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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.
1from collections import defaultdict
2
3def reachableNodes(n, edges, restricted):
4 adj_list = defaultdict(list)
5 restricted_set = set(restricted)
6 for a, b in edges:
7 adj_list[a].append(b)
8 adj_list[b].append(a)
9
10 def dfs(node, visited):
11 if node in visited or node in restricted_set:
12 return 0
13 visited.add(node)
14 count = 1
15 for neighbor in adj_list[node]:
16 count += dfs(neighbor, visited)
17 return count
18
19 return dfs(0, set())The Python solution uses defaultdict for adjacency list storage, and a set to keep track of visited nodes. DFS traverses from node 0 while avoiding restricted 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.