Implementing Radix Sort Algorithm in C++
Radix sort is a non-comparison integer sorting algorithm that uses the least significant digit first (LSD) approach, sorting numbers digit by digit (units, tens, etc.) without comparing element sizes. Its core idea is to process each digit using a stable counting sort, ensuring that the result of lower-digit sorting remains ordered during higher-digit sorting. Implementation steps: 1. Identify the maximum number in the array to determine the highest number of digits to process; 2. From the lowest digit to the highest, process each digit using counting sort: count the frequency of the current digit, compute positions, place elements stably from back to front, and finally copy back to the original array. In the C++ code, the `countingSort` helper function implements digit-wise sorting (counting frequencies, calculating positions, and stable placement), while the `radixSort` main function loops through each digit. The time complexity is O(d×(n+k)) (where d is the maximum number of digits, n is the array length, and k=10), making it suitable for scenarios with a large range of integers. The core lies in leveraging the stability of counting sort to ensure that the results of lower-digit sorting are not disrupted during higher-digit sorting. Test results show that the sorted array is ordered, verifying the algorithm's effectiveness.
Read MoreImplementing the Counting Sort Algorithm in C++
**Counting Sort** is a non-comparison sorting algorithm. Its core idea is to construct a sorted array by counting the occurrences of elements, making it suitable for scenarios where the range of integers is not large (e.g., student scores, ages). **Basic Idea**: Taking the array `[4, 2, 2, 8, 3, 3, 1]` as an example, the steps are: 1. Determine the maximum value (8) and create a count array `count` to statistics the occurrences of each element (e.g., `count[2] = 2`); 2. Insert elements into the result array in the order of the count array to obtain the sorted result `[1, 2, 2, 3, 3, 4, 8]`. **Implementation Key Points**: In C++ code, first find the maximum value, count the occurrences, construct the result array, and copy it back to the original array. Key steps include initializing the count array, counting occurrences, and filling the result array according to the counts. **Complexity**: Time complexity is O(n + k) (where n is the array length and k is the data range), and space complexity is O(k). **Applicable Scenarios**: Non-negative integers with a small range, requiring efficient sorting; negative numbers can be handled by offset conversion (e.g., adding the minimum value). Counting Sort achieves linear-time sorting through the "counting-construction" logic and is ideal for processing small-range integers.
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