Given A Graph, Build A New One With Reversed Edges
Given a strongly connected directed graph, build a new graph with the same number of nodes but every edge reversed. This is also called transposing a graph.
Input: Any node of this graph:
Output: Any node of the new:
Input Parameters: Function has one argument pointing to a node of the given graph.
Output: Return any node of the new graph.
● Value in any node will be a unique integer between 1 and number of nodes, inclusive.
● No multiple edges (connecting any pair of nodes in one direction) or self loops (edges connecting a node with itself) in the input graph.
● You are not allowed to modify the given graph. Return a newly built graph.
To solve this problem simple DFS will work. We provided one sample solution.
Our DFS-like algorithm takes O(n + m) time where n is the number of nodes and m is the number of edges.
Without multiple edges or self loops (which problem statement guarantees) the number of edges m can be as big as n*(n-1) in the worst case. So O(n^2) is the time complexity in terms of n.
Auxiliary Space Used:
O(n) for the call stack used by the recursive function dfs() in the worst case.
Same O(n + m) or O(n^2) as in Time Complexity. Both input and output graphs take that much space.