Implementing Bucket Sort Algorithm in C++

Bucket sort is a non-comparison sorting algorithm that sorts elements by distributing them into multiple "buckets", sorting each bucket individually, and then merging the sorted buckets. The core is to reasonably partition the buckets so that each bucket contains a small number of elements, thereby reducing the sorting cost. Taking floating-point numbers in the range [0,1) as an example, the algorithm steps are as follows: 1. Create n empty buckets (where n is the length of the array); 2. Assign each element x to the corresponding bucket using the bucket index calculated as the integer part of x * n; 3. Sort each bucket using std::sort; 4. Merge all elements from the buckets. In the C++ implementation, the `bucketSort` function creates n buckets using a vector of vectors of doubles, distributes elements into the buckets through traversal, sorts each bucket, and then merges the results. Testing verifies the correctness of the algorithm. Complexity analysis: The average time complexity is O(n) (when elements are uniformly distributed), and the worst-case time complexity is O(n log n) (when all elements are placed in the same bucket). The space complexity is O(n). It is suitable for numerical data with uniformly distributed values and a clear range; performance degrades when data distribution is uneven. This algorithm is efficient when the data distribution is reasonable, especially suitable for sorting interval data in statistical analysis.