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The Dancing Links algorithm solving a polycube puzzle. In computer science, dancing links (DLX) is a technique for adding and deleting a node from a circular doubly linked list. It is particularly useful for efficiently implementing backtracking algorithms, such as Knuth's Algorithm X for the exact cover problem. [1]
When manipulating linked lists in-place, care must be taken to not use values that have been invalidated in previous assignments. This makes algorithms for inserting or deleting linked list nodes somewhat subtle. This section gives pseudocode for adding or removing nodes from singly, doubly, and circularly linked lists in-place.
A linked list in an inconsistent state, caused by application of the naive lock-free deletion algorithm. Dotted lines are links that exist in intermediate states; solid lines represent the final state. Deletion of the node holding a has executed simultaneously with insertion of b after a, causing the insertion to be undone.
Knuth showed that Algorithm X can be implemented efficiently on a computer using dancing links in a process Knuth calls "DLX". DLX uses the matrix representation of the exact cover problem, implemented as doubly linked lists of the 1s of the matrix: each 1 element has a link to the next 1 above, below, to the left, and to the right of itself.
Linked list implementations, especially one of a circular, doubly-linked list, can be simplified remarkably using a sentinel node to demarcate the beginning and end of the list. The list starts out with a single node, the sentinel node which has the next and previous pointers point to itself. This condition determines if the list is empty.
A double-ended queue is represented as a sextuple (len_front, front, tail_front, len_rear, rear, tail_rear) where front is a linked list which contains the front of the queue of length len_front. Similarly, rear is a linked list which represents the reverse of the rear of the queue, of length len_rear.
Each terminal node is associated with a list of URLs—called occurrence list—to pages that match the keyword. The trie is stored in the main memory, whereas the occurrence is kept in an external storage, frequently in large clusters , or the in-memory index points to documents stored in an external location.
The first and last nodes of a doubly linked list for all practical applications are immediately accessible (i.e., accessible without traversal, and usually called head and tail) and therefore allow traversal of the list from the beginning or end of the list, respectively: e.g., traversing the list from beginning to end, or from end to beginning, in a search of the list for a node with specific ...