[leetcode323]Number of Connected Components in an Undirected Graph

Question:

Given n nodes labeled from 0 to n - 1 and a list of undirected edges (each edge is a pair of nodes), write a function to find the number of connected components in an undirected graph.

Example 1:

     0          3
     |          |
     1 --- 2    4

Given n = 5 and edges = [[0, 1], [1, 2], [3, 4]], return 2.

Example 2:

     0           4
     |           |
     1 --- 2 --- 3

Given n = 5 and edges = [[0, 1], [1, 2], [2, 3], [3, 4]], return 1.

Note:
You can assume that no duplicate edges will appear in edges. Since all edges are undirected, [0, 1] is the same as [1, 0] and thus will not appear together in edges.

分析：

就是根据节点的个数，和边缘信息，判断连通图的个数。

如果节点为0或者没有边，则连通图个数为0；

如果节点个数为1且只有1条边，则连通图个数为1；

有多个节点和多个边时则需要判断某个节点和边是否访问过，为每个节点建立邻接表，然后深度优先标记下一条相连的边。

代码如下：

public class Solution {
    public int countComponents(int n, int[][] edges) {
        if (n <= 0 || edges == null) {
            return 0;
        }
         
        if (n == 1 && edges.length == 0) {
            return 1;
        }
         
        int result = 0;
        boolean[] visited = new boolean[n];
         
        // step 1: create the adj list from edge list
        List[] adjList = new List[n];
        for (int i = 0; i < n; i++) {
            adjList[i] = new ArrayList<>();
        }
         
        for (int[] edge : edges) {
            int from = edge[0];
            int to = edge[1];
             
            adjList[from].add(to);
            adjList[to].add(from);
        }
         
        // step 2: calculate the number of cc
        for (int i = 0; i < n; i++) {
            if (!visited[i]) {
                result++;
                countCCHelper(i, adjList, visited);
            }
        }
         
        return result;
    }
     
    private void countCCHelper(int node, List[] adjList, boolean[] visited) {
        if (visited[node]) {
            return;
        }
         
        visited[node] = true;
         
        List neighbors = adjList[node];
         
        for (int neighbor : neighbors) {
            countCCHelper(neighbor, adjList, visited);
        }
    }
}