oj.uz

Submission #668106

# Submission time Handle Problem Language Result Execution time Memory
668106 2022-12-02T18:42:34 Z tibinyte Lampice (COCI19_lampice) C++17
110 / 110
 3437 ms 10288 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;
    }
    bool 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;
    }
    bool 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 (ans)
            {
                break;
            }
            if (!seen[i])
            {
                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 2 ms 340 KB Output is correct
2 Correct 6 ms 340 KB Output is correct
3 Correct 24 ms 468 KB Output is correct
4 Correct 30 ms 596 KB Output is correct
5 Correct 1 ms 288 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 1513 ms 8036 KB Output is correct
2 Correct 864 ms 8408 KB Output is correct
3 Correct 362 ms 9552 KB Output is correct
4 Correct 446 ms 9956 KB Output is correct
5 Correct 1067 ms 9560 KB Output is correct
6 Correct 224 ms 10288 KB Output is correct

Subtask #3
31.0 / 31.0

# Verdict Execution time Memory Grader output
1 Correct 3437 ms 7324 KB Output is correct
2 Correct 2300 ms 7624 KB Output is correct
3 Correct 2360 ms 7272 KB Output is correct
4 Correct 1752 ms 8264 KB Output is correct
5 Correct 1601 ms 7208 KB Output is correct
6 Correct 1918 ms 6008 KB Output is correct

Subtask #4
37.0 / 37.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 340 KB Output is correct
2 Correct 6 ms 340 KB Output is correct
3 Correct 24 ms 468 KB Output is correct
4 Correct 30 ms 596 KB Output is correct
5 Correct 1 ms 288 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1513 ms 8036 KB Output is correct
9 Correct 864 ms 8408 KB Output is correct
10 Correct 362 ms 9552 KB Output is correct
11 Correct 446 ms 9956 KB Output is correct
12 Correct 1067 ms 9560 KB Output is correct
13 Correct 224 ms 10288 KB Output is correct
14 Correct 3437 ms 7324 KB Output is correct
15 Correct 2300 ms 7624 KB Output is correct
16 Correct 2360 ms 7272 KB Output is correct
17 Correct 1752 ms 8264 KB Output is correct
18 Correct 1601 ms 7208 KB Output is correct
19 Correct 1918 ms 6008 KB Output is correct
20 Correct 1077 ms 6716 KB Output is correct
21 Correct 1032 ms 6684 KB Output is correct
22 Correct 1642 ms 6156 KB Output is correct
23 Correct 455 ms 6760 KB Output is correct
24 Correct 1679 ms 7596 KB Output is correct
25 Correct 1696 ms 7484 KB Output is correct
26 Correct 2368 ms 7576 KB Output is correct
27 Correct 2798 ms 6484 KB Output is correct
28 Correct 1347 ms 7136 KB Output is correct
29 Correct 1367 ms 7144 KB Output is correct
30 Correct 1968 ms 8160 KB Output is correct
31 Correct 1650 ms 7428 KB Output is correct
32 Correct 1319 ms 8556 KB Output is correct
33 Correct 614 ms 6968 KB Output is correct