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Submission #932441

# Submission time Handle Problem Language Result Execution time Memory
932441 2024-02-23T11:41:28 Z LucaIlie Star Trek (CEOI20_startrek) C++17
100 / 100
 108 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 a, b;
int calcDp( int n ) {
    if ( n == 0 )
        return 1;
    if ( n % 2 == 1 )
        return (lgPut( a, n ) + b * calcDp( n - 1 )) % MOD;

    int x = calcDp( n / 2 );
    x = (x * (lgPut( a, n / 2 ) + lgPut( b, n / 2)) % MOD - lgPut( a, n / 2 ) * lgPut( b, n / 2 ) % MOD + MOD) % MOD;
    return x;
}

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 );

    a = n * n % MOD;
    b = c;
    while ( b < 0 )
        b += MOD;

    int dpd = calcDp( d - 1 );
    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 6744 KB Output is correct
2 Correct 2 ms 6748 KB Output is correct

Subtask #2
7.0 / 7.0

# 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 2 ms 6748 KB Output is correct
4 Correct 2 ms 6748 KB Output is correct
5 Correct 1 ms 6748 KB Output is correct

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 6744 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 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 6744 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 77 ms 13428 KB Output is correct
13 Correct 84 ms 17724 KB Output is correct
14 Correct 53 ms 10184 KB Output is correct
15 Correct 78 ms 10052 KB Output is correct
16 Correct 78 ms 10180 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 6744 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 2 ms 6748 KB Output is correct
13 Correct 2 ms 7004 KB Output is correct
14 Correct 1 ms 6748 KB Output is correct
15 Correct 1 ms 6748 KB Output is correct
16 Correct 1 ms 6748 KB Output is correct
17 Correct 1 ms 6760 KB Output is correct
18 Correct 1 ms 6748 KB Output is correct
19 Correct 1 ms 6748 KB Output is correct
20 Correct 2 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 2 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 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

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 6744 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 77 ms 13428 KB Output is correct
13 Correct 84 ms 17724 KB Output is correct
14 Correct 53 ms 10184 KB Output is correct
15 Correct 78 ms 10052 KB Output is correct
16 Correct 78 ms 10180 KB Output is correct
17 Correct 2 ms 6748 KB Output is correct
18 Correct 2 ms 7004 KB Output is correct
19 Correct 1 ms 6748 KB Output is correct
20 Correct 1 ms 6748 KB Output is correct
21 Correct 1 ms 6748 KB Output is correct
22 Correct 1 ms 6760 KB Output is correct
23 Correct 1 ms 6748 KB Output is correct
24 Correct 1 ms 6748 KB Output is correct
25 Correct 2 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 2 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 2 ms 6748 KB Output is correct
32 Correct 2 ms 6748 KB Output is correct
33 Correct 1 ms 6748 KB Output is correct
34 Correct 2 ms 6748 KB Output is correct
35 Correct 2 ms 6748 KB Output is correct
36 Correct 95 ms 13396 KB Output is correct
37 Correct 92 ms 17680 KB Output is correct
38 Correct 53 ms 10188 KB Output is correct
39 Correct 68 ms 10064 KB Output is correct
40 Correct 71 ms 10320 KB Output is correct
41 Correct 81 ms 15696 KB Output is correct
42 Correct 104 ms 16764 KB Output is correct
43 Correct 53 ms 9816 KB Output is correct
44 Correct 75 ms 10180 KB Output is correct
45 Correct 71 ms 10068 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6744 KB Output is correct
2 Correct 2 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 2 ms 6748 KB Output is correct
6 Correct 2 ms 6748 KB Output is correct
7 Correct 1 ms 6748 KB Output is correct
8 Correct 1 ms 6748 KB Output is correct
9 Correct 1 ms 6748 KB Output is correct
10 Correct 1 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 1 ms 6748 KB Output is correct
14 Correct 2 ms 6744 KB Output is correct
15 Correct 2 ms 6748 KB Output is correct
16 Correct 2 ms 6748 KB Output is correct
17 Correct 2 ms 6748 KB Output is correct
18 Correct 2 ms 6748 KB Output is correct
19 Correct 77 ms 13428 KB Output is correct
20 Correct 84 ms 17724 KB Output is correct
21 Correct 53 ms 10184 KB Output is correct
22 Correct 78 ms 10052 KB Output is correct
23 Correct 78 ms 10180 KB Output is correct
24 Correct 2 ms 6748 KB Output is correct
25 Correct 2 ms 7004 KB Output is correct
26 Correct 1 ms 6748 KB Output is correct
27 Correct 1 ms 6748 KB Output is correct
28 Correct 1 ms 6748 KB Output is correct
29 Correct 1 ms 6760 KB Output is correct
30 Correct 1 ms 6748 KB Output is correct
31 Correct 1 ms 6748 KB Output is correct
32 Correct 2 ms 6748 KB Output is correct
33 Correct 2 ms 6748 KB Output is correct
34 Correct 2 ms 6748 KB Output is correct
35 Correct 2 ms 6748 KB Output is correct
36 Correct 2 ms 6748 KB Output is correct
37 Correct 2 ms 6748 KB Output is correct
38 Correct 2 ms 6748 KB Output is correct
39 Correct 2 ms 6748 KB Output is correct
40 Correct 1 ms 6748 KB Output is correct
41 Correct 2 ms 6748 KB Output is correct
42 Correct 2 ms 6748 KB Output is correct
43 Correct 95 ms 13396 KB Output is correct
44 Correct 92 ms 17680 KB Output is correct
45 Correct 53 ms 10188 KB Output is correct
46 Correct 68 ms 10064 KB Output is correct
47 Correct 71 ms 10320 KB Output is correct
48 Correct 81 ms 15696 KB Output is correct
49 Correct 104 ms 16764 KB Output is correct
50 Correct 53 ms 9816 KB Output is correct
51 Correct 75 ms 10180 KB Output is correct
52 Correct 71 ms 10068 KB Output is correct
53 Correct 108 ms 17488 KB Output is correct
54 Correct 77 ms 17344 KB Output is correct
55 Correct 41 ms 10184 KB Output is correct
56 Correct 73 ms 14904 KB Output is correct
57 Correct 70 ms 11600 KB Output is correct
58 Correct 90 ms 11844 KB Output is correct
59 Correct 72 ms 11152 KB Output is correct
60 Correct 66 ms 11196 KB Output is correct