What is the worst time complexity of checking node u and v are directly connected by an edge in a graph G = |V, E| when adjacency list is used

The worst time complexity of checking if nodes u and v are directly connected by an edge in a graph G = |V, E| when an adjacency list is used is O(n).

Here's the step-by-step explanation:

1. In an adjacency list representation of a graph, each node maintains a list of all other nodes that it is directly connected to.

2. To check if nodes u and v are directly connected, we would have to traverse the adjacency list of one of these nodes (let's say u) and check if the other node (v) is present in this list.

3. In the worst-case scenario, node v could be the last node in u's adjacency list, or it might not be present at all.

4. Therefore, we would have to traverse all the nodes in u's adjacency list.

5. Since the length of the adjacency list can be at most n (where n is the total number of nodes in the graph), the worst-case time complexity of this operation is O(n).