From elementary O(n²) sorts to divide-and-conquer, non-comparison linear sorts, and mathematical proofs of the Omega(n log n) lower bound.
Bubble Sort with early exit flag, Selection Sort minimal write guarantees, and Insertion Sort online adaptive behavior.
Merge Sort stable O(n log n) tree, Quick Sort Lomuto vs Hoare partitioning and median-of-three, and in-place Heap Sort.
Breaking the comparison barrier: Counting Sort prefix-sum stability, Radix Sort digit-by-digit passes, and Bucket Sort uniform hashing.
Decision tree lower-bound proof (log(n!) = Omega(n log n)), stability analysis across compound records, and hybrid TimSort architecture.