Submission #865555

#	Time	Username	Problem	Language	Result	Execution time	Memory
865555		boris_mihov	Star Trek (CEOI20_startrek)	C++17	0 / 100	1087 ms	2808 KiB

startrek

#include <algorithm>
#include <iostream>
#include <numeric>
#include <cassert>
#include <vector>
#include <random>
#include <queue>
#include <stack>
#include <set>

typedef long long llong;
const int MAXN = 100000 + 10;
const int MOD = 1e9 + 7;
const int INF = 2e9;

int n, d;
int sumL;
int sz[MAXN];
llong dp[MAXN];
bool win[MAXN];
int cntChildLoses[MAXN];
std::vector <int> g[MAXN];

llong power(int num, int base)
{
    if (base == 0) return 1;
    if (base & 1) return (num * power(num, base - 1)) % MOD;
    llong res = power(num, base >> 1);
    return (res * res) % MOD;
}

bool calcSubtreeWin(int node, int par)
{
    for (const int &u : g[node])
    {
        if (u == par)
        {
            continue;
        }

        cntChildLoses[node] += !calcSubtreeWin(u, node);
    }

    return cntChildLoses[node];
}

void calcUpWin(int node, int par)
{
    if (par != 0 && cntChildLoses[par] - cntChildLoses[node] > 0)
    {
        cntChildLoses[node]++;
    }

    for (const int &u : g[node])
    {
        if (u == par)
        {
            continue;
        }

        calcUpWin(u, node);
    }
}

int dfs(int node, int par)
{
    sz[node] = 1;
    for (const int &u : g[node])
    {
        if (u == par)
        {
            continue;
        }

        sz[node] += dfs(u, node);
    }

    return sz[node];
}

int currTry;
int calc(int node, int par)
{
    int cnt = 0;
    int which = -1;
    for (const int &u : g[node])
    {   
        if (u == par)
        {
            continue;
        }

        cnt += !win[u];
        if (!win[u]) which = u;
    }

    if (cnt >= 2)
    {
        dp[node] = ((1LL * (sz[node] * n) % MOD) * power(n, 2 * (currTry - 1))) % MOD;
    } else if (cnt == 0)
    {
        dp[node] = sumL;
        if (dp[node] < 0) dp[node] += MOD;
        for (const int &u : g[node])
        {
            if (u == par)
            {
                continue;
            }

            dp[node] += calc(u, node);
            if (dp[node] >= MOD) dp[node] -= MOD;
        }
    } else
    {
        dp[node] = ((1LL * ((sz[node] - sz[which]) * n) % MOD) * power(n, 2 * (currTry - 1))) % MOD;
        dp[node] += calc(which, node);
        if (dp[node] >= MOD) dp[node] -= MOD;
    }  

    assert(dp[node] >= 0 && dp[node] < MOD);
    return ((((1LL * (sz[node] * n) % MOD) * power(n, 2 * (currTry - 1))) % MOD) - dp[node] + MOD) % MOD;
}

void solve()
{
    calcSubtreeWin(1, 0);
    calcUpWin(1, 0);

    sumL = 0;
    for (int i = 1 ; i <= n ; ++i)
    {
        win[i] = (cntChildLoses[i] > 0);
        sumL += 1 - win[i];
    }

    for (int i = 1 ; i < d ; ++i)
    {
        currTry = i;
        int newSumL = 0;
        for (int j = 1 ; j <= n ; ++j)
        {
            dfs(j, 0);
            newSumL += calc(j, 0);
            if (newSumL >= MOD) newSumL -= MOD;
        }

        newSumL = power(n, 2 * i) - newSumL;
        if (newSumL < 0) newSumL += MOD;
        sumL = newSumL;
    }    

    dfs(1, 0);
    currTry = d;
    std::cout << (power(n, 2 * d) - calc(1, 0) + MOD) % MOD << '\n';
}   

void input()
{
    std::cin >> n >> d;
    for (int i = 1 ; i < n ; ++i)
    {
        int u, v;
        std::cin >> u >> v;
        g[u].push_back(v);
        g[v].push_back(u);
    }
}

void fastIOI()
{
    std::ios_base :: sync_with_stdio(0);
    std::cout.tie(nullptr);
    std::cin.tie(nullptr);
}

int main()
{
    fastIOI();
    input();
    solve();

    return 0;
}

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