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Submission #668102

# Submission time Handle Problem Language Result Execution time Memory
668102 2022-12-02T18:26:37 Z tibinyte Lampice (COCI19_lampice) C++17
110 / 110
 3743 ms 10324 KB 
#include <bits/stdc++.h>

using namespace std;

const int mod = 1e9 + 9;
const int base = 29;

int add(int x, int y)
{
    x += y;
    if (x >= mod)
    {
        return x - mod;
    }
    return x;
}

int mult(int x, int y)
{
    return (int64_t)x * y % mod;
}

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
int random(int st, int dr)
{
    uniform_int_distribution<mt19937::result_type> gen(st, dr);
    return gen(rng);
}
struct lampice
{
    int n;
    vector<vector<int>> g;
    vector<char> colors;
    vector<bool> seen;
    vector<int> sz;
    vector<int> depth;
    vector<int> hashup;
    vector<int> hashdown;
    vector<int> par;
    vector<int> nodes;
    vector<int> neortodox;
    vector<int> dp;
    void init(int _n)
    {
        n = _n;
        g = vector<vector<int>>(n + 1);
        colors = vector<char>(n + 1);
        seen = vector<bool>(n + 1);
        dp = neortodox = nodes = sz = depth = hashup = hashdown = par = vector<int>(n + 1);
    }
    void set_color(int pos, char x)
    {
        colors[pos] = x;
    }
    void add_edge(int a, int b)
    {
        g[a].push_back(b);
        g[b].push_back(a);
    }
    void dfs_size(int node, int parent)
    {
        sz[node] = 1;
        for (auto i : g[node])
        {
            if (i != parent && !seen[i])
            {
                dfs_size(i, node);
                sz[node] += sz[i];
            }
        }
    }
    int find_centroid(int node, int parent, int size)
    {
        for (auto i : g[node])
        {
            if (i != parent && !seen[i] && sz[i] > size / 2)
            {
                return find_centroid(i, node, size);
            }
        }
        return node;
    }
    int solve(int node, int k)
    {
        int max_depth = 0;
        function<void(int, int, int)> dfs_init = [&](int node, int parent, int d)
        {
            par[node] = parent;
            depth[node] = d;
            dp[node] = 1;
            max_depth = max(max_depth, d);
            for (auto i : g[node])
            {

                if (i != parent && !seen[i])
                {
                    dfs_init(i, node, d + 1);
                    dp[node] = max(dp[node], dp[i] + 1);
                }
            }
            int mx1 = 0, mx2 = 0;
            for (auto i : g[node])
            {
                if (i != parent && !seen[i])
                {
                    if (dp[i] > mx1)
                    {
                        mx2 = mx1;
                        mx1 = dp[i];
                    }
                    else
                    {
                        if (dp[i] > mx2)
                        {
                            mx2 = dp[i];
                        }
                    }
                }
            }
            neortodox[node] = mx1 + mx2 + 1;
        };
        dfs_init(node, 0, 0);
        if (neortodox[node] < k)
        {
            return 0;
        }
        vector<int> power(max_depth + 1);
        power[0] = 1;
        for (int i = 1; i <= max_depth; ++i)
        {
            power[i] = mult(power[i - 1], base);
        }
        function<void(int, int)> compute_hash = [&](int node, int parent)
        {
            hashup[node] = add(mult(base, hashup[parent]), colors[node] - 'a' + 1);
            hashdown[node] = add(hashdown[parent], mult(power[depth[node]], (colors[node] - 'a' + 1)));
            for (auto i : g[node])
            {
                if (i != parent && !seen[i])
                {
                    compute_hash(i, node);
                }
            }
        };
        compute_hash(node, 0);
        function<int(int, int)> get_hashup = [&](int a, int b)
        {
            int c = par[b];
            return add(hashup[a], mod - mult(hashup[c], power[depth[a] - depth[c]]));
        };
        unordered_multiset<int> exista;
        function<void(int, int, int, int)> add_subtree = [&](int node, int parent, int root, int d)
        {
            if (d + d <= k)
            {
                exista.insert(get_hashup(node, root));
            }
            for (auto i : g[node])
            {
                if (i != parent && !seen[i])
                {
                    add_subtree(i, node, root, d + 1);
                }
            }
        };
        function<void(int, int, int, int)> remove_subtree = [&](int node, int parent, int root, int d)
        {
            if (d + d <= k)
            {
                exista.erase(exista.find(get_hashup(node, root)));
            }
            for (auto i : g[node])
            {
                if (i != parent && !seen[i])
                {
                    remove_subtree(i, node, root, d + 1);
                }
            }
        };
        bool este = false;
        int m = 1;
        nodes[1] = node;
        function<void(int, int, int)> dfs = [&](int node, int parent, int d)
        {
            if (este)
            {
                return;
            }
            nodes[++m] = node;
            int t = 2 * d - k;
            int l = k - d;
            if (l >= 0 && t >= 0)
            {
                if (l == 0)
                {
                    if (hashup[node] == hashdown[node])
                    {
                        este = true;
                    }
                }
                else
                {
                    int qui = nodes[m - l];
                    if (hashup[qui] == hashdown[qui] && exista.count(get_hashup(node, nodes[m - l + 1])))
                    {
                        este = true;
                    }
                }
            }
            for (auto i : g[node])
            {
                if (i != parent && !seen[i])
                {
                    dfs(i, node, d + 1);
                }
            }
            --m;
        };
        for (auto i : g[node])
        {
            if (!seen[i])
            {
                add_subtree(i, node, i, 1);
            }
        }
        for (auto i : g[node])
        {
            if (!seen[i])
            {
                remove_subtree(i, node, i, 1);
                dfs(i, node, 2);
                if (este)
                {
                    break;
                }
                add_subtree(i, node, i, 1);
            }
        }
        return este;
    }
    int decomp(int node, int k)
    {
        dfs_size(node, 0);
        node = find_centroid(node, 0, sz[node]);
        int ans = solve(node, k);
        seen[node] = true;
        for (auto i : g[node])
        {
            if (!seen[i])
            {
                ans = max(ans, decomp(i, k));
            }
        }
        return ans;
    }
    void reinit()
    {
        seen = vector<bool>(n + 1);
    }
};
int32_t main()
{
    cin.tie(nullptr)->sync_with_stdio(false);
    int n;
    cin >> n;
    lampice g;
    g.init(n);
    for (int i = 1; i <= n; ++i)
    {
        char x;
        cin >> x;
        g.set_color(i, x);
    }
    for (int i = 1; i < n; ++i)
    {
        int u, v;
        cin >> u >> v;
        g.add_edge(u, v);
    }
    int ans = 1;
    int st = 1, dr = n / 2;
    while (st <= dr)
    {
        int mid = (st + dr) / 2;
        if (g.decomp(1, 2 * mid))
        {
            ans = max(ans, 2 * mid);
            st = mid + 1;
        }
        else
        {
            dr = mid - 1;
        }
        g.reinit();
    }
    st = max(1, ans / 2), dr = n / 2;
    while (st <= dr)
    {
        int mid = (st + dr) / 2;
        if (g.decomp(1, 2 * mid + 1))
        {
            ans = max(ans, 2 * mid + 1);
            st = mid + 1;
        }
        else
        {
            dr = mid - 1;
        }
        g.reinit();
    }
    cout << ans;
}

Subtask #1
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 340 KB Output is correct
2 Correct 8 ms 340 KB Output is correct
3 Correct 27 ms 516 KB Output is correct
4 Correct 43 ms 596 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct

Subtask #2
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1767 ms 8104 KB Output is correct
2 Correct 1214 ms 8276 KB Output is correct
3 Correct 685 ms 9548 KB Output is correct
4 Correct 743 ms 9912 KB Output is correct
5 Correct 1190 ms 9608 KB Output is correct
6 Correct 629 ms 10324 KB Output is correct

Subtask #3
31.0 / 31.0

# Verdict Execution time Memory Grader output
1 Correct 3743 ms 7268 KB Output is correct
2 Correct 2590 ms 7612 KB Output is correct
3 Correct 3022 ms 7184 KB Output is correct
4 Correct 2377 ms 8988 KB Output is correct
5 Correct 2261 ms 7732 KB Output is correct
6 Correct 2554 ms 6520 KB Output is correct

Subtask #4
37.0 / 37.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 340 KB Output is correct
2 Correct 8 ms 340 KB Output is correct
3 Correct 27 ms 516 KB Output is correct
4 Correct 43 ms 596 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1767 ms 8104 KB Output is correct
9 Correct 1214 ms 8276 KB Output is correct
10 Correct 685 ms 9548 KB Output is correct
11 Correct 743 ms 9912 KB Output is correct
12 Correct 1190 ms 9608 KB Output is correct
13 Correct 629 ms 10324 KB Output is correct
14 Correct 3743 ms 7268 KB Output is correct
15 Correct 2590 ms 7612 KB Output is correct
16 Correct 3022 ms 7184 KB Output is correct
17 Correct 2377 ms 8988 KB Output is correct
18 Correct 2261 ms 7732 KB Output is correct
19 Correct 2554 ms 6520 KB Output is correct
20 Correct 1388 ms 7320 KB Output is correct
21 Correct 1201 ms 7268 KB Output is correct
22 Correct 1976 ms 6600 KB Output is correct
23 Correct 485 ms 7428 KB Output is correct
24 Correct 2069 ms 8184 KB Output is correct
25 Correct 2531 ms 7976 KB Output is correct
26 Correct 3206 ms 7924 KB Output is correct
27 Correct 3196 ms 6968 KB Output is correct
28 Correct 1749 ms 7660 KB Output is correct
29 Correct 1623 ms 7776 KB Output is correct
30 Correct 2453 ms 8764 KB Output is correct
31 Correct 2792 ms 7896 KB Output is correct
32 Correct 1886 ms 9012 KB Output is correct
33 Correct 802 ms 7592 KB Output is correct