# Graph Valid Tree

{% embed url="<https://www.lintcode.com/problem/178/>" %}

## Solution 1 (Java)

```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) {
            graph.get(e[0]).add(e[1]);
            graph.get(e[1]).add(e[0]);
        }

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

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


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://blog.yushunchen.com/algo/bfs/2.-connected-graph-and-topologic-sorting/graph-valid-tree.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.