Sorting Lower Bounds Using Comparison Trees in Computer Science
In comparison-based sorting models, any deterministic algorithm is theoretically bounded by Ω(n log n) time because a decision tree representing the algorithm must have at least $n!$ leaves to uniquely identify all possible permutations of distinct inputs. This lower bound arises from the constraint that only element comparisons are permitted operations; thus, the minimum height of such a binary tree (representing worst-case comparison count) is $\lceil \log_2(n!) \rceil$, which simplifies using Stirling's approximation to show that no faster general-purpose sorting algorithm exists within this restriction.
Sorting Lower Bounds Using Comparison Trees in Computer Science
In comparison-based sorting models, any deterministic algorithm is theoretically bounded by Ω(n log n) time because a decision tree representing the algorithm must have at least $n!$ leaves to unique…