Abstract: A data structure and related data storage and retrieval method rapidly provide a count of elements stored or referenced by a hierarchical structure of ordered elements (e.g., a tree), access to elements based on their ordinal value in the structure, and identification of the ordinality of elements. In an ordered tree implementation of the invention, a count of elements stored in each subtree is stored, i.e., the cardinality of each subtree is stored either at or associated with a higher level node pointing to that subtree or at or associated with the head node of the subtree. In addition to data structure specific requirements (e.g., creation of a new node, reassignment of pointers, balancing, etc.) data insertion and deletion includes steps of updating affected counts. Elements may be target data itself (e.g., data samples, prime numbers); keys or indices associated with target data (e.g., social security numbers of employees, product numbers and codes, etc. uses to reference associated data records, etc.

Abstract: A data structure and related data storage and retrieval method rapidly provide a count of elements stored or referenced by a hierarchical structure of ordered elements (e.g. a tree), access to elements based on their ordinal value in the structure, and identification of the ordinality of elements. In an ordered tree implementation of the invention, a count of elements stored in each subtree is stored, i.e., the cardinality of each subtree is stored either at or associated with a higher level node pointing to that subtree or at or associated with the head node of the subtree. In addition to data structure specific requirements (e.g., creation of a new node, reassignment of pointers, balancing, etc.) data insertion and deletion includes steps of updating affected counts. Elements may be target data itself (e.g., data samples, prime numbers); keys or indices associated with target data (e.g., social security numbers of employees, product numbers and codes, etc. uses to reference associated data records, etc.