The reverse of a directed graph G=(V, E) is another directed...

The reverse of a directed graph $G=(V, E)$ is another directed graph $G^{R}=\left(V, E^{R}\right)$ on the same vertex set, but with all edges reversed; that is, $E^{R}=\{(v, u):(u, v) \in E\}$ Give a linear-time algorithm for computing the reverse of a graph in adjacency list format.

The reverse of a directed graph $G=(V, E)$ is another directed graph $G^{R}=\left(V, E^{R}\right)$ on the same vertex set, but with all edges reversed; that is, $E^{R}=\{(v, u):(u, v) \in E\}$
Give a linear-time algorithm for computing the reverse of a graph in adjacency list format.

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Key Concepts

Directed Graph

A directed graph is a set of vertices connected by edges where each edge has an orientation, indicating a one-way relationship from one vertex to another. This structure is commonly used to model asymmetric relationships in various contexts such as web links, social networks, or state transitions.

Graph Reversal

Graph reversal is the process of transforming a directed graph into a new graph where the direction of every edge is reversed. This concept is useful for algorithms that need to analyze the graph from an opposite perspective, such as finding strongly connected components or working with reverse-dependencies.

Adjacency List Representation

An adjacency list is a data structure used to represent graphs, where each vertex stores a list of its adjacent vertices (i.e., those that it connects to directly). This representation is often preferred for sparse graphs because it is memory efficient and facilitates operations that require iterating over a vertex’s neighbors.

Linear-Time Algorithm

A linear-time algorithm is one whose running time grows linearly with the size of the input. In the context of graphs, this means the algorithm's time complexity is proportional to the sum of the number of vertices and edges (O(|V| + |E|)), making it efficient for processing large graphs.

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