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Submission #999431

# Submission time Handle Problem Language Result Execution time Memory
999431 2024-06-15T13:24:18 Z yoav_s Star Trek (CEOI20_startrek) C++17
43 / 100
 1000 ms 34572 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, vvp &childrenS)
{
    ll N = graph.size();
    visited[i] = true;
    for (ll x : graph[i])
        if (!visited[x])
        {
            solve(x, graph, isWinning, res, visited, subtreeSize, childrenS);
            childrenS[i][0] += res[x][0];
            childrenS[i][1] += res[x][1];
        }

    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) + childrenS[i][0];
        res[i][0] = p(0, 1) + childrenS[i][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);
        vvp childrenS(N, vp(2, p(0, 0)));
        solve(i, graph, isWinning, dp, visited, subtreeSize, childrenS);
        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:191:26: warning: unused variable 'losingCount' [-Wunused-variable]
  191 |     ll winningCount = 0, losingCount = 0;
      |                          ^~~~~~~~~~~

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 117 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 0 ms 348 KB Output is correct
3 Execution timed out 1088 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 348 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 416 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 348 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 416 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 142 ms 604 KB Output is correct
8 Correct 124 ms 604 KB Output is correct
9 Correct 126 ms 664 KB Output is correct
10 Correct 114 ms 600 KB Output is correct
11 Correct 118 ms 668 KB Output is correct

Subtask #5
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 416 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 142 ms 604 KB Output is correct
8 Correct 124 ms 604 KB Output is correct
9 Correct 126 ms 664 KB Output is correct
10 Correct 114 ms 600 KB Output is correct
11 Correct 118 ms 668 KB Output is correct
12 Execution timed out 1061 ms 34572 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 348 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 416 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 142 ms 604 KB Output is correct
8 Correct 124 ms 604 KB Output is correct
9 Correct 126 ms 664 KB Output is correct
10 Correct 114 ms 600 KB Output is correct
11 Correct 118 ms 668 KB Output is correct
12 Correct 0 ms 344 KB Output is correct
13 Correct 116 ms 672 KB Output is correct
14 Correct 1 ms 344 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 1 ms 484 KB Output is correct
17 Correct 2 ms 348 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 2 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 149 ms 744 KB Output is correct
22 Correct 125 ms 604 KB Output is correct
23 Correct 116 ms 604 KB Output is correct
24 Correct 119 ms 604 KB Output is correct
25 Correct 113 ms 604 KB Output is correct
26 Correct 113 ms 600 KB Output is correct
27 Correct 128 ms 604 KB Output is correct
28 Correct 69 ms 856 KB Output is correct
29 Correct 110 ms 600 KB Output is correct
30 Correct 116 ms 600 KB Output is correct

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 416 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 142 ms 604 KB Output is correct
8 Correct 124 ms 604 KB Output is correct
9 Correct 126 ms 664 KB Output is correct
10 Correct 114 ms 600 KB Output is correct
11 Correct 118 ms 668 KB Output is correct
12 Execution timed out 1061 ms 34572 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 344 KB Output is correct
2 Correct 117 ms 604 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Execution timed out 1088 ms 348 KB Time limit exceeded
6 Halted 0 ms 0 KB -