目录
一，计数排序
计数排序也叫非比较排序；
1，基本思想
计数排序又称为鸽巢原理，是对哈希直接定址法的变形应用
操作步骤：
1，统计相同元素出现次数
2，根据统计的结果将序列回收到原来的序列中
图解原理：
对这样一个不需要比较的排序就完成了；
2，思路实现
// 计数排序void CountSort(int* arr, int n){int i = 0;int max = arr[0], min = arr[0];//找最大，最小值for (i = 0; i < n; i++){if (arr[i] > max){max = arr[i];}if (arr[i] < min){min = arr[i];}}//空间大小int sum = max - min + 1;//开辟空间并且使元素值都为0int* arr1 = (int*)calloc(sum, sizeof(int));//给新数组赋值for (i = 0; i < n; i++){arr1[arr[i] - min]++;}int j = 0;//回收到原来的序列中for (i = 0; i < sum; i++){while (arr1[i]--){arr[j++] = i + min;}}}然后我们运行测试一下：
可以看到是有序的，选择排序就 OK 了；
3，计数排序的特性总结：
1， 计数排序在数据范围集中时，效率很高，但是适用范围及场景有限
，时间复杂度：O(N+K)
3， 空间复杂度：O(N)
4, 稳定性：稳定
二，排序算法复杂度及稳定性分析
| 排序方法 | 平均情况 | 最好情况 | 最坏情况 | 辅助空间 | 稳定性 |
| 冒泡排序 | O(N^2) | O(N) | O(N^2) | O(1) | 稳定 |
| 选择排序 | O(N^2) | O(N^2) | O(N^2) | O(1) | 不稳定 |
| 直接插入排序 | O(N^2) | O(N) | O(N^2) | O(1) | 稳定 |
| 希尔排序 | O(NlongN)~O(N^2) | O(N^1.3) | O(N^2) | O(1) | 不稳定 |
| 堆排序 | O(NlongN) | O(NlongN) | O(NlongN) | O(1) | 不稳定 |
| 归并排序 | O(NlongN) | O(NlongN) | O(NlongN) | O(N) | 稳定 |
| 快速排序 | O(NlongN) | O(NlongN) | O(N^2) | O(N) | 不稳定 |
| 计数排序 | O(N+K) | O(N+K) | O(N+K) | O(K) | 稳定 |
三，排序系列所有源代码
Sort.h
#pragma once#include#include#include#include"Stack.h"//打印void PrintSort(int* arr, int n);//插入排序void InsertSort(int* arr, int n);//希尔排序void HillSort(int* arr, int n);//选择排序void SeleSort(int* arr, int n);//堆排序void HeapSort(int* arr, int n);//向下调整void DownAdjust(int* arr, int n, int i);冒泡排序//void BubblSort(int* arr, int n);//快速排序void QuickSort(int* arr, int begin, int end);//三数取中int middle(int* arr, int left, int right);//快慢指针法int PartSort3(int* arr, int left, int right);//挖坑法int PartSort2(int* arr, int left, int right);//霍尔排序int PartSort1(int* arr, int left, int right);//快速排序(非递归)void QuickNon(int* arr, int begin, int end);//归并排序void MergerSort(int* arr, int begin, int end);//归并排序(非递归)void MergerSortNon(int* arr, int begin, int end);// 计数排序void CountSort(int* arr, int n); Sort.c
#define _CRT_SECURE_NO_WARNINGS 1#include"Sort.h"//打印void PrintSort(int* arr, int n){int i = 0;for (i = 0; i < n; i++){printf("%d ", arr[i]);}}//交换void Swap(int* a, int* b){int tmp = *a;*a = *b;*b = tmp;}//插入排序void InsertSort(int* arr, int n){int i = 0;for (i = 0; i < n-1; i++){int end = i;int tmp = arr[end + 1];while (end >= 0){if (arr[end] >= tmp){//交换Swap(&arr[end], &arr[end+1]);end--;}else{break;}}arr[end + 1] = tmp;}}//希尔排序void HillSort(int* arr, int n){int gap = n;int i = 0;while (gap > 1){gap = gap / 2;for (i = 0; i < n-gap; i++){int end = i;int tmp = arr[end + gap];while (end >= 0){if (arr[end] >= tmp){//交换Swap(&arr[end], &arr[end + gap]);end -= gap;}else{break;}}arr[end + gap] = tmp;}}}//选择排序void SeleSort(int* arr, int n){int begin = 0, end = n - 1;while (begin < end){int maxi = begin, mini = begin;for (int i = begin; i <= end; i++){if (arr[i] > arr[maxi]){maxi = i;}if (arr[i] < arr[mini]){mini = i;}}Swap(&arr[begin], &arr[mini]);// 如果maxi和begin重叠，修正一下即可if (begin == maxi){maxi = mini;}Swap(&arr[end], &arr[maxi]);++begin;--end;}}//向下调整void DownAdjust(int* arr, int n, int i){int perent = i;int child = perent* 2 + 1;while (child arr[child]){child++;}if (arr[perent] < arr[child]){//交换Swap(&arr[perent], &arr[child]);perent = child;child = perent * 2 + 1;}else{break;}}}//堆排序void HeapSort(int* arr, int n){//建堆int i = 0;for (i = (n - 1 - 1) / 2; i >= 0; i--){//向下调整DownAdjust(arr, n, i);}//交换，删除排序法while (n > 1){//交换Swap(&arr[0], &arr[n - 1]);n--;//向下调整DownAdjust(arr, n, 0);}}//三数取中int middle(int* arr, int left, int right){//int mid = (left +right)/ 2;//随机数取中int mid = left + (rand() % (right - left));if (arr[left] < arr[mid]){if (arr[mid] < arr[right]){return mid;}if (arr[left] < arr[right]){return right;}else{return left;}}//arr[mid]<=arr[left]else{if (arr[mid] > arr[right]){return mid;}if (arr[left] > arr[right]){return right;}else{return left;}}}//霍尔排序int PartSort1(int* arr, int left, int right){//三数取中int ret = middle(arr, left, right);Swap(&arr[left], &arr[ret]);int keyi = left;while (left < right){//右边先走while (left=arr[keyi]){right--;}//左边后走while (left < right && arr[left] <= arr[keyi]){left++;}//交换Swap(&arr[left], &arr[right]);}Swap(&arr[left], &arr[keyi]);return left;}//挖坑法int PartSort2(int* arr, int left, int right){//三数取中int ret = middle(arr, left, right);Swap(&arr[left], &arr[ret]);int key = arr[left];int hole = left;while (left < right){while (left < right && arr[right] >= key){right--;}arr[hole] = arr[right];hole = right;while (left < right && arr[left] <= key){left++;}arr[hole] = arr[left];hole = left;}arr[hole] = key;return hole;}//前后指针法int PartSort3(int* arr, int left, int right){//三数取中int ret = middle(arr, left, right);Swap(&arr[left], &arr[ret]);int keyi = left;int slow = left, fast = left+1;while (fast<=right){if (arr[fast] < arr[keyi] && ++slow!=fast){//交换Swap(&arr[fast], &arr[slow]);}fast++;}Swap(&arr[slow], &arr[keyi]);return slow;}//插入排序(改造版)void InsertSort1(int* arr, int left, int right){int i = 0;for (i = left; i < right; i++){int end = i;int tmp = arr[end + 1];while (end >= 0){if (arr[end] >= tmp){//交换Swap(&arr[end], &arr[end + 1]);end--;}else{break;}}arr[end + 1] = tmp;}}//快速排序void QuickSort(int* arr, int begin, int end){srand(time(0));if (begin >= end){return NULL;}if (end - begin <10){InsertSort1(arr,begin,end);}else{int keyi = PartSort1(arr, begin, end);//排序[begin,keyi) & [keyi+1,end]QuickSort(arr, begin, keyi);QuickSort(arr, keyi + 1, end);}}//快速排序(非递归)void QuickNon(int* arr, int begin, int end){srand(time(0));ST ps;//初始化STInit(&ps);if (begin >= end){return;}//插入STPush(&ps, end);STPush(&ps, begin);//栈不为空就进去while (!STEmpty(&ps)){int left = STInsert(&ps);//栈顶元素STPop(&ps);//删除int right = STInsert(&ps);STPop(&ps);int keyi = PartSort1(arr, left, right);//排序[left,keyi-1] & [keyi+1,right]if (keyi + 1 < right){//插入STPush(&ps, right);STPush(&ps, keyi + 1);}if (left < keyi - 1){//插入STPush(&ps, keyi - 1);STPush(&ps, left);}}//销毁STDestroy(&ps);}//归并void Merger(int* arr, int* tmp,int begin,int end){int mid = (begin + end) / 2;if (begin == end){return;}//排序【begin,mid】& 【mid+1,end】Merger(arr, tmp, begin,mid);Merger(arr, tmp, mid+1, end);int begin1 = begin, end1 = mid;int begin2 = mid + 1, end2 = end;int i = 0;while (begin1 <= end1 && begin2 <= end2){if (arr[begin1] < arr[begin2]){tmp[i++] = arr[begin1++];}else{tmp[i++] = arr[begin2++];}}while(begin1 <= end1){tmp[i++] = arr[begin1++];}while (begin2 <= end2){tmp[i++] = arr[begin2++];}//进行拷贝memcpy(arr + begin, tmp, (end - begin+1)*sizeof(int));}//归并排序void MergerSort(int* arr, int begin, int end){if (begin >= end){return;}//开辟同等大小数组int* tmp = (int*)malloc((end - begin + 1)*sizeof(int));//归并Merger(arr, tmp, begin, end);free(tmp);tmp = NULL;}//归并排序(非递归)void MergerSortNon(int* arr, int begin, int end){if (begin >= end){return;}//开辟同等大小数组int* tmp = (int*)malloc((end - begin + 1) * sizeof(int));int gap = 1;int j = 0;while (gap < end){for (j = 0; j < end; j += 2 * gap){int begin1 = j, end1 = begin1+gap-1;int begin2 =end1+1, end2 = begin2+gap-1;int i = 0;//处理边界问题if (end1 >= end){break;}if (end2 >end){end2 = end;}while (begin1 <= end1 && begin2 <= end2){if (arr[begin1] < arr[begin2]){tmp[i++] = arr[begin1++];}else{tmp[i++] = arr[begin2++];}}while (begin1 <= end1){tmp[i++] = arr[begin1++];}while (begin2 <= end2){tmp[i++] = arr[begin2++];}//进行拷贝memcpy(arr + j, tmp, (end2 - j+ 1) * sizeof(int));}gap *= 2;}free(tmp);tmp = NULL;}// 计数排序void CountSort(int* arr, int n){int i = 0;int max = arr[0], min = arr[0];//找最大，最小值for (i = 0; i < n; i++){if (arr[i] > max){max = arr[i];}if (arr[i] < min){min = arr[i];}}//空间大小int sum = max - min + 1;//开辟空间并且使元素值都为0int* arr1 = (int*)calloc(sum, sizeof(int));//给新数组赋值for (i = 0; i < n; i++){arr1[arr[i] - min]++;}int j = 0;//回收到原来的序列中for (i = 0; i < sum; i++){while (arr1[i]--){arr[j++] = i + min;}}} Stack.h
#pragma once#include#include#include#includetypedef int STDataType;typedef struct StackTop{STDataType* a;int top;int capacity;}ST;//初始化void STInit(ST* ps);//销毁void STDestroy(ST* ps);//插入void STPush(ST* ps, STDataType x);//删除void STPop(ST* ps);//返回栈顶STDataType STInsert(ST* ps);//数量int STSize(ST* ps);//判断是否为空int STEmpty(ST* ps); Stack.c
#define _CRT_SECURE_NO_WARNINGS 1#include"Stack.h"//初始化void STInit(ST* ps){assert(ps);ps->a = NULL;ps->top = ps->capacity = 0;}//销毁void STDestroy(ST* ps){assert(ps);free(ps->a);ps->a = NULL;ps->top = ps->capacity = 0;}//插入void STPush(ST* ps, STDataType x){assert(ps);if (ps->top == ps->capacity){ps->capacity = ps->top == 0 ? 4 : ps->capacity*2;ps->a = (STDataType*)realloc(ps->a,sizeof(STDataType)*ps->capacity);}ps->a[ps->top] = x;ps->top++;}//删除void STPop(ST* ps){assert(ps);assert(ps->top > 0);ps->top--;}//返回栈顶STDataType STInsert(ST* ps){assert(ps);assert(ps->top > 0);return ps->a[ps->top-1];}//数量int STSize(ST* ps){assert(ps);return ps->top;}//判断是否为空int STEmpty(ST* ps){assert(ps);if (ps->top == 0){return 1;}else{return 0;}}
同志们！排序的知识就到这里了！
后面博主会陆续更新；
如有不足之处欢迎来补充交流！
完结。。
来源地址：https://blog.csdn.net/m0_71676870/article/details/133693820
