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Performing Depth-First Search (DFS) is a common way to traverse a tree or graph. We'll start from node 0 and explore as far as possible along each branch before backtracking, avoiding restricted nodes and those already visited.
Time Complexity: O(n) because each node is visited once.
Space Complexity: O(n) for storing the adjacency list and visited nodes information.
1#include <iostream>
2#include <vector>
3#include <unordered_set>
4using namespace std;
5
6int dfs(int node, vector<vector<int>>& adjList, unordered_set<int>& restricted, vector<bool>& visited) {
7 if (restricted.count(node) || visited[node])
8 return 0;
9 visited[node] = true;
10 int count = 1;
11 for (int neighbor : adjList[node]) {
12 count += dfs(neighbor, adjList, restricted, visited);
13 }
14 return count;
15}
16
17int reachableNodes(int n, vector<vector<int>>& edges, vector<int>& restricted) {
18 unordered_set<int> restrictedSet(restricted.begin(), restricted.end());
19 vector<vector<int>> adjList(n);
20 for (auto& edge : edges) {
21 adjList[edge[0]].push_back(edge[1]);
22 adjList[edge[1]].push_back(edge[0]);
23 }
24 vector<bool> visited(n, false);
25 return dfs(0, adjList, restrictedSet, visited);
26}This code builds an adjacency list and uses an unordered set for restricted nodes. It utilizes a DFS function to count and return reachable nodes starting from node 0.
Breadth-First Search (BFS) can also be used to traverse the tree level-by-level. Starting from node 0, visit all neighbors at the current depth before moving on to nodes at the next depth level, while skipping restricted nodes.
Time Complexity: O(n) because each node is processed once using BFS.
Space Complexity: O(n) for adjacency list and other arrays.
1using System.Collections.Generic;
public class Solution {
public int ReachableNodes(int n, int[][] edges, int[] restricted) {
var restrictedSet = new HashSet<int>(restricted);
var adjList = new Dictionary<int, List<int>>();
for (int i = 0; i < n; i++) adjList[i] = new List<int>();
foreach (var edge in edges) {
adjList[edge[0]].Add(edge[1]);
adjList[edge[1]].Add(edge[0]);
}
Queue<int> queue = new Queue<int>();
bool[] visited = new bool[n];
queue.Enqueue(0);
visited[0] = true;
int count = 0;
while (queue.Count > 0) {
int node = queue.Dequeue();
count++;
foreach (int neighbor in adjList[node]) {
if (!restrictedSet.Contains(neighbor) && !visited[neighbor]) {
visited[neighbor] = true;
queue.Enqueue(neighbor);
}
}
}
return count;
}
}This C# solution implements BFS using a Queue. Starting from node 0, each level of nodes is expanded by pushing non-restricted neighbors onto the queue and marking them as visited.