Implementing the Counting Sort Algorithm in Java

Counting sort is a simple and intuitive non-comparison sorting algorithm. It determines the position of elements by counting their occurrences and using prefix sums. It is suitable for scenarios where the element range is small (e.g., integers), there are many repeated elements, and stable sorting is required. The core idea is: first, determine the element range (find min and max), count the occurrences of each element, calculate the prefix sum to get the final position of the element, and then traverse the original array from the end to generate the sorted result. Implementation steps: handle edge cases (no sorting needed for empty/single-element arrays), determine min/max, create a count array to tally occurrences, compute prefix sums (accumulate to get the final position of elements), and traverse from the end to generate the result. The time complexity is O(n+k) (where n is the array length and k is the element range), and the space complexity is O(n+k). Applicable scenarios include small integer ranges (e.g., scores, ages), many repeated elements, and the need for stable sorting. This algorithm achieves sorting through counting and accumulation without comparisons, making it suitable for beginners to understand the basic ideas of sorting.