Submission #931969

#	Time	Username	Problem	Language	Result	Execution time	Memory
931969		LucaIlie	Star Trek (CEOI20_startrek)	C++17	23 / 100	1032 ms	18216 KiB

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], dp[MAX_D + 1][3];
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 );
    }
}

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";*/

    bool ok = true;
    int winners[2] = { 0, 0 };
    for ( int r = 1; r <= n; r++ ) {
        dfsGame( r, 0 );
        winners[0] += canWin[r];
        if ( ok && !canWin[r] ) {
            adj[r].push_back( n + 1 );
            ok = false;
            for ( int v = 1; v <= n; v++ ) {
                dfsGame( v, 0 );
                winners[1] += canWin[v];
            }
            adj[r].pop_back();
        }
    }

    /*for ( int v = 1; v <= n; v++ ) {
        dfsGame( v, 0 );
        if ( canWin[v] )
            continue;

        adj[v].push_back( n + 1 );
        int winners = 0;
        for ( int r = 1; r <= n; r++ ) {
            dfsGame( r, 0 );
            for ( int x = 1; x <= n; x++ )
                cout << canWin[x];
            cout << canWin[r] << "\n";
            winners += canWin[r];
        }
        cout << v << " " << winners;
        cout << "\n";
        adj[v].pop_back();
    }*/

    /*int pom = 0;
    int winners = 0;
    for ( int v = 1; v <= n; v++ ) {
        dfsGame( v, 0 );
        winners += canWin[v];
        int w = 0;
        for  ( int u = 1; u <= n; u++ )
            w += canWin[u];
        if ( pom == 0 )
            pom = w;
        if ( pom != w )
            exit( 1 );
    }

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

    int countAdd1 = 0;
    for ( int v = 1; v <= n; v++ )
        countAdd1 += (add[v] == 1), printf( "%d %d\n", v, reach[v], add[v] );*/


    dp[1][0] = 1;
    //cout << winners[0] << " " << winners[1] << "\n";
    for ( int i = 2; i <= d; i++ ) {
        for ( int a = 0; a < 2; a++ ) {
            int p1 = (n - winners[0]) * (n - winners[1]) % MOD;
            int p0 = (n * n % MOD - p1 + MOD) % MOD;
            dp[i][0] = (dp[i][0] + dp[i - 1][a] * p0) % MOD;
            dp[i][1] = (dp[i][1] + dp[i - 1][a] * p1) % MOD;
        }
        //printf( "%d %d\n", dp[i][0], dp[i][1] );
    }

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

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

    cout << ans << "\n";

    return 0;
}

• Subtask 1: 0 / 0
• Subtask 2: 0 / 7
• Subtask 3: 8 / 8
• Subtask 4: 15 / 15
• Subtask 5: 0 / 15
• Subtask 6: 0 / 20
• Subtask 7: 0 / 20
• Subtask 8: 0 / 15