Submission #932427

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
932427	2024-02-23T10:57:13 Z	LucaIlie	Star Trek (CEOI20_startrek)	C++17	43 / 100	1000 ms	16268 KB

startrek

#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 losers = 0, c = 0;
void dfs( int u, int p ) {
    losers += !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;
}

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 );*/

    c = 0;
    for ( int r = 1; r <= n; r++ ) {
        dfsGame( r, 0 );
        dfsCritical( r, 0 );
        c += (canWin[r] ? 1 : -1) * critical[r];
        losers += !canWin[r];
    }

    while ( c < 0 )
        c += MOD;
    dp[0] = losers;
    for ( int i = 1; i < d; i++ )
        dp[i] = (losers * lgPut( n, 2 * i ) + c * dp[i - 1]) % MOD;

    dfsGame( 1, 0 );
    dfsCritical( 1, 0 );
    if ( canWin[1] )
        cout << (lgPut( n, 2 * d ) - dp[d - 1] * critical[1] % MOD + MOD) % MOD;
    else
        cout << dp[d - 1] * critical[1] % MOD << "\n";

    return 0;
}

Subtask #1
0.0 / 0.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	6744 KB	Output is correct
2	Correct	17 ms	6808 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	2 ms	6748 KB	Output is correct
3	Runtime error	67 ms	13652 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	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	25 ms	6748 KB	Output is correct
8	Correct	26 ms	6876 KB	Output is correct
9	Correct	16 ms	6744 KB	Output is correct
10	Correct	23 ms	7000 KB	Output is correct
11	Correct	19 ms	6748 KB	Output is correct

Subtask #5
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	25 ms	6748 KB	Output is correct
8	Correct	26 ms	6876 KB	Output is correct
9	Correct	16 ms	6744 KB	Output is correct
10	Correct	23 ms	7000 KB	Output is correct
11	Correct	19 ms	6748 KB	Output is correct
12	Execution timed out	1036 ms	16268 KB	Time limit exceeded
13	Halted	0 ms	0 KB	-

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	25 ms	6748 KB	Output is correct
8	Correct	26 ms	6876 KB	Output is correct
9	Correct	16 ms	6744 KB	Output is correct
10	Correct	23 ms	7000 KB	Output is correct
11	Correct	19 ms	6748 KB	Output is correct
12	Correct	1 ms	6748 KB	Output is correct
13	Correct	17 ms	6800 KB	Output is correct
14	Correct	1 ms	6748 KB	Output is correct
15	Correct	2 ms	6748 KB	Output is correct
16	Correct	2 ms	7000 KB	Output is correct
17	Correct	1 ms	6748 KB	Output is correct
18	Correct	2 ms	6560 KB	Output is correct
19	Correct	2 ms	6748 KB	Output is correct
20	Correct	2 ms	7000 KB	Output is correct
21	Correct	23 ms	6848 KB	Output is correct
22	Correct	26 ms	6748 KB	Output is correct
23	Correct	16 ms	6744 KB	Output is correct
24	Correct	19 ms	6804 KB	Output is correct
25	Correct	19 ms	6808 KB	Output is correct
26	Correct	27 ms	6744 KB	Output is correct
27	Correct	35 ms	6744 KB	Output is correct
28	Correct	21 ms	6804 KB	Output is correct
29	Correct	27 ms	6748 KB	Output is correct
30	Correct	25 ms	6748 KB	Output is correct

Subtask #7
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	25 ms	6748 KB	Output is correct
8	Correct	26 ms	6876 KB	Output is correct
9	Correct	16 ms	6744 KB	Output is correct
10	Correct	23 ms	7000 KB	Output is correct
11	Correct	19 ms	6748 KB	Output is correct
12	Execution timed out	1036 ms	16268 KB	Time limit exceeded
13	Halted	0 ms	0 KB	-

Subtask #8
0 / 15.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	6744 KB	Output is correct
2	Correct	17 ms	6808 KB	Output is correct
3	Correct	1 ms	6748 KB	Output is correct
4	Correct	2 ms	6748 KB	Output is correct
5	Runtime error	67 ms	13652 KB	Execution killed with signal 11
6	Halted	0 ms	0 KB	-

Submission #932427

Compilation message