Senior Software Engineer

There is a directed graph consisting of ‘N’ nodes numbered from 0 to ‘N’-1. You are given a list ‘EDGES’ of size ‘M’, consisting of all the edges of this directed graph, and two nodes ‘SRC’ and ‘DEST’ of this graph. Determine whether or not all paths starting from node ‘SRC’ eventually end at node ‘DEST’, that is -:

1. At least one path exists from node ‘SRC’ to node ‘DEST’.

2. If there exists a path from the node ‘SRC’ to a node with no outgoing edges, then that node must be ‘DEST’.

3. There should be a finite number of paths from ‘SRC’ to ‘DEST’.

You should return True if all paths starting from node ‘SRC’ eventually end at node ‘DEST’, Otherwise, return False. See the example for more clarity.

Note :

1. The given graph may have self-loops and parallel edges.

Example :

Consider ‘N’ = 4, ‘EDGES’ = [[0, 1], [0, 3], [1, 2], [3, 2]],  ‘SRC’ = 0 and ‘DEST’ = 2. The given directed graph is shown below.

Here, all the paths that start from node 0 are -:
1. 0->1->2
2. 0->3->2
Both of these paths eventually end at node ‘2’ i.e node ‘DEST’. Thus we should return True.

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