Solution: Remove Edge from a Directed Graph
Let’s solve the Remove Edge from a Directed Graph problem.
We'll cover the following
Statement
Given an adjacency list of a directed graph consisting of n
vertices, modify the list after removing an edge between the source
and destination
vertices.
Constraints:
n
edges.length
edges[i].length
source
,destination
n
source
destination
There are no multiple edges between any two vertices
There are no self-loops
Solution
This solution aims to demonstrate the removal of an edge between two vertices in a graph represented by an adjacency list. An adjacency list is a common way to represent a graph in which each vertex is associated with a list of its neighboring vertices. By removing an edge between two vertices, we effectively sever their connection, altering the graph’s structure accordingly.
Removing an edge from a directed graph’s adjacency list involves traversing the dictionary structure to locate and manipulate the vertices involved. First, we ensure that both the source and destination vertices are present in the adjacency list. This is important because attempting to remove a nonexistent edge may lead to errors or unexpected behavior. If both the vertices exist, then we remove the edge connecting them. Given the directed nature of the graph, we only need to remove the destination vertex from the adjacency list of the source vertex. This step ensures that the graph structure remains consistent and accurately reflects the absence of the specified edge.
Now, let’s look at the algorithm for this approach:
Check if the source vertex,
source
exists in the graph’s adjacency list, and if the destination vertex,destination
exists in the adjacency list of the source vertex.If both vertices exist, remove the
destination
vertex from the adjacency list of thesource
vertex only since the graph is directed.Return the modified graph.
Let’s look at the illustration below to better understand the solution:
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