大家好，我是纪宁，这篇文章是关于八大排序的源代码，具体实现过程会在后续文章中介绍。

1、直接插入排序

时间复杂度O(N^2)，原数据越有序，效率越高。
当原数据有序时，则时间复杂度为O(N)。原数据倒序时，时间复杂度为O(N^2)

void InsertSort(int* a, int n)//直接插入排序
{for (int i = 0; i < n - 1; i++){int end = i;int tmp = a[end+1];while (end >= 0){if (a[end] >tmp){a[end + 1] = a[end];}else{break;}end--;}a[end + 1] = tmp;}
}

2、希尔排序

时间复杂度：O(N^1.3) 空间复杂度：O(1)
希尔排序是插入排序的优化，整体思路是先预排序，使原数据更接近有序，等到gap==1时，就变成了直接插入排序。

void ShellSort(int* arr, int n)
{int gap = n;while (gap > 1){gap = gap / 3 + 1;//gap也可以 /=2；奇特数字必须保证gap最后的值为1for (int i = 0; i < n - gap; i++){int end = i;int tmp = arr[end + gap];while (end >= 0){if (tmp < arr[end]){arr[end + gap] = arr[end];}else{break;}end -= gap;}arr[end + gap] = tmp;}}
}

3、选择排序

时间复杂度：O(N^2) 空间复杂度：O(1)
每次选择一个最大或者最小的数，使其出现在正确的位置。

void SelectSort(int* a, int n)
{for (int j = 0; j < n; j++){int mini = j;int maxi= n - j-1;for (int i = j; i < n-j; i++){if (a[i] < a[mini]){mini = i;}if (a[i] > a[maxi]){maxi = i;}}Swap(&a[mini], &a[j]);if (maxi == j){maxi = mini;//最大值如果在 j 这个位置的话，结果这个位置被换成了min 的值}Swap(&a[maxi], &a[n-1-j]);}
}

4、冒泡排序

时间复杂度：O(N^2) 空间复杂度：O(1)
思路最简单的排序，所有程序员的白月光！

void BubbleSort(int* a, int n)//冒泡排序
{for (int i = 0; i < n; i++){int ret = 0;//如果一趟后ret还等于0，说明数据已经有序for (int j = 0; j < n - i - 1; j++){if (a[j] > a[j + 1]){Swap(&a[j], &a[j + 1]);ret = 1;}}if (ret == 0)break;}
}

5、堆排序

时间复杂度：O(N*logN) 空间复杂度：O(1)
建堆的时候可以采用向上调整和向下调整建堆，而排序的时候只能使用向下调整算法。
排升序建大堆，降序建小堆。

void Adjustup(int* a, int child)//向上调整
{int parent = (child - 1) / 2;while (parent >= 0){if (a[child] > a[parent]){Swap(&a[child], &a[parent]);child = parent;parent = (child - 1) / 2;}else{break;}}
}void Adjustdown(int* a, int parent, int n)//向下调整
{int child = 2 * parent + 1;while (child < n){if (child + 1 < n && a[child + 1] > a[child]){child++;}if (a[child] > a[parent]){Swap(&a[child], &a[parent]);parent = child;child = 2 * parent + 1;}else{break;}}
}void HeapSort(int* arr, int sz)
{//第一步，建堆向上调整建堆//for (int i = 1; i < sz; i++)//{//	Adjustup(arr, i); //}//向下调整建堆for (int i = (sz - 1) / 2; i >= 0; i--){Adjustdown(arr, i, sz - 1);}int end = sz - 1;while (end > 0){Swap(&arr[0], &arr[end]);Adjustdown(arr, 0, end);end--;}
}

6、快速排序

时间复杂度：O(N*logN) 空间复杂度：O(1)

快速排序递归实现

霍尔法

int QuickSortPart1(int*a,int left,int right)//霍尔版本
{int* Maxi = (&a[left], &a[right], &(a[(left + right) / 2]));//三数取中Swap(&a[left], Maxi);//换到最左边int key = a[left];int keyi = left;while (left<right){while (left<right && a[right]>=key){right--;}while (left < right && a[left] <= key){left++;}Swap(&a[left], &a[right]);}Swap(&a[keyi], &a[left]);return left;
}
void QuickSort(int*arr, int begin, int end)
{if (begin >= end)//等于是只有一个数需要排，大于是没有数需要排{return;}int keyi = QuickSortPart1(arr, begin, end);/*int keyi = QuickSortPart2(arr, begin, end);int keyi = QuickSortPart3(arr, begin, end);*/QuickSort(arr, begin, keyi - 1);QuickSort(arr, keyi + 1, end);
}

挖坑法

int QuickSortPart2(int* arr, int left, int right)//挖坑法
{int* Maxi = (&arr[left], &arr[right], &(arr[(left + right) / 2]));Swap(&arr[left], Maxi);int holei = left;int hole = arr[left];while (left < right){while (left < right && arr[right] >= hole){right--;}arr[holei] = arr[right];holei = right;while (left < right && arr[left] <= hole){left++;}arr[holei] = arr[left];holei = left;}arr[holei] = hole;return left;
}
void QuickSort(int*arr, int begin, int end)
{if (begin >= end)//等于是只有一个数需要排，大于是没有数需要排{return;}/*int keyi = QuickSortPart1(arr, begin, end);*/int keyi = QuickSortPart2(arr, begin, end);/*int keyi = QuickSortPart3(arr, begin, end);*/QuickSort(arr, begin, keyi - 1);QuickSort(arr, keyi + 1, end);
}

前后指针法

int QuickSortPart3(int* a, int left, int right)//快排快慢指针
{int* Maxi = (&a[left], &a[right], &(a[(left + right) / 2]));Swap(&a[left], Maxi);int keyi = left;int prev = left;int cur = left+1;while (cur <= right){if (a[cur] < a[keyi]&& ++prev!= cur){Swap(&a[prev], &a[cur]);}cur++;}Swap(&a[prev],&a[keyi]);return prev;
}void QuickSort(int*arr, int begin, int end)
{if (begin >= end)//等于是只有一个数需要排，大于是没有数需要排{return;}//*int keyi = QuickSortPart1(arr, begin, end);*///int keyi = QuickSortPart2(arr, begin, end);int keyi = QuickSortPart3(arr, begin, end);QuickSort(arr, begin, keyi - 1);QuickSort(arr, keyi + 1, end);
}

快速排序小区间优化

void QuickSort1(int* a, int begin, int end)
{if (begin >= end)return;// 小区间优化，小区间不再递归分割排序，降低递归次数if ((end - begin + 1) > 10){int keyi = PartSort3(a, begin, end);// [begin, keyi-1] keyi [keyi+1, end]QuickSort1(a, begin, keyi - 1);QuickSort1(a, keyi + 1, end);}else{InsertSort(a + begin, end - begin + 1);//直接插入排序}
}

快速排序非递归实现

快排非递归要用栈来实现

void QuickSortNorn(int* a, int begin, int end)
{ST st;//创建数组栈STInit(&st);//初始化栈STPush(&st, end);//入栈STPush(&st, begin);//入栈while (!STEmpty(&st))//判空{int left = STTop(&st);//取栈顶数据STPop(&st);//出栈int right = STTop(&st);STPop(&st);int keyi = QuickSortPart1(a, left,right);if (keyi + 1 < right){STPush(&st, right);STPush(&st, keyi + 1);}if (keyi - 1 > left){STPush(&st, keyi - 1);STPush(&st, left);}}STDestroy(&st);//销毁栈
}

7、归并排序

时间复杂度：O(N*logN) 空间复杂度：O(N)

归并排序递归实现

void _MergeSortPart(int* a, int* tmp, int begin, int end)
{if (begin >= end)return;int midi = (begin + end) / 2;_MergeSortPart(a, tmp, begin, midi);_MergeSortPart(a, tmp, midi + 1, end);int begin1 = begin, end1 = midi;int begin2 = midi + 1, end2 = end;int index = begin;while (begin1 <= end1 && begin2 <= end2){if (a[begin1] < a[begin2]){tmp[index++] = a[begin1++];}else{tmp[index++] = a[begin2++];}}while (begin1 <= end1){tmp[index++] = a[begin1++];}while (begin2 <= end2){tmp[index++] = a[begin2++];}memcpy(a+begin, tmp+begin, sizeof(int) * (end - begin + 1));
}
void MergeSort(int* a, int n)
{int* tmp = (int*)malloc(sizeof(int) * n);_MergeSortPart(a, tmp, 0, n - 1);free(tmp);tmp = NULL;
}

归并排序非递归

void _MergeSortNonr(int* a, int* tmp, int begin, int end)
{int gap = 1;while (gap <= end){for (int i = 0; i <= end; i += 2 * gap){int begin1 = i, end1 = i + gap - 1;int begin2 = i + gap, end2 = i + 2 * gap - 1;int index = i;if (begin2 > end){break;}if (end2 > end){end2 = end;//对范围进行修正}while (begin1 <= end1 && begin2 <= end2){if (a[begin1] < a[begin2]){tmp[index++] = a[begin1++];}else{tmp[index++] = a[begin2++];}}while (begin1 <= end1){tmp[index++] = a[begin1++];}while (begin2 <= end2){tmp[index++] = a[begin2++];}memcpy(a + i, tmp + i, sizeof(int) * (end2-i+1));//拷贝回原数组}gap *= 2;}}
void MergeSortNonr(int* a, int n)//归并排序非递归
{int* tmp = (int*)malloc(sizeof(int) * n);_MergeSortNonr(a, tmp, 0, n - 1);free(tmp);tmp = NULL;
}

8、计数排序

时间复杂度：O(MAX(N,range)) 空间复杂度：O(range)

void CountSort(int* a, int n)//计数排序
{//先找最大值和最小值int maxi = 0, mini = 0;for (int i = 1; i < n; i++){if (a[i] > a[maxi]){maxi = i;}if (a[i] < a[mini]){mini = i;}}int max = a[maxi], min = a[mini];int range = a[maxi] - a[mini]+1;int* count = (int*)malloc(sizeof(int) * range);memset(count, 0, sizeof(int) * range);for (int j = 0; j < n; j++){count[a[j] - min]++;}int i = 0;for (int j = 0; j < n; j++){while (count[j]--){ a[i++] = j + min;}}
}