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.

這道題和numbers of islands II 是一個思路，一個count初始化為n，union find每次有新的edge就union兩個節點，如果兩個節點(u, v)原來不在一個連通圖裏面就減少count並且連起來，如果原來就在一個圖裏面就不管。用一個索引array來做，union find優化就是加權了，每次把大的樹的root當做parent，小的樹的root作為child。

Java:

public class Solution {
    public int countComponents(int n, int[][] edges) {
        int count = n;
        // array to store parent
        init(n, edges);
        for(int[] edge : edges) {
            int root1 = find(edge[0]);
            int root2 = find(edge[1]);
            if(root1 != root2) {
                union(root1, root2);
                count--;
            }
        }
        return count;
    }
    
    int[] map;
    private void init(int n, int[][] edges) {
        map = new int[n];
        for(int[] edge : edges) {
            map[edge[0]] = edge[0];
            map[edge[1]] = edge[1];
        }
    }
    
    private int find(int child) {
        while(map[child] != child) child = map[child];
        return child;
    }
    
    private void union(int child, int parent) {
        map[child] = parent;
    }
}

[LeetCode] 323. Number of Connected Components in an Undirected Graph 無向圖中的連通區域的個數