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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.
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.
Trie data structures are commonly used in predictive text or autocomplete dictionaries, and approximate matching algorithms. [11] Tries enable faster searches, occupy less space, especially when the set contains large number of short strings, thus used in spell checking, hyphenation applications and longest prefix match algorithms.
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 ...
To allow fast deletion and concatenation, the roots of all trees are linked using a circular doubly linked list. The children of each node are also linked using such a list. For each node, we maintain its number of children and whether the node is marked.
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.