Assuming you have a pointer to the node to set the value of, what is the time complexity of setting the value of the nth element in a doubly linked list?

To analyze the time complexity of setting the value of the nth element in a doubly linked list, we can break down the problem as follows:

1. Break Down the Problem

In a doubly linked list, each node contains a value and pointers to both the previous and next nodes. If we already have a pointer to a specific node (the nth node), we can directly access it without needing to traverse the list.

2. Relevant Concepts

• Accessing a node in a doubly linked list takes O(1) time because we have a direct pointer/reference to the node.
• We simply need to update the value of this node.

3. Analysis and Detail

When we set the value of the nth node:

• No traversal is needed, eliminating the need for O(n) time complexity associated with finding a node in a traditional list.
• The operation consists of a single assignment, which is performed in constant time.

4. Verify and Summarize

The operation does not depend on the length of the list since we already have access to the node. Therefore, the calculations confirm that the process requires a constant time regardless of the position of the node in the list.

Final Answer

The time complexity of setting the value of the nth element in a doubly linked list is $O(1)$.