Short answers, pulled from the story.
A search algorithm is an algorithm designed to solve a search problem by retrieving information stored within a particular data structure, or calculated in the search space of a problem domain. Search algorithms can work with either discrete or continuous values and are classified into three main types based on their mechanism: linear, binary, and hashing.
Linear search checks every record in sequence until the target is found. Binary search, also called half-interval search, repeatedly targets the center of a sorted structure and divides the search space in half with each step, giving it a maximum complexity of logarithmic time, which is far more efficient for large data sets.
Search algorithms are used to solve the vehicle routing problem, the knapsack problem, the nurse scheduling problem, map coloring, sudoku and crossword puzzles, integer factoring in cryptography, database record retrieval, and optimization of industrial processes such as chemical reactions.
American statistician Jack Kiefer devised Fibonacci search in 1953. The algorithm can be used to find the maximum of a unimodal function and has many other applications in computer science.
Grover's algorithm is a search method designed for quantum computers that is theoretically faster than linear or brute-force search, even without the help of data structures or heuristics. Studies have been conducted with Grover's algorithm that accurately replicate the hypothetical physical versions of quantum computing systems, though quantum computers remain entirely theoretical.
Completeness means that a search algorithm is guaranteed to find the exact or optimal solution if given enough time. Many tree-search methods such as depth-first search and breadth-first search have this property, unlike general metaheuristics such as simulated annealing and genetic programming, which work only in a probabilistic sense.