Sorting algorithms

Sorting algorithms are the fundamental procedures of computer science for arranging sequences in a specified order. They are not merely bookkeeping utilities. They are the canonical domain for understanding algorithmic efficiency, because sorting is both universally needed and structurally rich — it admits solutions ranging from quadratic naive methods to linearithmic divide-and-conquer approaches to linear specialized algorithms that exploit known structure. The study of sorting is the study of how much information a procedure needs to acquire and how much it can assume. A comparison sort cannot be faster than O(n log n) because each comparison yields at most one bit of information, and log(n!) bits are required to identify a single permutation. This is not an engineering limitation. It is an information-theoretic bound. The real power of sorting algorithms lies not in their speed but in what they reveal about the relationship between computation and information: the fastest sort is always a trade between the generality of the problem and the specificity of the solution.