Detect Cycle In A Directed Graph

Moderate

0/80

Average time to solve is 30m

139 upvotes

Asked in companies

Problem statement

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

Find whether the graph contains a cycle or not, return true if a cycle is present in the given directed graph else return false.

For Example :

In the following directed graph has a cycle i.e. B->C->E->D->B.

Note :

1. The cycle must contain at least two nodes.
2. It is guaranteed that the given graph has no self-loops in the graph.
3. The graph may or may not be connected.
4. Nodes are numbered from 1 to N.
5. Your solution will run on multiple test cases. If you are using global variables make sure to clear them.

Detailed explanation ( Input/output format, Notes, Images )

Input Format :

The first line of input contains an integer 'T' representing the number of the test case. Then the test cases are as follows.

The first line of each test case argument given is an integer ‘N’ representing the number of nodes in the graph.

The second line of each test case contains a given integer ‘M’ representing the number of edges. 

The next ‘M’ lines in each test case contain a matrix ‘EDGES’ of size M x 2 which represents the ‘M’ edges such that there is an edge directed from node EDGES[i][0] to node EDGES[i][1].

Output Format :

For each test case, print true if a cycle is present in the given directed graph else print false.

Note :

You do not need to print anything; It has already been taken care of.

Constraints :

1 ≤ T ≤ 5

2 <= N <= 100
1 <= M <= min(100,N(N-1)/2)
1 <= EDGES[i][0], EDGES[i][1] <= N

Where ‘T’ is the number of test cases.

Time Limit: 1 sec

Sample Input 1 :

Sample Output 1 :

true

Explanation For Input 1 :

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

Sample Input 2 :

Sample Output 2 :

false
false

Explanation For Input 2 :

The given graphs don’t contain any cycle.

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