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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.
1using System;
2using System.Collections.Generic;
3
4public class Solution {
5 public int ReachableNodes(int n, int[][] edges, int[] restricted) {
6 var restrictedSet = new HashSet<int>(restricted);
7 var adjList = new Dictionary<int, List<int>>();
8 for (int i = 0; i < n; i++) adjList[i] = new List<int>();
9 foreach (var edge in edges) {
10 adjList[edge[0]].Add(edge[1]);
11 adjList[edge[1]].Add(edge[0]);
12 }
13 return DFS(0, adjList, restrictedSet, new bool[n]);
14 }
15
16 private int DFS(int node, Dictionary<int, List<int>> adjList, HashSet<int> restricted, bool[] visited) {
17 if (restricted.Contains(node) || visited[node])
18 return 0;
19 visited[node] = true;
20 int count = 1;
21 foreach (int neighbor in adjList[node])
22 count += DFS(neighbor, adjList, restricted, visited);
23 return count;
24 }
25}In this C# solution, we use a Dictionary for the adjacency list, and a DFS method which counts nodes starting from node 0, skipping restricted and already visited nodes.
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.