[Algorithms] Radix Sort-优快云博客

本文详细介绍了基数排序算法的原理和实现过程，包括如何使用计数排序作为子过程进行数字从最低有效位到最高有效位的排序，确保算法正确性的前提条件，以及提供了一个C++代码实例。

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Radix sort is another linear time sorting algorithm. It sorts (using another sorting subroutine) the numbers from their least significant digits to most significant digits. To guarantee the correctness of radix sort, the sorting subroutine must be stable. Moreover, each digit falls in a fixed range. For example, if the numbers are decimal, then all digits fall in [0, 9]. So counting sort is usually used as the subroutine.

The code is as follows. For more on radix sort, please refer to Introduction to Algorithms, 3rd edition.

 1 #include <iostream>
 2 #include <vector>
 3 #include <ctime>
 4 #include <algorithm>
 5 
 6 using namespace std;
 7 
 8 int maximum(vector<int>& nums) {
 9     int mx = nums[0];
10     for (int i = 1; i < (int)nums.size(); i++)
11         mx = max(mx, nums[i]);
12     return mx;
13 }
14 
15 void countingSort(vector<int>& nums, int sig) {
16     vector<int> counts(10, 0);
17     for (int i = 0; i < (int)nums.size(); i++)
18         counts[nums[i] / sig % 10]++;
19     for (int i = 1; i < 10; i++)
20         counts[i] += counts[i - 1];
21     vector<int> sorted(nums.size());
22     for (int i = nums.size() - 1; i >= 0; i--) {
23         sorted[counts[nums[i] / sig % 10] - 1] = nums[i];
24         counts[nums[i] / sig % 10]--;
25     }
26     swap(nums, sorted);
27 }
28 
29 void radixSort(vector<int>& nums) {
30     int mx = maximum(nums);
31     for (int sig = 1; mx / sig; sig *= 10)
32         countingSort(nums, sig);
33 }
34 
35 void radixSortTest(void) {
36     int len = 1000;
37     vector<int> nums(len);
38     srand((unsigned)time(NULL));
39     for (int i = 0; i < (int)nums.size(); i++)
40         nums[i] = rand() % (len + 1);
41     vector<int> copy = nums;
42     radixSort(nums);
43     sort(copy.begin(), copy.end());
44     for (int i = 0; i < (int)nums.size(); i++) {
45         if (nums[i] != copy[i]) {
46             printf("radixSort() test failed!\n");
47             return;
48         }
49     }
50     printf("radixSort() test passed!\n");
51 }
52 
53 int main(void) {
54     radixSortTest();
55     system("pause");
56     return 0;
57 }