Implementing the Radix Sort Algorithm with Python
Radix sort is a non-comparative integer sorting algorithm. Its core idea is to distribute elements into buckets and collect them by each digit (from the least significant to the most significant). The basic steps are as follows: first, determine the number of digits of the maximum number in the array. Then, from the least significant digit to the most significant digit, perform "bucket distribution" (10 buckets for digits 0-9) and "collection" operations for each digit. Elements with the same current digit are placed into the same bucket, and the array is updated by collecting them in bucket order until all digits are processed. In Python, this is implemented by looping through the digits, calculating the current digit to distribute into buckets, and then collecting. The time complexity is O(d×(n+k)) (where d is the number of digits of the maximum number, n is the array length, and k=10), and the space complexity is O(n+k). It is suitable for integer arrays with few digits. When handling negative numbers, they can first be converted to positive numbers for sorting and then their signs can be restored.
Read MoreImplementing the Shell Sort Algorithm with Python
Shell Sort is an improved version of Insertion Sort, which enhances efficiency by "coarsely sorting" and then "finely sorting" through grouping to reduce element intervals. The core involves selecting an initial increment (e.g., half the array length), dividing the array into multiple groups where elements within each group are spaced by the increment, and applying Insertion Sort to each group. The process then repeats with the increment halved until the increment reaches 1, completing the "fine sorting." Its key logic is reducing element movement through grouping: initially grouping with large intervals allows the array to become nearly sorted first, and gradually shrinking the increment ensures the final Insertion Sort phase finishes efficiently. The average time complexity is O(n log n), worst-case O(n²), with a space complexity of O(1). Shell Sort is suitable for arrays of moderate size with uneven element distribution and is an efficient in-place sorting algorithm.
Read MoreInspiration from Poker Sorting: A Life Analogy and Implementation of Insertion Sort
This article introduces the insertion sort algorithm. Its core idea is to gradually build an ordered sequence: the first element is defaulted as sorted, and starting from the second element, each element (the element to be inserted) is inserted into the correct position in the previously sorted sequence (where larger elements need to be moved to make space). Taking the array `[5, 3, 8, 4, 2]` as an example, the process of comparing and moving elements from back to front is demonstrated. The key steps are: traversing the array, temporarily storing the element to be inserted, moving the sorted elements, and inserting at the correct position. Algorithm characteristics: Advantages include simplicity and intuitiveness, in-place sorting (space complexity O(1)), stability, and suitability for small-scale or nearly ordered data; disadvantages include the worst-case time complexity of O(n²) and a relatively large number of move operations. In summary, insertion sort is a foundation for understanding sorting algorithms. It is explained through a life analogy (e.g., sorting playing cards) to aid comprehension and is applicable to simple scenarios or sorting small-scale data.
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