This article discusses two methods for representing hierarchical structures like trees. It contrasts using an array of child pointers with a more memory-efficient approach that employs first-child and next-sibling pointers. Each method has its trade-offs in terms of memory management and access speed.

Bloom filters are efficient probabilistic data structures used to quickly determine if an element is part of a set, allowing for rapid membership queries with a trade-off for false positives. They utilize a bit vector and multiple hash functions, where the choice of hash functions and the size of the filter can be optimized based on the expected number of elements and acceptable false positive rates. The article also discusses various implementations and use cases of Bloom filters across different technologies.

A search engine performs two main tasks: retrieval, which involves finding documents that satisfy a query, and ranking, which determines the best matches. This article focuses on retrieval, explaining the use of forward and inverted indexes for efficient document searching and the concept of set intersection as a fundamental operation in retrieval processes.