Submission #932365

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
932365	2024-02-23T08:52:58 Z	LucaIlie	Star Trek (CEOI20_startrek)	C++17	43 / 100	1000 ms	16832 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], add[MAX_N + 1], reach[MAX_N + 1], reach1[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 dfsCalcAdd( int u, int p ) {
    if ( p == 0 ) {
        add[u] = (canWin[u] ? -1 : 1);
        reach[u] = u;
    } else {
        if ( canWin[u] ) {
            if ( canWin[p] ) {
                add[u] = -1;
                reach[u] = u;
            } else {
                add[u] = add[p] - 1;
                reach[u] = reach[p];
            }
        } else {
            if ( countChildrenLosers[p] >= 2 ) {
                add[u] = 1;
                reach[u] = u;
            } else {
                add[u] = add[p] + 1;
                reach[u] = reach[p];
            }
        }
    }

    for ( int v: adj[u] ) {
        if ( v == p )
            continue;
        dfsCalcAdd( 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 );
        /*adj[u + n].push_back( v + n );
        adj[v + n].push_back( u + n );
        adj[u + 2 * n].push_back( v + 2 * n );
        adj[v + 2 * n].push_back( u + 2 * n );*/
    }

    /*int an = 0;
    for ( int u = 1; u <= n; u++ ) {
        for ( int v = n + 1; v <= 2 * n; v++ ) {
            adj[u].push_back( v );
            adj[v].push_back( u );
            for ( int w = n + 1; w <= 2 * n; w++ ) {
                for ( int t = 2 * n + 1; t <= 3 * n; t++ ) {
                    adj[w].push_back( t );
                    adj[t].push_back( w );
                    dfsGame( 1, 0 );
                    if ( canWin[1] ) {
                        an++;
                        printf( "W %d-%d %d-%d\n", u, v, w, t );
                    }
                    adj[w].pop_back();
                    adj[t].pop_back();
                }
            }
            adj[u].pop_back();
            adj[v].pop_back();
        }
    }
    cout << an << "\n";*/

    int losers = 0, winners = 0, rch = 0;
    for ( int r = 1; r <= n; r++ ) {
        dfsGame( r, 0 );
        dfsCalcAdd( r, 0 );
        losers += !canWin[r];
        winners += canWin[r];
        reach1[r] = 0;
        for ( int v = 1; v <= n; v++ ) {
            if ( !canWin[v] && reach[v] == r )
                reach1[r]++;
        }
        rch += (canWin[r] ? 1 : -1) * reach1[r];
    }

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

    dfsGame( 1, 0 );
    dfsCalcAdd( 1, 0 );

    int ans = (canWin[1] ? 0 : lgPut( n, 2 * d ) );
    for ( int v = 1; v <= n; v++ ) {
        if ( canWin[1] ) {
            if ( !canWin[v] && reach[v] == 1 )
                ans = (ans + dp[d - 1]) % MOD;
        } else {
            if ( !canWin[v] && reach[v] == 1 )
                ans = (ans - dp[d - 1]) % MOD;
        }
    }

    cout << (lgPut( n, 2 * d ) - ans + MOD) % 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	19 ms	6748 KB	Output is correct

Subtask #2
0 / 7.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	6748 KB	Output is correct
2	Correct	3 ms	6744 KB	Output is correct
3	Runtime error	64 ms	13396 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	2 ms	7000 KB	Output is correct
2	Correct	2 ms	7004 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	2 ms	6748 KB	Output is correct

Subtask #4
15.0 / 15.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	7000 KB	Output is correct
2	Correct	2 ms	7004 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	2 ms	6748 KB	Output is correct
7	Correct	28 ms	6748 KB	Output is correct
8	Correct	32 ms	6748 KB	Output is correct
9	Correct	17 ms	6748 KB	Output is correct
10	Correct	20 ms	6820 KB	Output is correct
11	Correct	21 ms	6776 KB	Output is correct

Subtask #5
0 / 15.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	7000 KB	Output is correct
2	Correct	2 ms	7004 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	2 ms	6748 KB	Output is correct
7	Correct	28 ms	6748 KB	Output is correct
8	Correct	32 ms	6748 KB	Output is correct
9	Correct	17 ms	6748 KB	Output is correct
10	Correct	20 ms	6820 KB	Output is correct
11	Correct	21 ms	6776 KB	Output is correct
12	Execution timed out	1042 ms	16832 KB	Time limit exceeded
13	Halted	0 ms	0 KB	-

Subtask #6
20.0 / 20.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	7000 KB	Output is correct
2	Correct	2 ms	7004 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	2 ms	6748 KB	Output is correct
7	Correct	28 ms	6748 KB	Output is correct
8	Correct	32 ms	6748 KB	Output is correct
9	Correct	17 ms	6748 KB	Output is correct
10	Correct	20 ms	6820 KB	Output is correct
11	Correct	21 ms	6776 KB	Output is correct
12	Correct	2 ms	6748 KB	Output is correct
13	Correct	20 ms	6816 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	6772 KB	Output is correct
17	Correct	1 ms	6744 KB	Output is correct
18	Correct	2 ms	6744 KB	Output is correct
19	Correct	1 ms	6744 KB	Output is correct
20	Correct	1 ms	6748 KB	Output is correct
21	Correct	24 ms	6780 KB	Output is correct
22	Correct	32 ms	6748 KB	Output is correct
23	Correct	19 ms	6748 KB	Output is correct
24	Correct	20 ms	6816 KB	Output is correct
25	Correct	19 ms	6748 KB	Output is correct
26	Correct	29 ms	6748 KB	Output is correct
27	Correct	42 ms	6748 KB	Output is correct
28	Correct	22 ms	7000 KB	Output is correct
29	Correct	28 ms	6744 KB	Output is correct
30	Correct	24 ms	6748 KB	Output is correct

Subtask #7
0 / 20.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	7000 KB	Output is correct
2	Correct	2 ms	7004 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	2 ms	6748 KB	Output is correct
7	Correct	28 ms	6748 KB	Output is correct
8	Correct	32 ms	6748 KB	Output is correct
9	Correct	17 ms	6748 KB	Output is correct
10	Correct	20 ms	6820 KB	Output is correct
11	Correct	21 ms	6776 KB	Output is correct
12	Execution timed out	1042 ms	16832 KB	Time limit exceeded
13	Halted	0 ms	0 KB	-

Subtask #8
0 / 15.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	6744 KB	Output is correct
2	Correct	19 ms	6748 KB	Output is correct
3	Correct	2 ms	6748 KB	Output is correct
4	Correct	3 ms	6744 KB	Output is correct
5	Runtime error	64 ms	13396 KB	Execution killed with signal 11
6	Halted	0 ms	0 KB	-

Submission #932365

Compilation message