# Graph Valid Tree

ID: 178; medium

## Solution 1 (Java)

``````public class Solution {
/**
* @param n: An integer
* @param edges: a list of undirected edges
* @return: true if it's a valid tree, or false
*/
public boolean validTree(int n, int[][] edges) {
// condition check
if (n == 0) return false;
if (n - edges.length != 1) return false;

// 1. construct graph
Map<Integer, Set<Integer>> graph = new HashMap<>();
for (int i = 0; i < n; i++) {
graph.put(i, new HashSet<Integer>());
}
for (int[] e : edges) {
}

// 2. BFS
Queue<Integer> q = new ArrayDeque<>();
Set<Integer> visited = new HashSet<>();
q.offer(0);

while (!q.isEmpty()) {
int curr = q.poll();
for (int neighbor : graph.get(curr)) {
if (!visited.contains(neighbor)) {
q.offer(neighbor);
}
}
}

// condition check
return visited.size() == n;
}
}``````

### Notes

• In order to be a valid tree, the graph needs to satisfy the following three conditions:

• The number of nodes - the number of edges = 1

• No cycle

• Only one connected graph

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