Beam stack search is a search algorithm often used in artificial intelligence, particularly in the context of search problems like those found in natural language processing, robotics, or game playing. It combines elements of breadth-first and depth-first search strategies while maintaining a focus on efficiency and effectiveness. ### Key Concepts: 1. **Beam Width**: The "beam" in beam search refers to a fixed number of the most promising nodes (or paths) that the algorithm keeps track of at each level of the search tree.

Binary search is an efficient algorithm for finding a target value within a sorted array (or list). The core idea of binary search is to repeatedly divide the search interval in half, which significantly reduces the number of comparisons needed to find the target value compared to linear search methods. ### How Binary Search Works: 1. **Initial Setup**: Start with two pointers, `low` and `high`, which represent the boundaries of the search interval.

A Finger Search Tree is a type of data structure that provides an efficient way to perform dynamic set operations, such as search, insertion, and deletion. It is a variation of binary search trees (BST) that allows for quick searching and manipulating of elements, especially the ones that are accessed frequently or recently. ### Key Features: 1. **Finger Pointer**: The main distinguishing feature of a Finger Search Tree is the concept of a "finger".

A genetic algorithm (GA) is a search heuristic inspired by the process of natural selection and genetics. It is used to solve optimization and search problems by mimicking the principles of biological evolution. Here's a breakdown of how it works: 1. **Initialization**: A population of potential solutions, often represented as strings or arrays (analogous to chromosomes), is generated randomly.

BitFunnel is an open-source search engine built to be highly performant and scalable, particularly for large-scale data environments. It focuses on providing efficient indexing and retrieval of information. The architecture of BitFunnel is designed to support fast query performance and low-latency responses, making it suitable for applications that require quick access to vast amounts of data, such as enterprise search and data analytics.

An inversion list is a concept often used in the context of data structures and algorithms, particularly in sorting. Inversions in an array or a list refer to pairs of elements where the first element is greater than the second element but appears before it in the array. Specifically, for an array \(A\), an inversion is a pair of indices \( (i, j) \) such that \( i < j \) and \( A[i] > A[j] \).

An inverted index is a data structure used primarily in information retrieval systems, such as search engines, to efficiently store and retrieve documents based on the terms they contain. It enables fast full-text searches by mapping content keywords (or terms) to their locations in a set of documents. **How it works:** 1. **Indexing Process:** - Each document in the collection is tokenized into individual words or terms.

Knuth's Algorithm X is a backtracking algorithm designed to solve the Exact Cover problem. The Exact Cover problem involves finding a subset of rows in a binary matrix such that each column contains exactly one "1" from the selected rows. This can be thought of as a way to cover each column with exactly one selected row. The algorithm was introduced by Donald Knuth in his book "Dancing Links" and is noted for its efficiency in solving combinatorial problems.

Dichotomic search, more commonly known as binary search, is an efficient algorithm for finding a target value within a sorted array or list. The main idea is to repeatedly divide the search interval in half, which significantly reduces the number of comparisons needed compared to linear search methods.

A Disjoint-set data structure, also known as a union-find data structure, is a data structure that keeps track of a partition of a set into disjoint (non-overlapping) subsets. It supports two primary operations: 1. **Find**: This operation determines which subset a particular element is in. It can be used to check if two elements are in the same subset. 2. **Union**: This operation merges two subsets into a single subset.

Double hashing is a technique used in open addressing for resolving collisions in hash tables. When two keys hash to the same index, double hashing provides a way to find an alternative or "probe" location in the hash table based on a secondary hash function. This reduces clustering and improves the distribution of entries in the hash table. In double hashing, when a collision occurs, a secondary hash function is applied to generate a step size for probing.

Dynamic perfect hashing is a data structure technique designed to provide efficient and flexible handling of key-value pairs, enabling quick search, insertion, and deletion operations while maintaining constant time access complexity on average and supporting the dynamic nature of growing and shrinking datasets. The main goal of dynamic perfect hashing is to achieve constant time complexity for operations, such as searching for a key, inserting a new key, and deleting a key, while ensuring that all operations are performed in a way that avoids collisions between keys.

Expectiminimax is a decision-making algorithm used in game theory, particularly in the context of two-player games involving randomness, such as those where some outcomes are uncertain or probabilistic. It is an extension of the minimax algorithm, which is primarily used for deterministic games.

Exponential search is a searching algorithm that is used to find the position of a target value in a sorted array. It combines two techniques: binary search and an exponential range finding strategy. Exponential search is particularly useful for unbounded or infinite-sized search spaces, although it can also be applied to finite-sized arrays. ### Steps of Exponential Search: 1. **Check the First Element**: Start by comparing the target value with the first element of the array.

Extendible hashing is a dynamic hashing scheme that allows for efficient insertion, deletion, and searching of records in a database or a data structure, particularly in situations where the dataset can grow or shrink in size. It is designed to handle a dynamic set of keys while minimizing the need to reorganize the hash table structure. ### Key Features of Extendible Hashing: 1. **Directory Structure**: Extendible hashing uses a directory that points to one or more buckets. Each bucket can hold multiple entries.

Fibonacci search is a comparison-based search algorithm that utilizes the properties of Fibonacci numbers to efficiently find an element in a sorted array. It is particularly useful for large arrays when compared to binary search, especially when the cost of accessing elements is non-uniform or expensive.

Geometric hashing is a technique used in computer vision and computer graphics for object recognition and matching. It is particularly effective for recognizing shapes and patterns in 2D and 3D space. The main idea behind geometric hashing is to create a compact representation of geometric features from an object, which can then be used for rapid matching against other objects or scenes.

"God's algorithm" is a term used in the context of problem-solving and optimization, particularly in relation to puzzles and games like the Rubik's Cube. It refers to the most efficient way to solve a problem, achieving the solution in the least number of steps possible. In the case of the Rubik's Cube, for example, God's algorithm would mean finding the shortest sequence of moves that leads from any given scrambled state of the cube to the solved state.

A hash function is a mathematical algorithm that takes an input (or "message") and produces a fixed-size string of bytes, typically in the form of a hash value or hash code. The output is usually a numerical representation of the original data, and it is designed to uniquely correspond to the input data. Here are some key characteristics and properties of hash functions: 1. **Deterministic**: For a given input, a hash function will always produce the same output.

Multiplicative binary search is a variation of the standard binary search algorithm that is particularly useful when you're trying to find the smallest or largest index of a value in a sorted array or list, especially when the range of values is unknown or not well-defined. It combines elements of both expansion and binary searching.