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Counting sort is a non‑comparison integer sorting algorithm with O(n + k) time complexity, and this article explains its principles, step‑by‑step process, PHP implementation code, advantages, drawbacks, and suitable use cases for efficient data handling in backend development.
This article explains the insertion sort algorithm, describes how it repeatedly inserts each element into its correct position in a growing sorted portion of the array, and provides a complete PHP function that sorts a numeric array while preserving stability.
This article explains the Bubble Sort algorithm, its O(n²) time and O(1) space complexities, describes the step‑by‑step sorting process, provides a complete PHP implementation, and shows sample input and output to illustrate how the algorithm orders data.
The article demystifies Java’s Arrays.sort by tracing its call to TimSort.sort, explaining how the hybrid Timsort algorithm blends merge and insertion sorts, determines minimum run lengths, partitions and merges runs, addresses implementation bugs such as stack allocation and comparator misuse, and celebrates its elegant, efficient design.
This article explains heap sort by introducing its theory, visual step‑by‑step construction of a max‑heap, a complete Python implementation, and an analysis of its time and space complexities, including detailed code walkthrough and complexity derivations.
This article explains the heap sort algorithm, describing the heap data structure, the process of building a max‑heap, the sorting loop with element swaps, and provides detailed Java code examples along with key points and an illustrative example array.
The article presents a practical case of sorting a 4.6 GB file with 500 million random integers, evaluates in‑memory quicksort and merge‑sort implementations, discusses bitmap sorting, and finally details a multi‑phase external‑sort algorithm with measured runtimes and resource considerations.
This article explains the quick sort algorithm, covering its basic divide‑and‑conquer principle, a naïve C implementation, improvements such as two‑way partitioning, random and median‑of‑three pivot selection, and a non‑recursive version using an explicit stack, with full source code examples.
This comprehensive guide explains QuickSort’s divide‑and‑conquer principle, presents two PHP‑style implementations, analyzes its O(N log N) average and O(N²) worst‑case performance, and details practical optimizations such as random pivot selection, switching to insertion sort for small sub‑arrays, three‑way and dual‑pivot variants.