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Submission #999424

# Submission time Handle Problem Language Result Execution time Memory
999424 2024-06-15T13:01:52 Z yoav_s Star Trek (CEOI20_startrek) C++17
43 / 100
 1000 ms 20392 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;
}

p solve(ll i, vv &graph, vb &isWinning, vp &res, vb &visited, bool shouldWin, v &subtreeSize)
{
    ll N = graph.size();
    assert(!visited[i]);
    visited[i] = true;
    if (shouldWin)
    {
        if (isWinning[i])
        {
            ll losingChildren = 0;
            ll losingChild;
            for (ll x : graph[i])
                if (!visited[x] && !isWinning[x])
                {
                    losingChildren++;
                    losingChild = x;
                }
            if (losingChildren == 1)
            {
                res[i].f += (N * (subtreeSize[i] - subtreeSize[losingChild])) % mod;
                res[i] += solve(losingChild, graph, isWinning, res, visited, false, subtreeSize);
                res[i] %= mod;
                return res[i];
            }
            else
            {
                res[i] = p((N * subtreeSize[i]) % mod, 0);
                return res[i];
            }
        }
        else
        {
            res[i].s += mod - 1; res[i].f += N;
            for (ll x : graph[i])
            {
                if (!visited[x])
                {
                    res[i] += solve(x, graph, isWinning, res, visited, false, subtreeSize);
                }
            }
            res[i] %= mod;
            return res[i];
        }
    }
    else
    {
        //should be losing - all children should be winning
        if (!isWinning[i])
        {
            res[i].s++;
            for (ll x : graph[i])
            {
                if (!visited[x])
                    res[i] += solve(x, graph, isWinning, res, visited, true, subtreeSize);
            }
            res[i] %= mod;
            return res[i];
        }
        else
        {
            ll losingChildren = 0, losing;
            for (ll x : graph[i])
            {
                if (!visited[x] && !isWinning[x])
                {
                    losingChildren++; losing = x;
                }
            }
            if (losingChildren > 1) return p(0, 0);
            res[i] = solve(losing, graph, isWinning, res, visited, true, subtreeSize);
            return res[i];
        }
    }
}

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);
        vp dp(N, p(0, 0));
        visited = vb(N, false);
        amountOfWaysToWin[i] = solve(i, graph, isWinning, dp, visited, true, subtreeSize);
    }
    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:221:26: warning: unused variable 'losingCount' [-Wunused-variable]
  221 |     ll winningCount = 0, losingCount = 0;
      |                          ^~~~~~~~~~~
startrek.cpp: In function 'p solve(ll, vv&, vb&, vp&, vb&, bool, v&)':
startrek.cpp:175:85: warning: 'losing' may be used uninitialized in this function [-Wmaybe-uninitialized]
  175 |             res[i] = solve(losing, graph, isWinning, res, visited, true, subtreeSize);
      |                                                                                     ^

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 27 ms 560 KB Output is correct

Subtask #2
0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Execution timed out 1099 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 344 KB Output is correct
3 Correct 1 ms 344 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 344 KB Output is correct
3 Correct 1 ms 344 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 38 ms 604 KB Output is correct
8 Correct 48 ms 600 KB Output is correct
9 Correct 32 ms 348 KB Output is correct
10 Correct 30 ms 348 KB Output is correct
11 Correct 36 ms 348 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 344 KB Output is correct
3 Correct 1 ms 344 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 38 ms 604 KB Output is correct
8 Correct 48 ms 600 KB Output is correct
9 Correct 32 ms 348 KB Output is correct
10 Correct 30 ms 348 KB Output is correct
11 Correct 36 ms 348 KB Output is correct
12 Execution timed out 1031 ms 20392 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 344 KB Output is correct
3 Correct 1 ms 344 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 38 ms 604 KB Output is correct
8 Correct 48 ms 600 KB Output is correct
9 Correct 32 ms 348 KB Output is correct
10 Correct 30 ms 348 KB Output is correct
11 Correct 36 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 28 ms 348 KB Output is correct
14 Correct 0 ms 348 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 448 KB Output is correct
21 Correct 38 ms 604 KB Output is correct
22 Correct 55 ms 604 KB Output is correct
23 Correct 32 ms 344 KB Output is correct
24 Correct 30 ms 344 KB Output is correct
25 Correct 36 ms 344 KB Output is correct
26 Correct 32 ms 604 KB Output is correct
27 Correct 48 ms 604 KB Output is correct
28 Correct 22 ms 344 KB Output is correct
29 Correct 30 ms 344 KB Output is correct
30 Correct 34 ms 348 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 344 KB Output is correct
3 Correct 1 ms 344 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 38 ms 604 KB Output is correct
8 Correct 48 ms 600 KB Output is correct
9 Correct 32 ms 348 KB Output is correct
10 Correct 30 ms 348 KB Output is correct
11 Correct 36 ms 348 KB Output is correct
12 Execution timed out 1031 ms 20392 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 27 ms 560 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 344 KB Output is correct
5 Execution timed out 1099 ms 348 KB Time limit exceeded
6 Halted 0 ms 0 KB -