 Correct 17 ms 6744 KB Output is correct
35 Correct 12 ms 6748 KB Output is correct
36 Correct 73 ms 13392 KB Output is correct
37 Correct 85 ms 17488 KB Output is correct
38 Correct 52 ms 10184 KB Output is correct
39 Correct 65 ms 10096 KB Output is correct
40 Correct 66 ms 10324 KB Output is correct
41 Correct 112 ms 15792 KB Output is correct
42 Correct 87 ms 16760 KB Output is correct
43 Correct 62 ms 9680 KB Output is correct
44 Correct 69 ms 10328 KB Output is correct
45 Correct 100 ms 10264 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 3 ms 6748 KB Output is correct
5 Execution timed out 1082 ms 6748 KB Time limit exceeded
6 Halted 0 ms 0 KB -