Submission #1215061

#	Time	Username	Problem	Language	Result	Execution time	Memory
1215061		madamadam3	Cat in a tree (BOI17_catinatree)	C++20	0 / 100	0 ms	324 KiB

catinatree

#include <bits/stdc++.h>

using namespace std;

#define all(x) (x).begin(), (x).end()
#define bg(x) (x).begin()
#define en(x) (x).end()

const int MAXN = 200'001, MAXLOG = 18;

int n, d;
vector<vector<int>> adj, up;
vector<int> depth, tin, tout;
int timer = 0;

map<int, set<int>> depth_map;

void dfs(int u, int p) {
    tin[u] = timer++;

    if (u == 0) depth[u] = 0;
    else depth[u] = depth[p] + 1;

    up[u][0] = p;
    for (int i = 1; i < MAXLOG; i++) {
        up[u][i] = up[up[u][i - 1]][i-1];
    }

    // depth_map[depth[u]].push_back(tin[u]);
    depth_map[depth[u]].insert(u);
    for (auto &v : adj[u]) {
        if (v == p) continue;

        dfs(v, u);
    }

    tout[u] = timer;
}

bool is_ancestor(int u, int v) {
    return tin[u] <= tin[v] && tout[u] >= tout[v];
}

int find_lca(int u, int v) {
    if (is_ancestor(u, v)) return u;
    if (is_ancestor(v, u)) return v;

    for (int i = MAXLOG - 1; i >= 0; i--) {
        if (!is_ancestor(up[u][i], v)) {
            u = up[u][i];
        }
    }

    return up[u][0];
}

int dist(int u, int v) {
    return depth[u] + depth[v] - 2 * depth[find_lca(u, v)];
}

// // how many nodes are there in the subtree of u at depth d
// int nodes_depth(int u, int dpth) {
//     int upper =upper_bound(all(depth_map[dpth]), tout[u]) - bg(depth_map[dpth]);
//     int lower = lower_bound(all(depth_map[dpth]), tin[u]) - bg(depth_map[dpth]);

//     return upper - lower;
// }

void task1() { // n <= 18
    int most = 0;
    for (int mask = 0; mask < (1 << n); mask++) {
        vector<int> active;
        for (int bit = 0; bit < n; bit++) if (mask & (1 << bit)) active.push_back(bit);

        bool valid = true;
        for (auto &u : active) {
            for (auto &v : active) {
                if (u == v) continue;
                valid = valid && dist(u, v) >= d;
            }
        }

        if (valid) most = max(most, (int) active.size());
    }

    cout << most;
}

void remove_near(int u, int tim, vector<bool> &vis) {
    if (tim > d) return;
    vis[u] = true;
    depth_map[depth[u]].erase(u);
    
    for (auto &v : adj[u]) {
        if (vis[v]) continue;
        remove_near(v, tim+1, vis);
    }
}

void task2() { // n <= 1500
    int tl = 0;
    int cur_depth = *max_element(all(depth));
    vector<bool> vis(n, false);

    while (cur_depth >= 0) {
        if (depth_map[cur_depth].size() == 0) {
            cur_depth--;
            continue;
        }

        int cur_node = *depth_map[cur_depth].begin();
        remove_near(cur_node, 0, vis);

        tl++;
    }
    cout << tl;
}

void task3() { // n <= 2×10⁵

}

int main() {
    cin.tie(0)->sync_with_stdio(0);

    cin >> n >> d;
    adj.assign(n, vector<int>());
    for (int i = 1; i < n; i++) {
        int xi; cin >> xi;
        adj[i].push_back(xi);
        adj[xi].push_back(i);
    }

    up.assign(n, vector<int>(MAXLOG, 0));
    tin.assign(n, -1); tout.assign(n, -1); depth.assign(n, -1);
    dfs(0, 0);

    task2();
    // if (n <= 18) task1();
    // else if (n <= 1500) task2();
    // else task3();

    return 0;
}

• Subtask 1: 0 / 11
• Subtask 2: 0 / 40
• Subtask 3: 0 / 49