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堆排序：

在学习堆之后我们知道了大堆和小堆，对于大堆而言第一个节点就是对大值，对于小堆而言，第一个值就是最小的值。如果我们把第一个值与最后一个值交换再对最后一个值前面的数据重新建堆，如此下去就可以实现建堆排序。

建堆的两种方法：

向上调整建堆：

 向上调整建堆的思路是从第一个开始先后添加数据，在每次到一个数据是如果比父节点大（小）就与父节点交换位置并继续向上调整。

算法复杂度：O(N*logN) 

 向下调整建堆：

 因为对于大（小）堆来说它的左右子树也都应该是大（小）堆，以此类推我们最小的数也应该是大（小）堆，于是我们就从最小的树开始建堆。

算法复杂度：O(N) 

插入排序：

直接插入排序是认为要插入数之前的所有数据已经排序好,用一个tmp临时变量存储要插入的值,如果要插入值的前一个数据比他大,那么就向后覆盖,接着继续往前比,直到遇到比要插入值小的数据,将要插入值插入在该数据的后一位。

希儿排序:

 

事实上就是插入排序的升级版，对插入排序进行调整使数组趋于有序，最后一次进行一次插入排序。 

选择排序：

选择排序是从数据的首端去进行选择,遍历一遍数组取选出最大值和最小值,选出后交换放在两端排序,继续去选择。注意的是如果最大值是第一个数据,后面交换时会出现数据被替代的情况,这种情
况下我们需要在交换后将最大值下标指向最小值下标。

 

 

 快速排序：

递归：

 

 

 

非递归 ：

归并排序： 

递归：

 

 非递归：

计数排序 ：

其思想就是利用一个数组，数组名表示需要排序的数组里的数据，其大小就是出现次数，最后从大到小存在一个数组里。

#include "SORT.h"void swap(int* a, int* b)
{//printf("%d %d --", *a, *b);int tmp = *a;*a = *b;*b = tmp;//printf("%d %d\n", *a, *b);
}/*******************************************************************************/
/*---------------------------------堆排序------------------------------------- */
/*******************************************************************************/
void heapSort_F(int* arr,int n)//向下调整建堆
{//升序建大堆int last_father = (n - 1) / 2;					//找到第一个父while (last_father != -1){int father = last_father;int child = father * 2 + 1;while (child <= n){if (child + 1 <= n && arr[child + 1] > arr[child])		//找到最大的孩子{++child;}if (arr[father] < arr[child])					//孩子比父亲大就交换{int tmp = arr[father];arr[father] = arr[child];arr[child] = tmp;}father = child;						//继续向下（大的往上走作为父）child = father * 2 + 1;}									//大堆好了--last_father;}while (n){//交换首尾巴size--int tmp = arr[0];arr[0] = arr[n];arr[n] = tmp;--n;int father = 0;int child = father * 2 + 1;while (child <= n)				//向下找大的作为父{if (child + 1 <= n){if (arr[child + 1] > arr[child])++child;}if (arr[father] < arr[child]){int tmp = arr[father];arr[father] = arr[child];arr[child] = tmp;}father = child;child = father * 2 + 1;}}
}void heapSort_S(int* arr, int n)//向上调整建堆
{//降序建小堆for (int i = 1; i <= n; i++)			//从前往后插入，每插入一个判断上面的父是否需要向上改变{int child = n;while (child){int father = (child - 1) / 2;if (arr[father] > arr[child]){int tmp = arr[child];arr[child] = arr[father];arr[father] = tmp;}child = father;}}while (n){int tmp = arr[0];arr[0] = arr[n];arr[n] = tmp;--n;int father = 0;int child = father * 2 + 1;while (child <= n){if (child + 1 <= n){if (arr[child + 1] < arr[child])++child;}if (arr[father] > arr[child]){int tmp = arr[father];arr[father] = arr[child];arr[child] = tmp;}father = child;child = father * 2 + 1;}}
}
/*=======================================================================================*/
/*=======================================================================================*//*******************************************************************************/
/*--------------------------------插入排序------------------------------------ */
/*******************************************************************************/
void InsertSort(int* arr, int n)
{int end = 0;while (end != n - 1){++end;int val = arr[end];int change = end;while (change != 0){if (arr[change - 1] > val){arr[change] = arr[change - 1];--change;}else break;}arr[change] = val;}
}
//void InsertSort(int* a, int n)
//{
//	//  [0, n-1]
//	for (int i = 0; i < n - 1; i++)
//	{
//		// [0, n-2]是最后一组
//		// [0,end]有序 end+1位置的值插入[0,end]，保持有序
//		int end = i;
//		int tmp = a[end + 1];
//		while (end >= 0)
//		{
//			if (tmp < a[end])
//			{
//				a[end + 1] = a[end];
//				--end;
//			}
//			else
//			{
//				break;
//			}
//		}
//		a[end + 1] = tmp;
//	}
//}
//
/*=======================================================================================*/
/*=======================================================================================*//*******************************************************************************/
/*--------------------------------希儿排序------------------------------------ */
/*******************************************************************************/
void ShellSort(int* arr, int n)
{int gap = n;while(gap>1){gap = gap / 3 + 1;//for (size_t j=0; j < gap; j++)//{//	for (size_t i = j; i < n-gap; i+=gap)   //一组一组for (size_t i = 0; i < n - gap; ++i)    //多组并着走{int end = i;int tmp = arr[end + gap];while (end >= 0){if (tmp < arr[end]){arr[end + gap] = arr[end];end -= gap;}else{break;}}arr[end + gap] = tmp;}//}}
}
/*=======================================================================================*/
/*=======================================================================================*//*******************************************************************************/
/*------------------------------  选择排序  ---------------------------------- */
/*******************************************************************************/
void SelectSort(int* arr, int n)
{int start = 0; int end = n - 1;while (start < end){int mini = start;int maxi = end;for (int i = start; i <= end; i++){if (arr[i] < arr[mini])mini = i;if (arr[i] > arr[maxi])maxi = i;}swap(&arr[start], &arr[mini]);if (start == maxi){maxi = mini;}swap(&arr[end], &arr[maxi]);++start;--end;}
}
/*=======================================================================================*/
/*=======================================================================================*//*******************************************************************************/
/*--------------------------------快速排序------------------------------------ */
/*******************************************************************************/
int get_midi(int* arr, int left, int right)         //优化--三值取中
{int midi = (left + right) / 2;if (arr[midi] < arr[left]){if (arr[midi] > arr[right])return midi;else{if (arr[left] > arr[right])return left;else return right;}}else{if (arr[midi] < arr[right])return midi;else{if (arr[left] > arr[right])return left;else return right;}}
}
// 霍尔版
int partSort1(int* arr, int left, int right)
{if (right - left < 10)//小区间优化{InsertSort(&arr[left], right - left + 1);}int midi = get_midi(arr, left, right);int keyi = left;swap(&arr[midi], &arr[keyi]);int key = arr[left];int begin = left, end = right;while (begin < end){//向右找小while (arr[end] >= key && begin < end){--end;}//向左找大while (arr[begin] <= key && begin < end){++begin;}swap(&arr[begin], &arr[end]);}swap(&arr[keyi], &arr[end]);return begin;
}
// 双指针
int partSort2(int* arr, int left, int right)
{int keyi = left;int key = arr[left];int prev = left;int cur = prev + 1;while (cur<=right){if (arr[cur] < key && ++prev != cur)swap(&arr[cur], &arr[prev]);++cur;}swap(&arr[prev], &arr[keyi]);return prev;
}void QuickSort(int* arr, int left, int right)
{if (left >= right)return;else{int begin = partSort2(arr, left, right);    //双指针//int begin = partSort1(arr, left, right);    //霍尔版QuickSort(arr, left, begin - 1);QuickSort(arr, begin + 1, right);}}
/*=======================================================================================*/
/*=======================================================================================*//*******************************************************************************/
/*---------------------------快速排序（非递归）------------------------------- */
/*******************************************************************************/
void quickSortNonR(int* arr, int left, int right)
{ST st;STinit(&st);STpush(&st, left);STpush(&st, right);while (!STEmpty(&st)){int end = STtop(&st);STpop(&st);int begin = STtop(&st);STpop(&st);int mid = partSort1(arr, begin, end);if (mid - 1 > begin){STpush(&st, begin);STpush(&st, mid - 1);}if (mid + 1 < end){STpush(&st, mid + 1);STpush(&st, end);}}
}
/*=======================================================================================*/
/*=======================================================================================*//*******************************************************************************/
/*--------------------------------归并排序------------------------------------ */
/*******************************************************************************/
void _mergeSort(int* arr, int* tmp, int begin, int end)
{if (begin >= end)return;int mid = (begin + end) / 2;_mergeSort(arr, tmp, begin, mid);_mergeSort(arr, tmp, mid + 1, end);int begin1 = begin, end1 = mid;int begin2 = mid + 1, end2 = end;int i = begin;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++];memcpy(arr + begin, tmp + begin, sizeof(int) * (end - begin + 1));
}
void mergeSort(int* arr, int n)
{int* tmp = (int*)malloc(sizeof(int) * n);_mergeSort(arr, tmp, 0, n-1);free(tmp);
}
/*=======================================================================================*/
/*=======================================================================================*//*******************************************************************************/
/*---------------------------归并排序（非递归）------------------------------- */
/*******************************************************************************/
void mergeSortNonR(int* arr, int n)
{int* tmp = (int*)malloc(sizeof(int) * n);int gap = 1;while (gap < n){for (int i = 0; i < n; i += gap * 2){int j = i;int begin1 = i, end1 = i + gap - 1;int begin2 = i + gap, end2 = i + 2 * gap - 1;if (begin2 >= n)break;if (end2 >= n)end2 = n - 1;while (begin1 <= end1 && begin2 <= end2){if (arr[begin1] < arr[begin2]){tmp[j++] = arr[begin1++];}else{tmp[j++] = arr[begin2++];}}while (begin1 <= end1)tmp[j++] = arr[begin1++];while (begin2 <= end2)tmp[j++] = arr[begin2++];memcpy(arr + i, tmp + i, sizeof(int) * (end2 - i + 1));}gap *= 2;}free(tmp);
}
/*=======================================================================================*/
/*=======================================================================================*//*******************************************************************************/
/*--------------------------------计数排序------------------------------------ */
/*******************************************************************************/void count_Sort(int* arr, int sz)
{int max = arr[0];int min = arr[0];for (int i = 0; i < sz; i++){if (arr[i] > max)max = arr[i];if (arr[i] < min)min = arr[i];}int* tmp = (int*)calloc(max - min + 1, sizeof(int));for (int i = 0; i < sz; i++){tmp[arr[i] - min]++;}int i = 0;for (int j = 0; j < max - min + 1; j++){while (tmp[j]--){arr[i++] = j + min;}}
}/*=======================================================================================*/
/*=======================================================================================*/