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Number of Connected Components in an Undirected Graph (Python)

66. Number of Connected Components in an Undirected Graph


Question Link : check here

Givennnodes labeled from0ton - 1and 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

Givenn = 5andedges = [[0, 1], [1, 2], [3, 4]], return2.

Example 2:

     0           4

     |           |

     1 --- 2 --- 3

Givenn = 5andedges = [[0, 1], [1, 2], [2, 3], [3, 4]], return1.

Note:

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


Solution :

class Solution:
    def counComponents(self, n: int, edges : List[List[int]]) -> int:
        p = [ i for i in range(n)]
        r = [1] * n
        
        def find(n1) :
            ans = n1
            
            while ans != p[ans] :
                p[ans] = p[p[ans]]
                ans = p[ans]
            
            return ans
        
        def union(n1, n2):
            p1, p2 = find(n1), find(n2)
            
            if p1==p2:
                return 0
            
            if r[p2] > r[p1]:
                p[p1] = p2
                r[p2] += r[p1]
                
            else:
                p[p2] = p1
                r[p1] += r[p2]
                
            return 1
        
        ans = n #5 - 1 - 1 - 1 = 2
        
        for n1, n2 in edges:
            ans -= union(n1,n2)
        return ans

        

        

       Explaination :



        

                

        

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