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Submission #932429

# Submission time Handle Problem Language Result Execution time Memory
932429 2024-02-23T11:00:40 Z LucaIlie Star Trek (CEOI20_startrek) C++17
38 / 100
 105 ms 17748 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 n;
int calcDp( int d ) {
    if ( d == 0 )
        return l;
    return (l * lgPut( n, 2 * d ) + c * calcDp( d - 1 )) % MOD;
}

signed main() {
    int 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 = (n == 2 ? lgPut( n, 2 * d ) : calcDp( 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 2 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 Incorrect 2 ms 6748 KB Output isn't correct
2 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 2 ms 6620 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 6744 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 2 ms 6620 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 6744 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 1 ms 6748 KB Output is correct
2 Correct 2 ms 6620 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 6744 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 79 ms 13560 KB Output is correct
13 Correct 105 ms 17748 KB Output is correct
14 Correct 49 ms 10284 KB Output is correct
15 Correct 64 ms 10064 KB Output is correct
16 Correct 91 ms 10312 KB Output is correct

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6748 KB Output is correct
2 Correct 2 ms 6620 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 6744 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 6748 KB Output is correct
13 Correct 2 ms 6748 KB Output is correct
14 Incorrect 1 ms 6748 KB Output isn't correct
15 Halted 0 ms 0 KB -

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6748 KB Output is correct
2 Correct 2 ms 6620 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 6744 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 79 ms 13560 KB Output is correct
13 Correct 105 ms 17748 KB Output is correct
14 Correct 49 ms 10284 KB Output is correct
15 Correct 64 ms 10064 KB Output is correct
16 Correct 91 ms 10312 KB Output is correct
17 Correct 1 ms 6748 KB Output is correct
18 Correct 2 ms 6748 KB Output is correct
19 Incorrect 1 ms 6748 KB Output isn't correct
20 Halted 0 ms 0 KB -

Subtask #8
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 Incorrect 2 ms 6748 KB Output isn't correct
4 Halted 0 ms 0 KB -