What is the time complexity of inserting an element at the beginning of a linked list?

Inserting an element at the beginning of a linked list is a common operation in computer programming, especially for dynamic data structures that require frequent updates. The time complexity of this operation depends on the length of the linked list, as well as the implementation of the data structure.

In a singly linked list, where each node only has a reference to the next node, inserting an element at the beginning of the list requires creating a new node and setting its "next" reference to the current head of the list. Then, the head of the list is updated to point to the new node. This operation takes constant time, or O(1), regardless of the length of the list. This is because the operation only requires updating the references of two nodes, regardless of the size of the list.

In a doubly linked list, where each node has a reference to both the previous and next nodes, inserting an element at the beginning of the list also requires creating a new node and setting its "next" reference to the current head of the list, as well as setting the "previous" reference of the current head to the new node. Then, the head of the list is updated to point to the new node. This operation also takes constant time, or O(1), regardless of the length of the list. This is because the operation only requires updating the references of three nodes, regardless of the size of the list.

In summary, the time complexity of inserting an element at the beginning of a linked list is O(1) in both singly linked lists and doubly linked lists. This operation is efficient and can be performed quickly regardless of the size of the list, making linked lists a useful data structure for applications that require frequent updates.