In computer science, sorting algorithms are crucial for data processing and machine learning. Large datasets and high efficiency requirements provide challenges for comparison-based algorithms like Quicksort and Merge sort, which achieve O(n log n) time complexity. Non-comparison-based algorithms like Spreadsort and Counting Sort have memory consumption issues and a relatively high computational demand, even if they can attain linear time complexity under certain circumstances. We present TwinArray Sort, a novel conditional non-comparison-based sorting algorithm that effectively uses array indices. When it comes to worst-case time and space complexities, TwinArray Sort achieves O(n+k). The approach remains efficient under all settings and works well with datasets with randomly sorted, reverse-sorted, or nearly sorted distributions. TwinArray Sort can handle duplicates and optimize memory efficiently since thanks to its two auxiliary arrays for value storage and frequency counting, as well as a conditional distinct array verifier. TwinArray Sort constantly performs better than conventional algorithms, according to experimental assessments and particularly when sorting unique arrays under all data distribution scenarios. The approach is suitable for massive data processing and machine learning dataset management due to its creative use of dual auxiliary arrays and a conditional distinct array verification, which improves memory use and duplication handling. TwinArray Sort overcomes conventional sorting algorithmic constraints by combining cutting-edge methods with non-comparison-based sorting advantages. Its reliable performance in a range of data distributions makes it an adaptable and effective answer for contemporary computing requirements.

翻译：在计算机科学中，排序算法对于数据处理和机器学习至关重要。大规模数据集和高效率要求对基于比较的算法（如快速排序和归并排序）提出了挑战，这些算法的时间复杂度为O(n log n)。基于非比较的算法（如Spreadsort和计数排序）虽然在某些情况下可以达到线性时间复杂度，但存在内存消耗问题且计算需求相对较高。本文提出TwinArray Sort，一种新颖的条件性非比较排序算法，该算法有效利用数组索引。在最坏情况下的时间和空间复杂度方面，TwinArray Sort达到O(n+k)。该方法在所有设置下均保持高效，并能很好地处理随机排序、逆序或接近有序分布的数据集。得益于其用于值存储和频率计数的两个辅助数组以及条件性唯一数组验证器，TwinArray Sort能够高效处理重复数据并优化内存使用。实验评估表明，TwinArray Sort始终优于传统算法，特别是在所有数据分布场景下排序唯一数组时表现尤为突出。该方法通过创新性地使用双辅助数组和条件性唯一数组验证机制，改善了内存利用和重复数据处理能力，适用于大规模数据处理和机器学习数据集管理。TwinArray Sort通过将先进方法与基于非比较的排序优势相结合，克服了传统排序算法的局限性。其在多种数据分布下的可靠性能使其成为满足现代计算需求的适应性高效解决方案。