UVA_10459.cpp

/*This problem asks us to find all possible paths which form the diameter of the given tree. 
So first we do a BFS/DFS from any vertex uu, and find the vertex xx which is farthest from ss.
 Note xx must be an end of a longest path. Then, we do another BFS/DFS traversal from xx to 
 find all vertices {s}{s}which are farthest from xx. Every single vertex here, including xx, 
 is one worst root, and the mid point, or points if the length is even, of every single path 
 is/are the best roots. After that, we need to do a third traversal from any vertex in {s} 
 to find any remaining worst roots which are close to xx, and so were not discovered by our 
 second traversal.*/

#include <bits/stdc++.h>

using namespace std;

void DFS(int node, const vector<vector<int>> &adj_list,
         vector<bool> &visited, 
         int len, int &long_dist, int start, vector<int> &path,
         set<int> &best, set<int> &worst) {
    path.push_back(node);
    visited[node] = true;

    if (len > long_dist) {
        best.clear();
        worst.clear();

        long_dist = len;
    }

    if (len == long_dist) {
        worst.insert(node);
        worst.insert(start);

        if (len % 2 == 0)
            best.insert(path[len / 2]);
        else {
            best.insert(path[len / 2]);
            best.insert(path[len / 2 + 1]);
        }
    }

    for (int dest : adj_list[node])
        if (!visited[dest]) {
            DFS(dest, adj_list, visited, len + 1, long_dist,
                start, path, best, worst);
        }

    visited[node] = false;
    path.pop_back();
}

int main() {
    int N;
    while (scanf("%d", &N) == 1) {
        vector<vector<int>> adj_list(N);
        for (int i = 0; i < N; i++) {
            int K;
            scanf("%d", &K);
            for (int j = 0; j < K; j++) {
                int node;
                scanf("%d", &node);
                adj_list[i].push_back(node - 1);
            }
        }

        vector<bool> visited(N, false);

        queue<pair<int, int>> q;
        visited[0] = true;
        q.push({0, 0});
        int long_dist = 0;
        
        int potential = 0;
        while (!q.empty()) {
            auto front = q.front();
            q.pop();
            int u = front.first;
            int len = front.second;
            if (len > long_dist) {
                long_dist = len;
                potential = u;
            }

            for (int v : adj_list[u])
                if (!visited[v]) {
                    visited[v] = true;
                    q.push({v, len + 1});
                }
        }


        visited.assign(N, false);
        vector<int> path;
        
        set<int> best, worst;

        DFS(potential, adj_list, visited, 0,
            long_dist, potential, path, best, worst);

        for (int node : worst)
            if (node != potential) {
                potential = node;
                break;
            }

        visited.assign(N, false);
        path.clear();
        DFS(potential, adj_list, visited, 0,
            long_dist, potential, path, best, worst);


        printf("Best Roots  :");
        for (int root : best)
            printf(" %d", root + 1);
        printf("\n");

        printf("Worst Roots :");
        for (int root : worst)
            printf(" %d", root + 1);
        printf("\n");
    }
    return 0;
}