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Cycle in Undirected Graph


Problem Description

Given an undirected graph having A nodes labelled from 1 to A with M edges given in a form of matrix B of size M x 2 where (B[i][0], B[i][1]) represents two nodes B[i][0] and B[i][1] connected by an edge.

Find whether the graph contains a cycle or not, return 1 if cycle is present else return 0.

NOTE:

  • The cycle must contain atleast three nodes.
  • There are no self-loops in the graph.
  • There are no multiple edges between two nodes.
  • The graph may or may not be connected.
  • Nodes are numbered from 1 to A.
  • Your solution will run on multiple test cases. If you are using global variables make sure to clear them.



Problem Constraints

1 <= A, M <= 3105

1 <= B[i][0], B[i][1] <= A



Input Format

The first argument given is an integer A representing the number of nodes in the graph.

The second argument given is an matrix B of size M x 2 which represents the M edges such that there is a edge between node B[i][0] and node B[i][1].



Output Format

Return 1 if cycle is present else return 0.



Example Input

Input 1:

 A = 5
 B = [  [1. 2]
        [1, 3]
        [2, 3]
        [1, 4]
        [4, 5]
     ]

Input 2:

 A = 3
 B = [  [1. 2]
        [1, 3]
     ]



Example Output

Output 1:

 1

Output 2:

 0



Example Explanation*

Explanation 1:

 There is a cycle in the graph i.e 1 -> 2 -> 3 -> 1 so we will return 1

Explanation 2:

 No cycle present in the graph so we will return 0.



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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