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Submission #999429

# Submission time Handle Problem Language Result Execution time Memory
999429 2024-06-15T13:22:00 Z yoav_s Star Trek (CEOI20_startrek) C++17
43 / 100
 1000 ms 26300 KB 
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef vector<ll> v;
typedef vector<v> vv;
typedef vector<vv> vvv;
typedef pair<ll,ll> p;
typedef vector<p> vp;
typedef vector<vp> vvp;
typedef vector<vvp> vvvp;
typedef pair<ll, p> tri;
typedef vector<tri> vtri;
typedef vector<vtri> vvtri;
typedef vector<vvtri> vvvtri;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<vvb> vvvb;

#define f first
#define s second
#define pb push_back
#define eb emplace_back
#define all(v) (v).begin(),(v).end()

const ll INF = 1e18;
const ll mod = 1e9 + 7;

ll modPow(ll a, ll b)
{
    if (b == 0) return 1;
    ll res = modPow(a, b / 2);
    res = (res * res) % mod;
    if (b % 2 == 1) res = (res * a) % mod;
    return res;
}

void getWinningStates(ll i, vv &graph, vb &winning, vb &visited, v &losingChildrenCount)
{
    if (visited[i]) return;
    visited[i] = true;
    for (ll x : graph[i])
    {
        if (!visited[x])
        {
            getWinningStates(x, graph, winning, visited, losingChildrenCount);
            if (!winning[x])
            {
                winning[i] = true;
                losingChildrenCount[i]++;
            }
        }
    }
}

void winningAsRoot(ll i, vv &graph, vb &visited, v &losingChildrenCount, vb &res, ll par)
{
    if (visited[i]) return;
    visited[i] = true;
    if (par != -1)
    {
        if (losingChildrenCount[i] == 0) losingChildrenCount[par]--;
        if (losingChildrenCount[par] == 0) losingChildrenCount[i]++;
    }
    res[i] = losingChildrenCount[i] > 0;
    for (ll x : graph[i])
    {
        winningAsRoot(x, graph, visited, losingChildrenCount, res, i);
    }
    if (par != -1)
    {
        if (losingChildrenCount[par] == 0) losingChildrenCount[i]--;
        if (losingChildrenCount[i] == 0) losingChildrenCount[par]++;
    }
}

ll getSubtreeSize(ll i, vv &graph, v &res)
{
    if (res[i] != 0) return 0;
    res[i] = 1;
    for (ll x : graph[i]) res[i] += getSubtreeSize(x, graph, res);
    return res[i];
}

p operator+(p a, p b)
{
    return p(a.f + b.f, a.s + b.s);
}

void operator+=(p &a, p b)
{
    a.f += b.f; a.s += b.s;
}

p operator%(p a, ll mod)
{
    return p(a.f % mod, a.s % mod);
}

void operator%=(p &a, ll mod)
{
    a = a % mod;
}

void solve(ll i, vv &graph, vb &isWinning, vvp &res, vb &visited, v &subtreeSize)
{
    ll N = graph.size();
    visited[i] = true;
    for (ll x : graph[i]) if (!visited[x]) solve(x, graph, isWinning, res, visited, subtreeSize);

    ll losingChildren = 0;
    ll losingChild;
    for (ll x : graph[i])
    {
        if (!visited[x] && !isWinning[x])
        {
            losingChildren++;
            losingChild = x;
        }
    }
    if (losingChildren == 0)
    {
        res[i][1] = p(N, mod - 1);
        for (ll x : graph[i])
        {
            if (!visited[x])
            {
                res[i][1] += res[x][0];
            }
        }
        res[i][0] = p(0, 1);
        for (ll x : graph[i])
        {
            if (!visited[x])
                res[i][0] += res[x][1];
        }
        res[i][0] %= mod;
    }
    else if (losingChildren == 1)
    {
        res[i][1] = p((N * (subtreeSize[i] - subtreeSize[losingChild])) % mod, 0);
        res[i][1] += res[losingChild][0];
        res[i][0] = res[losingChild][1];
    }
    else
    {
        res[i][0] = p(0, 0);
        res[i][1] = p((N * subtreeSize[i]) % mod, 0);
    }
    res[i][1] %= mod;
    visited[i] = false;
}

int main()
{
    ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
    long long N, D;
    cin >> N >> D;
    vv graph(N);
    for (ll i=  0; i < N - 1; i++)
    {
        long long a, b;
        cin >> a >> b;
        a--; b--;
        graph[a].pb(b);
        graph[b].pb(a);
    }
    vp amountOfWaysToWin(N);
    for (ll i=  0; i < N; i++)
    {
        vb isWinning(N), visited(N, false);
        v losingChildrenCount(N, 0);
        getWinningStates(i, graph, isWinning, visited, losingChildrenCount);
        vb winAsRoot(N, false);
        visited = vb(N, false);
        winningAsRoot(i, graph, visited, losingChildrenCount, winAsRoot, -1);
        ll winningCount = 0, losingCount = 0;
        for (auto x : winAsRoot)
        {
            if (x) winningCount++;
            else losingCount++;
        }
        v subtreeSize(N, 0);
        getSubtreeSize(i, graph, subtreeSize);
        vvp dp(N, vp(2, p(0, 0)));
        visited = vb(N, false);
        solve(i, graph, isWinning, dp, visited, subtreeSize);
        amountOfWaysToWin[i] = dp[i][1];
    }
    vb isWinning(N), visited(N, false);
    v losingChildrenCount(N, 0);
    getWinningStates(0, graph, isWinning, visited, losingChildrenCount);
    vb winAsRoot(N, false); visited = vb(N, false);
    winningAsRoot(0, graph, visited, losingChildrenCount, winAsRoot, -1);
    ll winningCount = 0, losingCount = 0;
    for (auto x : winAsRoot)
    {
        if (x) winningCount++;
    }
    p sum = p(0, 0);
    for (auto x : amountOfWaysToWin) sum += x;
    sum %= mod;
    ll weighted = winningCount, absolute = 1;
    for (ll i = 1; i < D; i++)
    {
        weighted = sum.f * absolute + sum.s * weighted;
        weighted %= mod;
        absolute *= (N * N) % mod;
        absolute %= mod;
    }
    cout << (weighted * amountOfWaysToWin[0].s + absolute * amountOfWaysToWin[0].f) % mod << "\n";
    return 0;
}

Compilation message

startrek.cpp: In function 'int main()':
startrek.cpp:196:26: warning: unused variable 'losingCount' [-Wunused-variable]
  196 |     ll winningCount = 0, losingCount = 0;
      |                          ^~~~~~~~~~~

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 68 ms 604 KB Output is correct

Subtask #2
0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Execution timed out 1010 ms 348 KB Time limit exceeded
4 Halted 0 ms 0 KB -

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 78 ms 604 KB Output is correct
8 Correct 102 ms 720 KB Output is correct
9 Correct 69 ms 604 KB Output is correct
10 Correct 72 ms 604 KB Output is correct
11 Correct 73 ms 604 KB Output is correct

Subtask #5
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 78 ms 604 KB Output is correct
8 Correct 102 ms 720 KB Output is correct
9 Correct 69 ms 604 KB Output is correct
10 Correct 72 ms 604 KB Output is correct
11 Correct 73 ms 604 KB Output is correct
12 Execution timed out 1077 ms 26300 KB Time limit exceeded
13 Halted 0 ms 0 KB -

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 78 ms 604 KB Output is correct
8 Correct 102 ms 720 KB Output is correct
9 Correct 69 ms 604 KB Output is correct
10 Correct 72 ms 604 KB Output is correct
11 Correct 73 ms 604 KB Output is correct
12 Correct 1 ms 344 KB Output is correct
13 Correct 67 ms 604 KB Output is correct
14 Correct 1 ms 344 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 344 KB Output is correct
21 Correct 80 ms 668 KB Output is correct
22 Correct 88 ms 604 KB Output is correct
23 Correct 69 ms 600 KB Output is correct
24 Correct 71 ms 604 KB Output is correct
25 Correct 74 ms 604 KB Output is correct
26 Correct 77 ms 604 KB Output is correct
27 Correct 88 ms 856 KB Output is correct
28 Correct 45 ms 344 KB Output is correct
29 Correct 72 ms 604 KB Output is correct
30 Correct 100 ms 600 KB Output is correct

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 78 ms 604 KB Output is correct
8 Correct 102 ms 720 KB Output is correct
9 Correct 69 ms 604 KB Output is correct
10 Correct 72 ms 604 KB Output is correct
11 Correct 73 ms 604 KB Output is correct
12 Execution timed out 1077 ms 26300 KB Time limit exceeded
13 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 68 ms 604 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 1 ms 344 KB Output is correct
5 Execution timed out 1010 ms 348 KB Time limit exceeded
6 Halted 0 ms 0 KB -