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Cycle in Directed Graph


Problem Description

Given an directed graph having A nodes. A matrix B of size M x 2 is given which represents the M edges such that there is a edge directed from node B[i][0] to node B[i][1].

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

NOTE:

  • The cycle must contain atleast two 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

2 <= A <= 105

1 <= M <= min(200000,A(A-1))

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 a matrix B of size M x 2 which represents the M edges such that there is a edge directed from node B[i][0] to node B[i][1].



Output Format

Return 1 if cycle is present else return 0.



Example Input

Input 1:

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

Input 2:

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



Example Output

Output 1:

 1

Output 2:

 0



Example Explanation*

Explanation 1:

 The given graph contain cycle 1 -> 3 -> 4 -> 1 or the cycle 1 -> 2 -> 4 -> 1

Explanation 2:

 The given graph doesn't contain any cycle.



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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