【数据结构】排序--快速排序

一概念

二快速排序的实现

1. hoare版本

(1)代码实现

(2)单趟排序图解

(3) 递归实现图解

(4)细节控制

(5)时间复杂度

(6)三数取中优化

2 挖坑法

(1)代码实现

(2)单趟图解

3 前后指针法

(1) 代码实现

(2) 单趟图解

编辑4 优化子区间

5 非递归快速排序

三快速排序的特性总结

一概念

快速排序是Hoare于1962年提出的一种二叉树结构的交换排序方法，其基本思想为：任取待排序元素序列中的某元素作为基准值，按照该排序码将待排序集合分割成两子序列，左子序列中所有元素均小于基准值，右子序列中所有元素均大于基准值，然后最左右子序列重复该过程，直到所有元素都排列在相应位置上为止

二快速排序的实现

上述为快速排序递归实现的主框架，发现与二叉树前序遍历规则非常像

1. hoare版本

(1)代码实现

#include<stdio.h>
void Swap(int* x, int* y)
{int tmp = *x;*x = *y;*y = tmp;
}int PartSort1(int* a, int left, int right)
{int keyi = left;while (left < right){//找小while (left < right && a[right] >= a[keyi]){right--;}//找大while (left < right && a[left] <= a[keyi]){left++;}Swap(&a[left], &a[right]);}Swap(&a[keyi], &a[left]);return left;
}void QuickSort(int* a, int begin, int end)
{if (begin >= end){return;}int key = PartSort1(a, begin, end);QuickSort(a, begin, key - 1);QuickSort(a, key + 1, end);
}
int main()
{int arr[] = {6,1,2,7,9,3,4,5,10,8};QuickSort(arr, 0, (sizeof(arr) / sizeof(int)) - 1);for (int i = 0; i < sizeof(arr) / sizeof(int); i++){printf("%d ", arr[i]);}
}

(2)单趟排序图解

我们看看单趟排序怎么排的

(3) 递归实现图解

再来看看递归怎么实现的

(4)细节控制

对细节控制上我要做一下解释

那这里相遇位置一定比a[keyi]小呢? 右边先走导致的

(5)时间复杂度

我们来算一下快速排序的时间复杂度(需要对二叉树的基本性质熟悉)

(6)三数取中优化

那针对有序的情况我们可以采取三数取中的方式解决

#include<stdio.h>
void Swap(int* x, int* y)
{int tmp = *x;*x = *y;*y = tmp;
}int GetMidi(int* a, int left, int right)
{int mid = (left + right) / 2;if (a[left] < a[mid]){if (a[mid] < a[right]){return mid;}else if (a[left] > a[right]){return left;}else{return right;}}else// a[left] > a[mid]{if (a[left] < a[right]){return left;}else if (a[mid] > a[right]){return mid;}else{return right;}}
}int PartSort1(int* a, int left, int right)
{int midi = GetMidi(a, left, right);Swap(&a[midi], &a[left]);int keyi = left;while (left < right){//找小while (left < right && a[right] >= a[keyi]){right--;}//找大while (left < right && a[left] <= a[keyi]){left++;}Swap(&a[left], &a[right]);}Swap(&a[keyi], &a[left]);return left;
}void QuickSort(int* a, int begin, int end)
{if (begin >= end){return;}int key = PartSort1(a, begin, end);QuickSort(a, begin, key - 1);QuickSort(a, key + 1, end);
}
int main()
{int arr[] = {6,1,2,7,9,3,4,5,10,8};QuickSort(arr, 0, (sizeof(arr) / sizeof(int)) - 1);for (int i = 0; i < sizeof(arr) / sizeof(int); i++){printf("%d ", arr[i]);}
}

2 挖坑法

(1)代码实现

#include<stdio.h>
void Swap(int* x, int* y)
{int tmp = *x;*x = *y;*y = tmp;
}int GetMidi(int* a, int left, int right)
{int mid = (left + right) / 2;if (a[left] < a[mid]){if (a[mid] < a[right]){return mid;}else if (a[left] > a[right]){return left;}else{return right;}}else// a[left] > a[mid]{if (a[left] < a[right]){return left;}else if (a[mid] > a[right]){return mid;}else{return right;}}
}int PartSort2(int* a, int left, int right)
{int midi = GetMidi(a, left, right);Swap(&a[left], &a[midi]);int key = a[left];//保存key值以后 左边形成第一个坑位int hole = left;while (left < right){//右边先走，找小，填到左边的坑，右边形成新的坑位if (left < right && a[right] >= key){right--;}a[hole] = a[right];hole = right;//左边再走，找大，填到右边的坑，左边形成新的坑位if (left < right && a[left] <= key){left++;}a[hole] = a[left];hole = left;}a[hole] = key;return hole;
}void QuickSort(int* a, int begin, int end)
{if (begin >= end){return;}int key = PartSort2(a, begin, end);QuickSort(a, begin, key - 1);QuickSort(a, key + 1, end);
}
int main()
{int arr[] = {6,1,2,7,9,3,4,5,10,8};QuickSort(arr, 0, (sizeof(arr) / sizeof(int)) - 1);for (int i = 0; i < sizeof(arr) / sizeof(int); i++){printf("%d ", arr[i]);}
}

(2)单趟图解

3 前后指针法

(1) 代码实现

int PartSort3(int* a, int left, int right)
{int keyi = left;int prev = left;int cur = prev + 1;while (cur <= right){if (a[cur] < a[keyi] && ++prev != cur){Swap(&a[cur], &a[prev]);}cur++;}Swap(&a[keyi], &a[prev]);return prev;
}
void QuickSort(int* a, int begin, int end)
{if (begin >= end){return;}int key = PartSort3(a, begin, end);QuickSort(a, begin, key - 1);QuickSort(a, key + 1, end);
}
int main()
{int arr[] = {6,1,2,7,9,3,4,5,10,8};QuickSort(arr, 0, (sizeof(arr) / sizeof(int)) - 1);for (int i = 0; i < sizeof(arr) / sizeof(int); i++){printf("%d ", arr[i]);}
}

(2) 单趟图解

4 优化子区间

递归到小的子区间时, 不在递归分割排序,可以考虑使用插入排序

因为区间比较小的时候节点数开的很多特别是最后一层节点数占了整个数大致百分之五十

int PartSort(int* a, int left, int right)
{int midi = GetMidi(a, left, right);Swap(&a[left], &a[midi]);int keyi = left;int prev = left;int cur = prev + 1;while (cur <= right){if (a[cur] < a[keyi] && ++prev != cur){Swap(&a[cur], &a[prev]);}cur++;}Swap(&a[prev], &a[keyi]);return prev;
}void QuickSort(int* a, int begin, int end)
{if (begin >= end){return;}if ((end - begin + 1) > 10){int keyi = PartSort(a, begin, end);QuickSort(a, begin, keyi - 1);QuickSort(a, keyi + 1, end);}else{//插入排序InsertSort(a + begin, end - begin + 1);}
}

5 非递归快速排序

需要有对栈的基础不会的可以看前面的博客

#include<stdio.h>
#include<stdbool.h>
#include<stdlib.h>
#include<assert.h>
typedef struct STList
{int* a;int size;int capacity;
}ST;void STInit(ST* ps)
{assert(ps);ps->a = NULL;ps->size = ps->capacity = 0;
}void STDestroy(ST* ps)
{assert(ps);free(ps->a);ps->a = NULL;ps->size = ps->capacity = 0;
}
void STPush(ST* ps, int x)
{assert(ps);if (ps->size == ps->capacity){int newcapacity = (ps->capacity == 0 ? 4 : ps->capacity * 2);int* tmp = (int*)realloc(ps->a, sizeof(int) * newcapacity);if (tmp == NULL){perror("realloc fail");exit(-1);}ps->a = tmp;ps->capacity = newcapacity;}ps->a[ps->size] = x;ps->size++;
}void STPop(ST* ps)
{assert(ps);assert(ps->size > 0);ps->size--;
}bool STEmpty(ST* ps)
{assert(ps);return ps->size == 0;
}int STTop(ST* ps)
{assert(ps);assert(ps->size > 0);return ps->a[ps->size - 1];
}
void Swap(int* x, int* y)
{int tmp = *x;*x = *y;*y = tmp;
}int GetMidi(int* a, int left, int right)
{int mid = (left + right) / 2;if (a[left] < a[mid]){if (a[mid] < a[right]){return mid;}else if (a[left] > a[right]){return left;}else{return right;}}else// a[left] > a[mid]{if (a[left] < a[right]){return left;}else if (a[mid] > a[right]){return mid;}else{return right;}}
}int PartSort(int* a, int left, int right)
{int midi = GetMidi(a, left, right);Swap(&a[left], &a[midi]);int keyi = left;int prev = left;int cur = prev + 1;while (cur <= right){if (a[cur] < a[keyi] && ++prev != cur){Swap(&a[cur], &a[prev]);}cur++;}Swap(&a[prev], &a[keyi]);return prev;
}void QuickSortNonR(int* a, int begin, int end)
{ST st;//创建一个栈 STInit(&st);//初始化STPush(&st, end);STPush(&st, begin);while (!STEmpty(&st)){int left = STTop(&st);STPop(&st);int right = STTop(&st);STPop(&st);int keyi = PartSort(a, left, right);// [lefy,keyi-1] keyi [keyi+1, right]if (keyi + 1 < right){STPush(&st, right);STPush(&st, keyi + 1);}if (left < keyi - 1){STPush(&st, keyi - 1);STPush(&st, left);}}STDestroy(&st);
}int main()
{int arr[] = {6,1,2,7,9,3,4,5,10,8};QuickSortNonR(arr, 0, (sizeof(arr) / sizeof(int)) - 1);for (int i = 0; i < sizeof(arr) / sizeof(int); i++){printf("%d ", arr[i]);}
}