# LeetCode – Number of Connected Components in an Undirected Graph (Java)

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.

**Java Solution - Union-find**

This problem can be solved by using union-find beautifully. Initially, there are n nodes. The nodes that are involved in each edge is merged.

There are k loops and each loop processing the root array costs log(n). Therefore, time complexity is O(k*log(n)).

public int countComponents(int n, int[][] edges) { int count = n; int[] root = new int[n]; // initialize each node is an island for(int i=0; i<n; i++){ root[i]=i; } for(int i=0; i<edges.length; i++){ int x = edges[i][0]; int y = edges[i][1]; int xRoot = getRoot(root, x); int yRoot = getRoot(root, y); if(xRoot!=yRoot){ count--; root[xRoot]=yRoot; } } return count; } public int getRoot(int[] arr, int i){ while(arr[i]!=i){ arr[i]= arr[arr[i]]; i=arr[i]; } return i; } |

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