323. Number of Connected Components in an Undirected Graph

最新推荐文章于 2021-12-03 05:59:04 发布

原创最新推荐文章于 2021-12-03 05:59:04 发布 · 597 阅读

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#Depth-first Search #Breadth-first Search #Union Find #Graph #Number of Connected

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本文介绍了一个算法问题：如何计算无向图中连通组件的数量。通过使用并查集（Union-Find）的数据结构，文章提供了一种有效的解决方案，并给出了具体的Java实现代码。

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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.

Union Find的题，find加union之后，roots为-1的是它的根，有几个根就有几个union。代码如下：

public class Solution {
    public int countComponents(int n, int[][] edges) {
        int[] roots = new int[n];
        Arrays.fill(roots, -1);
        for (int[] edge: edges) {
            int x = find(roots, edge[0]);
            int y = find(roots, edge[1]);
            if (x != y)
                roots[x] = y;
        }
        int count = 0;
        for (int root: roots) {
            if (root == - 1) {
                count ++;
            }
        }
        return count;
    }
    
    private int find(int[] roots, int n) {
        while (roots[n] != -1) {
            n = roots[n];
        }
        return n;
    }
}