Minimum edges to reverse to make path from a source to a destination
Given a directed graph and a source node and destination node, we need to find how many edges we need to reverse in order to make at least 1 path from the source node to the destination node.
In above graph there were two paths from node 0 to node 6, 0 -> 1 -> 2 -> 3 -> 6 0 -> 1 -> 5 -> 4 -> 6 But for first path only two edges need to be reversed, so answer will be 2 only.
This problem can be solved assuming a different version of the given graph. In this version we make a reverse edge corresponding to every edge and we assign that a weight 1 and assign a weight 0 to original edge. After this modification above graph looks something like below,
Now we can see that we have modified the graph in such a way that, if we move towards original edge, no cost is incurred, but if we move toward reverse edge 1 cost is added. So if we apply Dijkstra’s shortest path on this modified graph from given source, then that will give us minimum cost to reach from source to destination i.e. minimum edge reversal from source to destination.
Below is the code based on above concept.
One more efficient approach to this problem would be by using 0-1 BFS concept.
Below is the implementation of that algorithm:
Time Complexity: O(V+E)
Space Complexity: O(V+2*E)
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