How is the insertion operation's time complexity in a doubly linked list determined?

The time complexity of inserting an element into a doubly linked list depends on whether we have a pointer to the insertion position:

• If a pointer to the node after which the element should be inserted already exists, then the insertion is performed in O(1), as it only requires changing a few pointers.
• If we need to first find the insertion position, the search time will depend on the size of the list (O(n)), and the insertion itself is O(1).

Example of inserting after a given node:

 type Node struct {
    value int
    prev  *Node
    next  *Node
}

func insertAfter(node *Node, newNode *Node) {
    newNode.prev = node
    newNode.next = node.next
    if node.next != nil {
        node.next.prev = newNode
    }
    node.next = newNode
}