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Submission #1116500

# Submission time Handle Problem Language Result Execution time Memory
1116500 2024-11-21T18:06:17 Z Thunnus Star Trek (CEOI20_startrek) C++17
100 / 100
 97 ms 18828 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 2 ms 6736 KB Output is correct
2 Correct 2 ms 6736 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 6736 KB Output is correct
2 Correct 1 ms 6736 KB Output is correct
3 Correct 2 ms 6904 KB Output is correct
4 Correct 2 ms 6736 KB Output is correct
5 Correct 2 ms 6736 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 6736 KB Output is correct
2 Correct 2 ms 6748 KB Output is correct
3 Correct 2 ms 6736 KB Output is correct
4 Correct 2 ms 6736 KB Output is correct
5 Correct 2 ms 6736 KB Output is correct
6 Correct 2 ms 6736 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 6736 KB Output is correct
2 Correct 2 ms 6748 KB Output is correct
3 Correct 2 ms 6736 KB Output is correct
4 Correct 2 ms 6736 KB Output is correct
5 Correct 2 ms 6736 KB Output is correct
6 Correct 2 ms 6736 KB Output is correct
7 Correct 3 ms 6736 KB Output is correct
8 Correct 2 ms 6736 KB Output is correct
9 Correct 2 ms 6736 KB Output is correct
10 Correct 2 ms 6736 KB Output is correct
11 Correct 3 ms 6736 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 6736 KB Output is correct
2 Correct 2 ms 6748 KB Output is correct
3 Correct 2 ms 6736 KB Output is correct
4 Correct 2 ms 6736 KB Output is correct
5 Correct 2 ms 6736 KB Output is correct
6 Correct 2 ms 6736 KB Output is correct
7 Correct 3 ms 6736 KB Output is correct
8 Correct 2 ms 6736 KB Output is correct
9 Correct 2 ms 6736 KB Output is correct
10 Correct 2 ms 6736 KB Output is correct
11 Correct 3 ms 6736 KB Output is correct
12 Correct 97 ms 14664 KB Output is correct
13 Correct 84 ms 18752 KB Output is correct
14 Correct 50 ms 11200 KB Output is correct
15 Correct 62 ms 11336 KB Output is correct
16 Correct 60 ms 11348 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 6736 KB Output is correct
2 Correct 2 ms 6748 KB Output is correct
3 Correct 2 ms 6736 KB Output is correct
4 Correct 2 ms 6736 KB Output is correct
5 Correct 2 ms 6736 KB Output is correct
6 Correct 2 ms 6736 KB Output is correct
7 Correct 3 ms 6736 KB Output is correct
8 Correct 2 ms 6736 KB Output is correct
9 Correct 2 ms 6736 KB Output is correct
10 Correct 2 ms 6736 KB Output is correct
11 Correct 3 ms 6736 KB Output is correct
12 Correct 2 ms 6912 KB Output is correct
13 Correct 2 ms 6736 KB Output is correct
14 Correct 1 ms 6736 KB Output is correct
15 Correct 2 ms 6736 KB Output is correct
16 Correct 2 ms 6736 KB Output is correct
17 Correct 2 ms 6736 KB Output is correct
18 Correct 2 ms 6736 KB Output is correct
19 Correct 2 ms 6752 KB Output is correct
20 Correct 3 ms 6772 KB Output is correct
21 Correct 3 ms 6736 KB Output is correct
22 Correct 2 ms 6788 KB Output is correct
23 Correct 2 ms 6736 KB Output is correct
24 Correct 2 ms 6736 KB Output is correct
25 Correct 2 ms 6736 KB Output is correct
26 Correct 2 ms 6736 KB Output is correct
27 Correct 2 ms 6736 KB Output is correct
28 Correct 2 ms 6736 KB Output is correct
29 Correct 2 ms 6736 KB Output is correct
30 Correct 2 ms 6796 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 6736 KB Output is correct
2 Correct 2 ms 6748 KB Output is correct
3 Correct 2 ms 6736 KB Output is correct
4 Correct 2 ms 6736 KB Output is correct
5 Correct 2 ms 6736 KB Output is correct
6 Correct 2 ms 6736 KB Output is correct
7 Correct 3 ms 6736 KB Output is correct
8 Correct 2 ms 6736 KB Output is correct
9 Correct 2 ms 6736 KB Output is correct
10 Correct 2 ms 6736 KB Output is correct
11 Correct 3 ms 6736 KB Output is correct
12 Correct 97 ms 14664 KB Output is correct
13 Correct 84 ms 18752 KB Output is correct
14 Correct 50 ms 11200 KB Output is correct
15 Correct 62 ms 11336 KB Output is correct
16 Correct 60 ms 11348 KB Output is correct
17 Correct 2 ms 6912 KB Output is correct
18 Correct 2 ms 6736 KB Output is correct
19 Correct 1 ms 6736 KB Output is correct
20 Correct 2 ms 6736 KB Output is correct
21 Correct 2 ms 6736 KB Output is correct
22 Correct 2 ms 6736 KB Output is correct
23 Correct 2 ms 6736 KB Output is correct
24 Correct 2 ms 6752 KB Output is correct
25 Correct 3 ms 6772 KB Output is correct
26 Correct 3 ms 6736 KB Output is correct
27 Correct 2 ms 6788 KB Output is correct
28 Correct 2 ms 6736 KB Output is correct
29 Correct 2 ms 6736 KB Output is correct
30 Correct 2 ms 6736 KB Output is correct
31 Correct 2 ms 6736 KB Output is correct
32 Correct 2 ms 6736 KB Output is correct
33 Correct 2 ms 6736 KB Output is correct
34 Correct 2 ms 6736 KB Output is correct
35 Correct 2 ms 6796 KB Output is correct
36 Correct 68 ms 14676 KB Output is correct
37 Correct 86 ms 18828 KB Output is correct
38 Correct 48 ms 11156 KB Output is correct
39 Correct 65 ms 11400 KB Output is correct
40 Correct 66 ms 11396 KB Output is correct
41 Correct 72 ms 16828 KB Output is correct
42 Correct 66 ms 17748 KB Output is correct
43 Correct 42 ms 10696 KB Output is correct
44 Correct 60 ms 11344 KB Output is correct
45 Correct 65 ms 11424 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 6736 KB Output is correct
2 Correct 2 ms 6736 KB Output is correct
3 Correct 2 ms 6736 KB Output is correct
4 Correct 1 ms 6736 KB Output is correct
5 Correct 2 ms 6904 KB Output is correct
6 Correct 2 ms 6736 KB Output is correct
7 Correct 2 ms 6736 KB Output is correct
8 Correct 2 ms 6736 KB Output is correct
9 Correct 2 ms 6748 KB Output is correct
10 Correct 2 ms 6736 KB Output is correct
11 Correct 2 ms 6736 KB Output is correct
12 Correct 2 ms 6736 KB Output is correct
13 Correct 2 ms 6736 KB Output is correct
14 Correct 3 ms 6736 KB Output is correct
15 Correct 2 ms 6736 KB Output is correct
16 Correct 2 ms 6736 KB Output is correct
17 Correct 2 ms 6736 KB Output is correct
18 Correct 3 ms 6736 KB Output is correct
19 Correct 97 ms 14664 KB Output is correct
20 Correct 84 ms 18752 KB Output is correct
21 Correct 50 ms 11200 KB Output is correct
22 Correct 62 ms 11336 KB Output is correct
23 Correct 60 ms 11348 KB Output is correct
24 Correct 2 ms 6912 KB Output is correct
25 Correct 2 ms 6736 KB Output is correct
26 Correct 1 ms 6736 KB Output is correct
27 Correct 2 ms 6736 KB Output is correct
28 Correct 2 ms 6736 KB Output is correct
29 Correct 2 ms 6736 KB Output is correct
30 Correct 2 ms 6736 KB Output is correct
31 Correct 2 ms 6752 KB Output is correct
32 Correct 3 ms 6772 KB Output is correct
33 Correct 3 ms 6736 KB Output is correct
34 Correct 2 ms 6788 KB Output is correct
35 Correct 2 ms 6736 KB Output is correct
36 Correct 2 ms 6736 KB Output is correct
37 Correct 2 ms 6736 KB Output is correct
38 Correct 2 ms 6736 KB Output is correct
39 Correct 2 ms 6736 KB Output is correct
40 Correct 2 ms 6736 KB Output is correct
41 Correct 2 ms 6736 KB Output is correct
42 Correct 2 ms 6796 KB Output is correct
43 Correct 68 ms 14676 KB Output is correct
44 Correct 86 ms 18828 KB Output is correct
45 Correct 48 ms 11156 KB Output is correct
46 Correct 65 ms 11400 KB Output is correct
47 Correct 66 ms 11396 KB Output is correct
48 Correct 72 ms 16828 KB Output is correct
49 Correct 66 ms 17748 KB Output is correct
50 Correct 42 ms 10696 KB Output is correct
51 Correct 60 ms 11344 KB Output is correct
52 Correct 65 ms 11424 KB Output is correct
53 Correct 75 ms 18760 KB Output is correct
54 Correct 81 ms 17224 KB Output is correct
55 Correct 40 ms 10176 KB Output is correct
56 Correct 67 ms 14940 KB Output is correct
57 Correct 75 ms 11604 KB Output is correct
58 Correct 59 ms 11512 KB Output is correct
59 Correct 65 ms 11336 KB Output is correct
60 Correct 60 ms 11344 KB Output is correct