Submission #702119

#	Time	Username	Problem	Language	Result	Execution time	Memory
702119		Shreyan_Paliwal	Love Polygon (BOI18_polygon)	C++17	0 / 100	2069 ms	17228 KiB

polygon

#include <iostream>
#include <vector>
#include <map>
using namespace std;

const int maxn = 1e5 + 5;

int n;
int par[maxn];

int vis[maxn];
vector<int> cycle_starts;

vector<int> adj[maxn];

bool dfs_find_cycle(int nd) {
    vis[nd] = 1; // current vertex visited

    if (vis[par[nd]] == 0) { // if next vertex unvisited dfs_find_cycle into it
        if (dfs_find_cycle(par[nd])) {
            vis[nd] = 2;
            return true;
        }
    } else if (vis[par[nd]] == 1) { // if visited next vertex in current iteration
        cycle_starts.push_back(nd);
        vis[nd] = 2;
        return true; // back out
    }

    vis[nd] = 2; // mark current vertex visited
    return false;
}

void find_components() {
    for (int i = 0; i < n; i++) {
        if (vis[i]) continue;
        dfs_find_cycle(i);
    }
}

void read_input() {
    cin >> n;
    
    map<string, int> m;
    int cnt = 0;
    for (int i = 0; i < n; i++) {
        string a, b; cin >> a >> b;
        // if (m.find(a) == m.end()) cout << a << ' ' << cnt << endl;
        if (m.find(a) == m.end())
            m[a] = cnt++;
        // if (m.find(b) == m.end()) cout << b << ' ' << cnt << endl;
        if (m.find(b) == m.end())
            m[b] = cnt++;
        par[m[a]] = m[b];

        adj[m[a]].push_back(m[b]);
        adj[m[b]].push_back(m[a]);
    }
}

int cur_root = -1;

int F[maxn], G[maxn];
int f(int x, int par); int g(int x, int par);
int f(int x, int par) {
    F[x] = 1;
    for (auto i : adj[x])
        if (i != par && i != cur_root)
            F[x] += g(i, x);
    // cout << "f " << x << ' ' << F[x] << endl;
    return F[x];
}
int g(int x, int par) {
    G[x] = f(x, par) - 1;
    int max_fg = 0;
    for (auto i : adj[x])
        if (i != par && i != cur_root)
            max_fg = max(max_fg, f(i, x) - g(i, x));
    G[x] += max_fg;
    // cout << "g " << x << ' ' << G[x] << endl;
    return G[x];
}

int main() {
    // freopen("main.in", "r", stdin);

    read_input();

    find_components();

    fill(F, F + maxn, -1);
    fill(G, G + maxn, -1);
    int sum_root_g = 0;
    for (auto i : cycle_starts) {
        // cycle starts @ i & size 1
        if (i == par[i]) {
            cur_root = i;
            sum_root_g += g(i, i);
        }

        // size 2
        else if (i == par[par[i]]) {
            // cout << sum_root_g << ' ';
            // optimal to take arc
            // i, par[i]
            for (auto j : adj[i])
                if (j != par[i])
                    sum_root_g += g(j, i);
            for (auto j : adj[par[i]])
                if (j != i)
                    sum_root_g += g(j, par[j]);
            sum_root_g += 2;
            // cout << sum_root_g << endl;
        }

        else {
            // cout << i << endl;
            // par[i] --> ... --> i --> par[i]
            cur_root = par[i];

            // take arc
            int with_arc = 1;
            for (auto j : adj[i])
                if (j != par[i])
                    with_arc += g(j, i);
            for (auto j : adj[par[i]])
                if (j != i)
                    with_arc += g(j, par[i]);
            // cout << "with arc " << i << ' ' << par[i] << ' ' << with_arc << endl;

        
            int without_arc = g(par[i], i);
            // cout << "without arc " << i << ' ' << par[i] << ' ' << without_arc << endl;

            sum_root_g += max(with_arc, without_arc);
        }
    }

    cout << n - sum_root_g << endl;

    return 0;
}

• Subtask 1: 0 / 21
• Subtask 2: 0 / 25
• Subtask 3: 0 / 29
• Subtask 4: 0 / 25