[winstonewert]

But how do you find the element to be moved from the middle if not by iterating over the list?

[KMag]

You use a hash map, and make the linked list a linked list of hash entries. So, if you're using chaining (as opposed to the many variations on open addressing):

    class Entry<K,V> {
        Entry<K,V> younger;  // LRU doubly linked list
        Entry<K,V> older;    // LRU doubly linked list
        Entry<K,V> next;     // for hash map bucket chaining
        V value;
        K key;
    }

The naive solution using two separate data structures would look like:

    class MapEntry<K,V> {
        Entry<K,V> next;
        DoublyLinkedListEntry<MapEntry<K,V>> LruEntry;
        K key;
        V value;
    }

    class DoublyLinkedListEntry<T> {
        ListEntry<T> prev;
        LintEntry<T> next;
        T value;
    }

[baddox]

The commenter mentions that in the last sentence. There is some separate data structure that also has references to nodes in the middle of the linked list.

[KMag]

Or, you've removed one indirection and made the linked list actually a part of another data structure, as in how LRU caches are generally implemented.

[baddox]

The entire LRU used multiple data structures, but the ability to efficiently remove from the middle of the linked list is still important.

[winstonewert]

Oy! I can't believe I missed that.