分配类排序——基数排序

         基数排序属于“分配式排序”（distribution sort），基数排序法又称“桶子法”（bucket sort）或bin sort，顾名思义，它是透过键值的部份资讯，将要排序的元素分配至某些“桶”中，藉以达到排序的作用，基数排序法是属于稳定性的排序。

时间效率：设待排序列为n个记录，d个关键码，关键码的取值范围为radix，则进行链式基数排序的时间复杂度为O(d(n+radix))，其中，一趟分配时间复杂度为O(n)，一趟收集时间复杂度为O(radix)，共进行d趟分配和收集。 
空间效率：需要2*radix个指向队列的辅助空间，以及用于静态链表的n个指针。

最高位优先(Most Significant Digit first)法，简称MSD法：先按k1排序分组，同一组中记录，关键码k1相等，再对各组按k2排序分成子组，之后，对后面的关键码继续这样的排序分组，直到按最次位关键码kd对各子组排序后。再将各组连接起来，便得到一个有序序列。
最低位优先(Least Significant Digit first)法，简称LSD法：先从kd开始排序，再对kd-1进行排序，依次重复，直到对k1排序后便得到一个有序序列。

下面是C语言实现的一个例子（使用最低优先法）

#include <unistd.h>#include <assert.h>#include <stdio.h>#include <stdlib.h>#define RADIX 10                      //基数#define KEY_SIZE 6                    //键的最大个数#define LIST_SIZE 20                  //需要排序数的个数typedef struct{    int key;    int next;                          //静态链域} RecordType1;typedef struct {RecordType1 r[LIST_SIZE + 1];int length;int keynum;} SLinkList;                            //静态链表typedef int PVector[RADIX];int num[LIST_SIZE][KEY_SIZE];            //将整数进行分离/*将输入的十进制数的每一位拆分开来*/void Order(SLinkList *s_num){int i, m, j, tmp;int r_num;        m = s_num->keynum;for (i = 1; i <= s_num->length; i++){       r_num = s_num->r[i].key;for (j = m-1; j >= 0; j--)                  {tmp = r_num % 10;num[i][j] = tmp;r_num = r_num / 10;while (r_num == 0 && j != 0){j--;num[i][j] = 0;break;}}}}/*分配*/void Distribute(SLinkList *s_num, int i, PVector head, PVector tail){int j, p;for (j = 0; j <= RADIX-1; ++j){head[j] = 0;}p = s_num->r[0].next;while(p != 0){j = num[p][i];if (head[j] == 0)      head[j] = p;        else      s_num->r[tail[j]].next = p;tail[j] = p;p = s_num->r[p].next;}}/*回收*/void Collect(SLinkList *s_num, PVector head, PVector tail){int j, t;j = 0;while (head[j] == 0)      ++j;s_num->r[0].next = head[j];t = tail[j];while (j < RADIX - 1){++j;while ((j < RADIX - 1) && (head[j] == 0)){++j;}if (head[j] != 0){s_num->r[t].next = head[j];t = tail[j];}}s_num->r[t].next = 0;}//找最大数int maxNum(SLinkList *s_num){int i, max = 0;for (i = 1; i <= s_num->length; i++){if (s_num->r[i].key > max)      max = s_num->r[i].key;}return max;}/*确定关键字的个数(找最大数关键子的位数)*/void Keynum(SLinkList *s_num){int max_num, temp = 0, count = 1;max_num = maxNum(s_num);                  //找最大数temp = max_num / 10;while (temp != 0){count++;temp = temp / 10;}s_num->keynum = count;}/*基数排序*/void RadixSort(SLinkList *s_num){PVector head, tail;int i, d, n;n = s_num->length;for (i = 0; i <= n-1; ++i)      s_num->r[i].next = i+1;s_num->r[n].next = 0;d = s_num->keynum;                          //关键字的个数for (i = d-1; i >= 0; i--){Distribute(s_num, i, head, tail);         //第ｉ趟分配Collect(s_num, head, tail);               //第ｉ趟回收}}/*输出排序后的结果*/void Print(SLinkList *s_num){int j;j = s_num->r[0].next;printf("\nsort finish:");while (j != 0){printf("%d  ", s_num->r[j].key);j = s_num->r[j].next;}printf("\n");}int main(int argc, char *argv[]){SLinkList *s_num;        int i;s_num = (SLinkList *)malloc(sizeof(SLinkList));printf("input sort count is : ");scanf("%d", &s_num->length);printf("\nPlease input sort number is :");for (i = 1; i <= s_num->length; i++){scanf("%d", &s_num->r[i].key);}        Keynum(s_num);             //计算关键字的个数Order(s_num);              //将输入的十进制数进行拆分RadixSort(s_num);Print(s_num);return EXIT_SUCCESS;}