Implementing Bucket Sort Algorithm with Python
Bucket sort is a non-comparison-based sorting algorithm based on the divide-and-conquer principle. It achieves overall order by dividing data into buckets, sorting elements within each bucket, and then merging the results. Core steps: First, divide data into buckets based on distribution characteristics; then sort elements in each bucket using simple sorting methods (e.g., built-in sort); finally, merge all bucket results. Applicable scenarios: When data is uniformly distributed and within a limited range, its efficiency approaches linear time complexity (O(n)). However, non-uniform distribution may degrade it to O(n²), making it less performant than quicksort. Python implementation (taking 0-1 interval floating-point numbers as an example): Create n empty buckets (where n is the length of the data), assign data to corresponding buckets using the formula `int(num * n)`, sort elements within each bucket, and merge all bucket elements. The code is concise but requires adjusting the bucket index calculation according to the data range and optimizing bucket size to avoid extreme value concentration. Summary: Bucket sort is suitable for uniformly distributed data. It leverages divide-and-conquer to reduce complexity but requires attention to data distribution characteristics to avoid performance degradation.
Read MoreImplementing the Counting Sort Algorithm in Python
Counting sort is an efficient non-comparison sorting algorithm suitable for integers with a small value range. Its time complexity is O(n + k), where n is the number of elements and k is the data range. Core steps: 1. Determine the data range (find min and max); 2. Construct a counting array to count the occurrences of each element; 3. Output the elements of the counting array in order (outputting the number of times corresponding to the count). It is stable (relative order of duplicate elements remains unchanged), and memory usage depends on the data range. It is suitable for integer data with many duplicates or a small range (e.g., exam scores). The Python implementation completes sorting through boundary handling, counting occurrences, etc. Test cases verify its applicability to arrays with duplicate elements and negative numbers.
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