数据结构与算法基础-学习-34-基数排序（桶排序）
目录
一、基本思想
二、算法思路
1、个位排序
（1）分配
（2）收集
2、十分位排序
（1）分配
（2）收集
三、源码分享
1、InitMyBucket
2、DestroyMyBucket
3、ClearMyBucket
4、PushData2Bucket
5、PopDataFromBucket
6、GetIntegerDigit
7、BucketSortSentryQueue
四、算法效率
五、Linux环境编译测试
排序的其他相关知识点和源码分享可以参考之前的博客：
《数据结构与算法基础-学习-30-插入排序之直接插入排序、二分插入排序、希尔排序》，
《数据结构与算法基础-学习-31-交换排序之冒泡排序、快速排序》，
《数据结构与算法基础-学习-32-选择排序之简单选择排序、堆排序》，
《数据结构与算法基础-学习-33-归并排序》
一、基本思想
基数排序的基本思想就是分配和收集。
基数排序也叫桶排序、箱排序，设置若干个桶，将关键字为k的记录放入第k个桶，然后再按照序号将非空的连接。
二、算法思路
我们还是以升序为例，初始化10个桶来存放数据，因为上面的数据最多到十分位，我们只需要两部就可以完成排序。
1、个位排序
（1）分配
10的个位是0，放到0号桶。
34的个位是4，放到4号桶。
1的个位是1，放到1号桶。
后面的数据以此类推。
（2）收集
我们按照顺序从第0个桶、第1个桶。。。。的顺序取数据，可以发现个位已经有序。并且只有个位的元素就不需要进行下一轮十分位的排序，我们只用比较有十分位的元素，这样可以减少排序时间。收集前桶中数据是全部，为了效率我们可以直接把只有个位的放入原序列中。
2、十分位排序
（1）分配
我们清空桶，将临时队列中的元素按照十分位的数值放入桶中。
（2）收集
我们按照顺序从第0个桶、第1个桶。。。。的顺序取数据，由于这些元素只有最大十分位，我们可以直接放入原队列中，这样就排好序啦。
三、源码分享
1、InitMyBucket
Status InitMyBucket(MyBucket** Bucket, QueueLenType BucketGroupNums, QueueLenType OneBucketNums, JudgeTypeFlag Flag)
{
JudgeAllNullPointer(Bucket);
if (BucketGroupNums * OneBucketNums > __LONG_LONG_MAX__)
{
LogFormat(Error,"Init Bucket Fail, Reason : BucketGroupNums(%lld) * OneBucketNums(%lld) > %lld.\n",
BucketGroupNums,OneBucketNums,__LONG_LONG_MAX__);
return FailFlag;
}
QueueLenType i;
(*Bucket) = (MyBucket*)MyMalloc(sizeof(MyBucket));
(*Bucket)->BucketArrayMaxLen = BucketGroupNums;
(*Bucket)->BucketDataUseNums = 0;
(*Bucket)->BucketDataMaxUseNums = BucketGroupNums * OneBucketNums;
(*Bucket)->BucketArray = (SqQueue**)MyMalloc(BucketGroupNums * sizeof(SqQueue*));
for ( i = 0; i < (*Bucket)->BucketArrayMaxLen; i++)
{
InitSqQueue(&((*Bucket)->BucketArray[i]),OneBucketNums,Flag);
}
LogFormat(Debug,"Init Bucket OK.\n");
return SuccessFlag;
}2、DestroyMyBucket
Status DestroyMyBucket(MyBucket** Bucket)
{
JudgeAllNullPointer(*Bucket);
QueueLenType i;
for ( i = 0; i < (*Bucket)->BucketArrayMaxLen; i++)
{
DestroySqQueue(&((*Bucket)->BucketArray[i]));
}
free((*Bucket)->BucketArray);
(*Bucket)->BucketArray = NULL;
(*Bucket)->BucketArrayMaxLen = 0;
(*Bucket)->BucketDataUseNums = 0;
(*Bucket)->BucketDataMaxUseNums = 0;
free(*Bucket);
*Bucket = NULL;
LogFormat(Debug,"Destroy Bucket OK.\n");
return SuccessFlag;
}3、ClearMyBucket
Status ClearMyBucket(MyBucket* Bucket)
{
JudgeAllNullPointer(Bucket);
QueueLenType i;
for ( i = 0; i < Bucket->BucketArrayMaxLen; i++)
{
ClearSqQueue(Bucket->BucketArray[i]);
}
Bucket->BucketDataUseNums = 0;
LogFormat(Debug,"Clear Bucket OK.\n");
return SuccessFlag;
}4、PushData2Bucket
//将数据压入桶中。
Status PushData2Bucket(MyBucket* Bucket, QueueLenType BucketGroupIndex, void* Data)
{
JudgeAllNullPointer(Bucket);
JudgeAllNullPointer(Data);
if (BucketGroupIndex < 0 || BucketGroupIndex >= Bucket->BucketArrayMaxLen)
{
LogFormat(Error,"Push Data To Bucket Fail, Reason : Illegal BucketGroupIndex(%lld).\n",BucketGroupIndex);
return FailFlag;
}
if (Bucket->BucketDataUseNums == Bucket->BucketDataMaxUseNums)
{
LogFormat(Warning,"Push Data To Bucket Fail, Reason : Bucket Is Full(%lld).\n",Bucket->BucketDataMaxUseNums);
return NormalFlag;
}
Status ReturnStatus;
ReturnStatus = EnterSqQueue(Bucket->BucketArray[BucketGroupIndex],Data);
if (ReturnStatus == SuccessFlag)
{
Bucket->BucketDataUseNums++;
LogFormat(Debug,"Push Data To Bucket OK.\n");
}
return ReturnStatus;
}5、PopDataFromBucket
//将数据从桶中取出来。
Status PopDataFromBucket(MyBucket* Bucket, QueueLenType BucketGroupIndex, void* Data)
{
JudgeAllNullPointer(Bucket);
JudgeAllNullPointer(Data);
if (BucketGroupIndex < 0 || BucketGroupIndex >= Bucket->BucketArrayMaxLen)
{
LogFormat(Error,"Pop Data From Bucket Fail, Reason : Illegal BucketGroupIndex(%lld).\n",BucketGroupIndex);
return FailFlag;
}
if (Bucket->BucketDataUseNums == 0)
{
LogFormat(Warning,"Pop Data From Bucket Fail, Reason : Bucket Is Empty.\n");
return NormalFlag;
}
Status ReturnStatus;
ReturnStatus = LeaveSqQueue(Bucket->BucketArray[BucketGroupIndex],Data);
if (ReturnStatus == SuccessFlag)
{
Bucket->BucketDataUseNums--;
LogFormat(Debug,"Pop Data From Bucket OK.\n");
}
return ReturnStatus;
}6、GetIntegerDigit
//给出一个正整数，和你想要的位数，返回相应的位数。
//例如1234，你要十分位，返回一个3。
//1表示个位，2表示十分位，以此类推。
//目前只支持int类型
int GetIntegerDigit(int Num, int Digit)
{
// LogFormat(Debug,"Num : %d, Digit : %d\n",Num,Digit);
if (Digit < 1 || Digit > 9)
{
return GET_INTEGER_DIGIT_FAIL_FLAG;
}
if (Num < 0)
{
return GET_INTEGER_DIGIT_FAIL_FLAG;
}
if (Digit == 1)
{
return Num % 10;
}
else if (MyIntSquare(10,Digit - 1) > Num)//如果Num不存在Digit相应的位数，如89不存在百分位的情况。
{
return GET_INTEGER_DIGIT_NO_EXISTS_FLAG;
}
else
{
return (Num % MyIntSquare(10,Digit) - Num % MyIntSquare(10,Digit - 1)) / MyIntSquare(10,Digit - 1);
}
}7、BucketSortSentryQueue
//由于GetIntegerDigit实现的原因，导致BucketSortSentryQueue只支持正整数排序。
//此函数如果执行出错，会改变Queue的值，里面存了中间结果。
Status BucketSortSentryQueue(SqQueue* Queue)
{
JudgeAllNullPointer(Queue);
MyBucket* Bucket = NULL;
SqQueue* TmpQueue = NULL;//临时队列，存放中间数据。
switch(Queue->Flag)
{
case INT_TYPE_FLAG :
InitMyBucket(&Bucket,INTEGER_BUCKET_NUMS,Queue->SqQueueLen,Queue->Flag);
InitSqQueue(&TmpQueue,Queue->SqQueueLen,Queue->Flag);
break;
default :
LogFormat(Error,"BucketSortSentry Function , Queue->Flag(%d) Is Unknow Type Flag, Exit!!!\n",Queue->Flag);
exit(ExceptionExitFlag);
}
//后续再做成万能数据型
//现在只支持整型
int ReutrnVal = 0;
QueueLenType i;
QueueLenType BucketGroupIndex = 0;
Status ReturnStatus;
int Digit = 1;//计算的位数
QueueLenType MaxQueueLen = Queue->SqQueueLen;
do
{
if (Digit != 1)
{
//第n次收集是从TmpQueue读取数据，做整数Digit位的排序，放入桶中。
for ( i = 0; i < TmpQueue->SqQueueLen; i++)
{
ReadSqQueue(TmpQueue,i,&ReutrnVal);
BucketGroupIndex = GetIntegerDigit(ReutrnVal,Digit);
PushData2Bucket(Bucket, BucketGroupIndex, &ReutrnVal);
}
//清理临时队列。
ClearSqQueue(TmpQueue);
}
else
{
//第一次收集是从传入参数Queue读取数据，做整数个位的排序，放入桶中。
for ( i = 1; i < Queue->SqQueueLen; i++)
{
ReadSqQueue(Queue,i,&ReutrnVal);
BucketGroupIndex = GetIntegerDigit(ReutrnVal,Digit);
PushData2Bucket(Bucket, BucketGroupIndex, &ReutrnVal);
}
ReadSqQueue(Queue,0,&ReutrnVal);
ClearSqQueue(Queue);
EnterSqQueue(Queue,&ReutrnVal);
}
//第n次分配，从桶中把顺序数据读取出来。
i = 0;
Digit++;
while (Bucket->BucketDataUseNums != 0)
{
ReturnStatus = PopDataFromBucket(Bucket, i, &ReutrnVal);
if (ReturnStatus == SuccessFlag)//成功读出数据，放入临时队列中。
{
if (GetIntegerDigit(ReutrnVal,Digit) == GET_INTEGER_DIGIT_NO_EXISTS_FLAG)//如果给的数没有Digit，放到最终队列中。
{
EnterSqQueue(Queue,&ReutrnVal);
}
else if (GetIntegerDigit(ReutrnVal,Digit) != GET_INTEGER_DIGIT_FAIL_FLAG)//有Digit的进行下一步计算。
{
EnterSqQueue(TmpQueue,&ReutrnVal);
}
else//异常情况
{
LogFormat(Error,"Bucket Sort Sentry Queue Fail, Reason : Error Data(%d).\n",ReutrnVal);
exit(ExceptionExitFlag);
}
}
else if (ReturnStatus == NormalFlag)//由于第i个桶的数据被读取完了，读下一个桶。
{
i++;
}
else//读取数据失败
{
DestroyMyBucket(&Bucket);
DestroySqQueue(&TmpQueue);
Bucket = NULL;
TmpQueue = NULL;
LogFormat(Error,"Bucket Sort Sentry Queue Fail, Reason : Pop Data From Bucket Fail.\n");
return FailFlag;
}
}
//清理桶
ClearMyBucket(Bucket);
}while (GetSqQueueLen(Queue) < MaxQueueLen);//如果最终结果队列的元素个数小于Queue队列的元素个数，说明数据没有排序完。
DestroyMyBucket(&Bucket);
DestroySqQueue(&TmpQueue);
Bucket = NULL;
TmpQueue = NULL;
LogFormat(Debug,"Bucket Sort Sentry Queue OK.\n");
return SuccessFlag;
}四、算法效率
| 情况 | 时间复杂度 | 是否稳定 |
| 最好 | O(n + m) | 稳定 |
| 最坏 | O(k * (n + m)) | |
| 平均 | O(k * (n + m)) |
例如我们上面这个计算时间复杂度是多少呢？
(10个数字 + 10个桶）* 2位数 = 40
五、Linux环境编译测试
[gbase@czg2 Sort]$ make
gcc -Wall -Wextra -O3 InsertSort.c SwapSort.c SelectSort.c MergeSort.c BucketSort.c main.c -o TestSort -I /opt/Developer/ComputerLanguageStudy/C/DataStructureTestSrc/Log/ -I /opt/Developer/ComputerLanguageStudy/C/DataStructureTestSrc/PublicFunction/ -I /opt/Developer/ComputerLanguageStudy/C/DataStructureTestSrc/PublicFunction/HashTable/include/ -I /opt/Developer/ComputerLanguageStudy/C/DataStructureTestSrc/PublicFunction/SqQueue/ -I /opt/Developer/ComputerLanguageStudy/C/DataStructureTestSrc/PublicFunction/SqStack/ -L /opt/Developer/ComputerLanguageStudy/C/DataStructureTestSrc/PublicFunction/Make/Libs/ -lPublicFunction -lLog -lSqQueue
[gbase@czg2 Sort]$ time ./TestSort
2023-9-12--[ Debug ]--Init SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Info ]--SqQueue Data :
Data : [ 0 ,5 ,6 ,7 ,8 ,9 ,0 ,1 ,2 ,3 ,4 ]
FrontIndex : 0
RearIndex : 0
SqQueueLen : 11
SqQueueMaxLen : 11
Flag : INT_TYPE_FLAG
2023-9-12--[ Debug ]--Init SqQueue OK
2023-9-12--[ Debug ]--Init SqQueue OK
2023-9-12--[ Debug ]--Init SqQueue OK
2023-9-12--[ Debug ]--Init SqQueue OK
2023-9-12--[ Debug ]--Init SqQueue OK
2023-9-12--[ Debug ]--Init SqQueue OK
2023-9-12--[ Debug ]--Init SqQueue OK
2023-9-12--[ Debug ]--Init SqQueue OK
2023-9-12--[ Debug ]--Init SqQueue OK
2023-9-12--[ Debug ]--Init SqQueue OK
2023-9-12--[ Debug ]--Init Bucket OK.
2023-9-12--[ Debug ]--Init SqQueue OK
2023-9-12--[ Debug ]--Read SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Push Data To Bucket OK.
2023-9-12--[ Debug ]--Read SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Push Data To Bucket OK.
2023-9-12--[ Debug ]--Read SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Push Data To Bucket OK.
2023-9-12--[ Debug ]--Read SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Push Data To Bucket OK.
2023-9-12--[ Debug ]--Read SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Push Data To Bucket OK.
2023-9-12--[ Debug ]--Read SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Push Data To Bucket OK.
2023-9-12--[ Debug ]--Read SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Push Data To Bucket OK.
2023-9-12--[ Debug ]--Read SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Push Data To Bucket OK.
2023-9-12--[ Debug ]--Read SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Push Data To Bucket OK.
2023-9-12--[ Debug ]--Read SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Push Data To Bucket OK.
2023-9-12--[ Debug ]--Read SqQueue OK
2023-9-12--[ Debug ]--Clear SqQueue OK
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Leave SqQueue OK
2023-9-12--[ Debug ]--Pop Data From Bucket OK.
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--SqQueue is Empty, Data cannot be left
2023-9-12--[ Debug ]--Leave SqQueue OK
2023-9-12--[ Debug ]--Pop Data From Bucket OK.
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--SqQueue is Empty, Data cannot be left
2023-9-12--[ Debug ]--Leave SqQueue OK
2023-9-12--[ Debug ]--Pop Data From Bucket OK.
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--SqQueue is Empty, Data cannot be left
2023-9-12--[ Debug ]--Leave SqQueue OK
2023-9-12--[ Debug ]--Pop Data From Bucket OK.
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--SqQueue is Empty, Data cannot be left
2023-9-12--[ Debug ]--Leave SqQueue OK
2023-9-12--[ Debug ]--Pop Data From Bucket OK.
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--SqQueue is Empty, Data cannot be left
2023-9-12--[ Debug ]--Leave SqQueue OK
2023-9-12--[ Debug ]--Pop Data From Bucket OK.
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--SqQueue is Empty, Data cannot be left
2023-9-12--[ Debug ]--Leave SqQueue OK
2023-9-12--[ Debug ]--Pop Data From Bucket OK.
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--SqQueue is Empty, Data cannot be left
2023-9-12--[ Debug ]--Leave SqQueue OK
2023-9-12--[ Debug ]--Pop Data From Bucket OK.
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--SqQueue is Empty, Data cannot be left
2023-9-12--[ Debug ]--Leave SqQueue OK
2023-9-12--[ Debug ]--Pop Data From Bucket OK.
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--SqQueue is Empty, Data cannot be left
2023-9-12--[ Debug ]--Leave SqQueue OK
2023-9-12--[ Debug ]--Pop Data From Bucket OK.
2023-9-12--[ Debug ]--Enter SqQueue OK
2023-9-12--[ Debug ]--Clear SqQueue OK
2023-9-12--[ Debug ]--Clear SqQueue OK
2023-9-12--[ Debug ]--Clear SqQueue OK
2023-9-12--[ Debug ]--Clear SqQueue OK
2023-9-12--[ Debug ]--Clear SqQueue OK
2023-9-12--[ Debug ]--Clear SqQueue OK
2023-9-12--[ Debug ]--Clear SqQueue OK
2023-9-12--[ Debug ]--Clear SqQueue OK
2023-9-12--[ Debug ]--Clear SqQueue OK
2023-9-12--[ Debug ]--Clear SqQueue OK
2023-9-12--[ Debug ]--Clear Bucket OK.
2023-9-12--[ Debug ]--Destroy SqQueue OK
2023-9-12--[ Debug ]--Destroy SqQueue OK
2023-9-12--[ Debug ]--Destroy SqQueue OK
2023-9-12--[ Debug ]--Destroy SqQueue OK
2023-9-12--[ Debug ]--Destroy SqQueue OK
2023-9-12--[ Debug ]--Destroy SqQueue OK
2023-9-12--[ Debug ]--Destroy SqQueue OK
2023-9-12--[ Debug ]--Destroy SqQueue OK
2023-9-12--[ Debug ]--Destroy SqQueue OK
2023-9-12--[ Debug ]--Destroy SqQueue OK
2023-9-12--[ Debug ]--Destroy Bucket OK.
2023-9-12--[ Debug ]--Destroy SqQueue OK
2023-9-12--[ Debug ]--Bucket Sort Sentry Queue OK.
2023-9-12--[ Info ]--Sort Function Elapsed Time : 0 s
2023-9-12--[ Info ]--SqQueue Data :
Data : [ 0 ,0 ,1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ]
FrontIndex : 0
RearIndex : 0
SqQueueLen : 11
SqQueueMaxLen : 11
Flag : INT_TYPE_FLAG
2023-9-12--[ Debug ]--Destroy SqQueue OK
real 0m0.002s
user 0m0.002s
sys 0m0.000s