oj.uz

Submission #253081

# Submission time Handle Problem Language Result Execution time Memory
253081 2020-07-26T21:15:50 Z Kubin Tropical Garden (IOI11_garden) C++17
100 / 100
 264 ms 40448 KB 
// this is O(n+m+q) instead of O(m+nq) like the model solution
// why?

#include <functional>
#include <cstdint>
#include <cassert>
#include <climits>
#include <vector>
#include <array>

using namespace std;

const size_t nil = SIZE_MAX;

void answer(int);


void count_routes(int _n, int _m, int _t, int E[][2], int _q, int K[])
{
    const size_t n = _n, m = _m, target = _t, q = _q;

    // get edges
    vector<array<size_t, 2>> to(n, {nil, nil});
    for(size_t i = 0; i < m; i++)
    {
        size_t u = E[i][0], v = E[i][1];
        if(to[u][0] == nil)
            to[u][0] = v;
        else if(to[u][1] == nil)
            to[u][1] = v;
        if(to[v][0] == nil)
            to[v][0] = u;
        else if(to[v][1] == nil)
            to[v][1] = u;
    }

    vector<size_t> F(2*n, nil);
    // vertex i+n is vertex after coming through best edge of vertex i
    auto nfix = [&](size_t v, size_t u) {
        return v + (to[v][0] == u ? n : 0);
    };
    for(size_t u = 0; u < n; u++)
    {
        F[u] = nfix(to[u][0], u);
        F[u+n] = nfix(to[u][1] == nil ? to[u][0] : to[u][1], u);
    }

    // rho computation
    vector<bool> vis(2*n), on(2*n);
    vector<size_t> st; st.reserve(2*n);

    vector<size_t> top(2*n, nil);
    vector<int> lambda(2*n), omega(2*n);

    vector<vector<size_t>> G(2*n);

    for(size_t s = 0; s < 2*n; s++)
    {
        G[F[s]].push_back(s);
        // cout << s << " " << F[s] << endl;
        if(vis[s])
            continue;

        assert(st.empty());
        size_t u = s;
        while(true)
        {
            vis[u] = on[u] = true;
            st.push_back(u);

            if(on[F[u]])
            {
                vector<size_t> cycle;
                while(true)
                {
                    auto v = st.back(); st.pop_back();
                    on[v] = false;
                    cycle.push_back(v);
                    if(v == F[u])
                        break;
                }
                for(auto v : cycle)
                    omega[v] = cycle.size(), top[v] = v;
            }
            else if(vis[F[u]])
            {
                lambda[u] = lambda[F[u]] + 1;
                top[u] = top[F[u]];
            }
            else
                { u = F[u]; continue; }
            break;
        }
        while(not st.empty())
        {
            auto v = st.back(); st.pop_back();
            lambda[v] = lambda[F[v]] + 1;
            top[v] = top[F[v]];
            on[v] = false;
        }
    }


    // queries

    vector<pair<vector<int>, int>> tabs(2*n);
    function<pair<vector<int>, int>(size_t)> get_tab = [&](size_t t) -> pair<vector<int>, int> {
        if(not tabs[t].first.empty())
            return tabs[t];
        else if(lambda[t])
        {
            vector<int> cnt;
            function<void(size_t, size_t)> dfs = [&](size_t u, size_t d) {
                while(cnt.size() <= d) cnt.push_back(0);
                cnt[d] += (u < n);
                for(auto v : G[u])
                    dfs(v, d + 1);
            };
            dfs(t, 0);
            return tabs[t] = {cnt, 0};
        }
        else
        {
            size_t u = t;
            vector<int> cnt(omega[t]);
            for(int i = 0; i < omega[t]; i++, u = F[u])
            {
                int sh = (i ? omega[t] - i : 0);
                cnt[sh] += (u < n);
                sh++;
                for(auto v : G[u])
                  if(lambda[v])
                {
                    auto [sub, _] = get_tab(v);
                    (void)_;
                    while(cnt.size() < sh + sub.size()) cnt.push_back(0);
                    for(size_t d = 0; d < sub.size(); d++)
                        cnt[sh + d] += sub[d];
                }
            }
            for(size_t i = omega[t]; i < cnt.size(); i++)
                cnt[i] += cnt[i - omega[t]];
            return tabs[t] = {cnt, omega[t]};
        }
    };

    auto count = [&](int k, size_t t) {
        auto [T, mod] = get_tab(t);
        if(mod)
        {
            if((size_t)k >= T.size())
                k = (k - T.size()) % mod + T.size();
            while((size_t)k >= T.size())
                k -= mod;
            return T[k];
        }
        else
            return (size_t)k < T.size() ? T[k] : 0;
    };

    for(size_t que = 0; que < q; que++)
    {
        int k = K[que];
        answer(count(k, target) + count(k, target + n));
    }
}

Subtask #1
49.0 / 49.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 640 KB Output is correct
2 Correct 1 ms 512 KB Output is correct
3 Correct 1 ms 640 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 1 ms 256 KB Output is correct
6 Correct 1 ms 768 KB Output is correct
7 Correct 0 ms 384 KB Output is correct
8 Correct 1 ms 512 KB Output is correct
9 Correct 3 ms 640 KB Output is correct

Subtask #2
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 640 KB Output is correct
2 Correct 1 ms 512 KB Output is correct
3 Correct 1 ms 640 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 1 ms 256 KB Output is correct
6 Correct 1 ms 768 KB Output is correct
7 Correct 0 ms 384 KB Output is correct
8 Correct 1 ms 512 KB Output is correct
9 Correct 3 ms 640 KB Output is correct
10 Correct 0 ms 384 KB Output is correct
11 Correct 12 ms 5504 KB Output is correct
12 Correct 27 ms 8832 KB Output is correct
13 Correct 46 ms 25140 KB Output is correct
14 Correct 99 ms 30072 KB Output is correct
15 Correct 125 ms 30504 KB Output is correct
16 Correct 120 ms 21496 KB Output is correct
17 Correct 97 ms 17784 KB Output is correct
18 Correct 26 ms 8832 KB Output is correct
19 Correct 123 ms 30072 KB Output is correct
20 Correct 122 ms 30456 KB Output is correct
21 Correct 91 ms 21240 KB Output is correct
22 Correct 78 ms 17916 KB Output is correct
23 Correct 104 ms 33392 KB Output is correct

Subtask #3
31.0 / 31.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 640 KB Output is correct
2 Correct 1 ms 512 KB Output is correct
3 Correct 1 ms 640 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 1 ms 256 KB Output is correct
6 Correct 1 ms 768 KB Output is correct
7 Correct 0 ms 384 KB Output is correct
8 Correct 1 ms 512 KB Output is correct
9 Correct 3 ms 640 KB Output is correct
10 Correct 0 ms 384 KB Output is correct
11 Correct 12 ms 5504 KB Output is correct
12 Correct 27 ms 8832 KB Output is correct
13 Correct 46 ms 25140 KB Output is correct
14 Correct 99 ms 30072 KB Output is correct
15 Correct 125 ms 30504 KB Output is correct
16 Correct 120 ms 21496 KB Output is correct
17 Correct 97 ms 17784 KB Output is correct
18 Correct 26 ms 8832 KB Output is correct
19 Correct 123 ms 30072 KB Output is correct
20 Correct 122 ms 30456 KB Output is correct
21 Correct 91 ms 21240 KB Output is correct
22 Correct 78 ms 17916 KB Output is correct
23 Correct 104 ms 33392 KB Output is correct
24 Correct 1 ms 384 KB Output is correct
25 Correct 13 ms 5504 KB Output is correct
26 Correct 25 ms 8824 KB Output is correct
27 Correct 236 ms 25012 KB Output is correct
28 Correct 100 ms 30072 KB Output is correct
29 Correct 126 ms 30584 KB Output is correct
30 Correct 103 ms 21500 KB Output is correct
31 Correct 90 ms 17788 KB Output is correct
32 Correct 29 ms 8832 KB Output is correct
33 Correct 112 ms 30076 KB Output is correct
34 Correct 152 ms 30456 KB Output is correct
35 Correct 90 ms 21112 KB Output is correct
36 Correct 85 ms 17912 KB Output is correct
37 Correct 124 ms 33392 KB Output is correct
38 Correct 264 ms 40448 KB Output is correct