Explain the execution flow of putFirst() on a LinkedHashMap?

Internally, LinkedHashMap maintains a doubly linked list threaded through its entries in addition to the usual hash table, and that linked list is what actually defines the map's encounter order.

sequenceDiagram
    participant Caller
    participant LinkedHashMap
    participant HashTable
    participant LinkedList as Internal Linked List
    Caller->>LinkedHashMap: putFirst(key, value)
    LinkedHashMap->>HashTable: Check if key exists
    alt Key exists
        LinkedHashMap->>LinkedList: Unlink existing entry
    end
    LinkedHashMap->>HashTable: Insert/update key-value pair
    LinkedHashMap->>LinkedList: Link entry at the head
    LinkedList-->>LinkedHashMap: Head pointer updated
    LinkedHashMap-->>Caller: Return previous value or null

If the key already existed somewhere in the map, its old node is first unlinked from wherever it sat in the linked list; if it's new, a fresh node is created. Either way, the node is then linked in at the head of that internal list, which is what makes it the new "first" entry for iteration and for firstEntry().

The hash table itself is used only for the O(1) key lookup - the actual iteration order that firstEntry(), lastEntry(), and reversed() rely on comes entirely from the linked list, not from hash bucket order.