归并排序（MERGE-SORT）是建立在归并操作上的一种有效的排序算法,该算法是采用分治法（Divide and Conquer）的一个非常典型的应用。将已有序的子序列合并，得到完全有序的序列；即先使每个子序列有序，再使子序列段间有序。若将两个有序表合并成一个有序表，称为二路归并。 归并排序核心步骤：
cpp复制代码
void _MergeSort(int* a, int begin, int end, int* tmp)
{
if (begin >= end)
{
return;
}
int mid = (begin + end) / 2;
//[begin,mid] [mid+1,end]
_MergeSort(a, begin, mid, tmp);
_MergeSort(a, mid + 1, end, tmp);
//归并两个区间
int begin1 = begin;
int begin2 = mid + 1;
int end1 = mid;
int end2 = end;
int i = begin;
while (begin1 <= end1 && begin2 <= end2)
{
if (a[begin1] < a[begin2])
{
tmp[i++] = a[begin1++];
}
else
{
tmp[i++] = a[begin2++];
}
}
while (begin1 <= end1)
{
tmp[i++] = a[begin1++];
}
while (begin2 <= end2)
{
tmp[i++] = a[begin2++];
}
memcpy(a + begin, tmp + begin, sizeof(int) * (end - begin + 1));
}
//归并排序
void MergeSort(int* a, int n)
{
int* tmp = (int*)malloc(sizeof(int) * n);
_MergeSort(a, 0, n - 1, tmp);
free(tmp);
}
void MergeSortNonR(int* a, int n)
{
int* tmp = (int*)malloc(sizeof(int) * n);
if (tmp == NULL)
{
perror("malloc失败!!!");
return;
}
int gap = 1;
while (gap < n)
{
int j = 0;
for (int i = 0; i < n; i += gap)
{
//每组的合并数据
int begin1 = i;
int end1 = i + gap - 1;
int begin2 = i + gap;
int end2 = i + 2 * gap - 1;
while (begin1 <= end1 && begin2 <= end2)
{
if (a[begin1] < a[begin2])
{
tmp[j++] = a[begin1++];
}
else
{
tmp[j++] = a[begin2++];
}
}
while (begin1 <= end1)
{
tmp[j++] = a[begin1++];
}
while (begin2 <= end2)
{
tmp[j++] = a[begin2++];
}
}
memcpy(a, tmp, sizeof(int) * n);
gap *= 2;
}
free(tmp);
}
但是这个代码是有非常严重的越界问题的，只有有2的次方的数据的时候，才不会越界！！！
小雅兰在这里打印几组数据看得更加清楚：
cpp复制代码
void MergeSortNonR(int* a, int n)
{
int* tmp = (int*)malloc(sizeof(int) * n);
if (tmp == NULL)
{
perror("malloc失败!!!");
return;
}
// 1 2 4 ....
int gap = 1;
while (gap < n)
{
int j = 0;
for (int i = 0; i < n; i += 2 * gap)
{
// 每组的合并数据
int begin1 = i;
int end1 = i + gap - 1;
int begin2 = i + gap;
int end2 = i + 2 * gap - 1;
printf("[%d,%d][%d,%d]\n", begin1, end1, begin2, end2);
if (end1 >= n || begin2 >= n)
{
break;
}
// 修正
if (end2 >= n)
{
end2 = n - 1;
}
while (begin1 <= end1 && begin2 <= end2)
{
if (a[begin1] < a[begin2])
{
tmp[j++] = a[begin1++];
}
else
{
tmp[j++] = a[begin2++];
}
}
while (begin1 <= end1)
{
tmp[j++] = a[begin1++];
}
while (begin2 <= end2)
{
tmp[j++] = a[begin2++];
}
// 归并一组，拷贝一组
memcpy(a + i, tmp + i, sizeof(int) * (end2 - i + 1));
}
printf("\n");
gap *= 2;
}
free(tmp);
}
这样修正一下就可以啦！！！
这个越界问题还有第二种解决方案：
cpp复制代码
void MergeSortNonR(int* a, int n)
{
int* tmp = (int*)malloc(sizeof(int) * n);
// 1 2 4 ....
int gap = 1;
while (gap < n)
{
int j = 0;
for (int i = 0; i < n; i += 2 * gap)
{
// 每组的合并数据
int begin1 = i, end1 = i + gap - 1;
int begin2 = i + gap, end2 = i + 2 * gap - 1;
printf("修正前：[%d,%d][%d,%d]\n", begin1, end1, begin2, end2);
if (end1 >= n)
{
end1 = n - 1;
// 不存在区间
begin2 = n;
end2 = n - 1;
}
else if (begin2 >= n)
{
// 不存在区间
begin2 = n;
end2 = n - 1;
}
else if(end2 >= n)
{
end2 = n - 1;
}
printf("修正后：[%d,%d][%d,%d]\n", begin1, end1, begin2, end2);
while (begin1 <= end1 && begin2 <= end2)
{
if (a[begin1] <= a[begin2])
{
tmp[j++] = a[begin1++];
}
else
{
tmp[j++] = a[begin2++];
}
}
while (begin1 <= end1)
{
tmp[j++] = a[begin1++];
}
while (begin2 <= end2)
{
tmp[j++] = a[begin2++];
}
}
printf("\n");
memcpy(a, tmp, sizeof(int) * n);
gap *= 2;
}
free(tmp);
}
测试各种排序
cpp复制代码
// 测试排序的性能对比
void TestOP()
{
srand(time(0));
const int N = 1000000;
int* a1 = (int*)malloc(sizeof(int) * N);
int* a2 = (int*)malloc(sizeof(int) * N);
int* a3 = (int*)malloc(sizeof(int) * N);
int* a4 = (int*)malloc(sizeof(int) * N);
int* a5 = (int*)malloc(sizeof(int) * N);
int* a6 = (int*)malloc(sizeof(int) * N);
int* a7 = (int*)malloc(sizeof(int) * N);
for (int i = 0; i < N; ++i)
{
a1[i] = rand();
a2[i] = a1[i];
a3[i] = a1[i];
a4[i] = a1[i];
a5[i] = a1[i];
a6[i] = a1[i];
a7[i] = a1[i];
}
int begin1 = clock();
InsertSort(a1, N);
int end1 = clock();
int begin2 = clock();
ShellSort(a2, N);
int end2 = clock();
int begin3 = clock();
SelectSort(a3, N);
int end3 = clock();
int begin4 = clock();
HeapSort(a4, N);
int end4 = clock();
int begin5 = clock();
QuickSort(a5, 0, N - 1);
int end5 = clock();
int begin6 = clock();
MergeSort(a6, N);
int end6 = clock();
int begin7 = clock();
BubbleSort(a7, N);
int end7 = clock();
printf("InsertSort:%d\n", end1 - begin1);
printf("ShellSort:%d\n", end2 - begin2);
printf("SelectSort:%d\n", end3 - begin3);
printf("HeapSort:%d\n", end4 - begin4);
printf("QuickSort:%d\n", end5 - begin5);
printf("MergeSort:%d\n", end6 - begin6);
printf("BubbleSort:%d\n", end7 - begin7);
free(a1);
free(a2);
free(a3);
free(a4);
free(a5);
free(a6);
free(a7);
}
所有排序源代码：
Sort.h的内容：
#pragma once
#include<stdio.h>
#include<stdlib.h>
#include<time.h>
#include<stdbool.h>
#include<string.h>
void PrintArray(int* a, int n);
// 直接插入排序
void InsertSort(int* a, int n);
// 希尔排序
void ShellSort(int* a, int n);
// 直接选择排序
void SelectSort(int* a, int n);
// 堆排序
void AdjustDown(int* a, int n, int root);
void HeapSort(int* a, int n);
// 冒泡排序
void BubbleSort(int* a, int n);
//快速排序
int PartSort1(int* a, int left, int right);
int PartSort2(int* a, int left, int right);
int PartSort3(int* a, int left, int right);
void QuickSort(int* a, int begin, int end);
void QuickSortNonR(int* a, int begin, int end);
//归并排序
void MergeSort(int* a, int n);
void MergeSortNonR(int* a, int n);
Sort.c的内容：
#include"Sort.h"
#include"Stack.h"
void PrintArray(int* a, int n)
{
int i = 0;
for (i = 0; i < n; i++)
{
printf("%d ", a[i]);
}
printf("\n");
}
//直接插入排序
void InsertSort(int* a, int n)
{
int i = 0;
for (i = 1; i < n; i++)
{
int end = i - 1;
int tmp = a[i];
while (end >= 0)
{
//插入的数据比原来的数据小
if (a[end] > tmp)
{
a[end + 1] = a[end];
--end;
}
else
{
break;
}
}
a[end + 1] = tmp;
}
}
//希尔排序
void ShellSort(int* a, int n)
{ //1.gap>1,预排序 //2.gap==1,直接插入排序
int gap = n;
while (gap > 1)
{
gap = gap / 3 + 1;
//+1可以保证最后一次一定是1
for (int i = 0; i < n - gap; i++)
{
int end = i;
int tmp = a[end + gap];
while (end >= 0)
{
if (a[end] > tmp)
{
a[end + gap] = a[end];
end = end - gap;
}
else
{
break;
}
}
a[end + gap] = tmp;
}
}
}
//冒泡排序
void BubbleSort(int* a, int n)
{
for (int j = 0; j < n; j++)
{
bool exchange = false;
for (int i = 1; i < n - j; i++)
{
if (a[i - 1] > a[i])
{
int tmp = a[i];
a[i] = a[i - 1];
a[i - 1] = tmp;
exchange = true;
}
}
if (exchange == false)
{
break;
}
}
}
//直接选择排序
void SelectSort(int* a, int n)
{
int begin = 0;
int end = n - 1;
while (begin < end)
{
int maxi = begin;
int mini = begin;
for (int i = begin; i <= end; i++)
{
if (a[i] > a[maxi])
{
maxi = i;
}
if (a[i] < a[mini])
{
mini = i;
}
}
Swap(&a[begin], &a[mini]);
//如果maxi和begin重叠，修正一下即可
if (begin ==maxi)
{
maxi = mini;
}
Swap(&a[end], &a[maxi]);
++begin;
--end;
}
}
//向下调整算法
void AdjustDown(int* a, int n, int parent)
{
//默认左孩子小
int child = parent * 2 + 1;
while (child < n)//孩子在数组范围内
{
//选出左右孩子中大的那一个
//有可能假设错了
//左孩子不存在，一定没有右孩子------完全二叉树
//左孩子存在，有可能没有右孩子
if (child + 1 < n && a[child + 1] > a[child])
// 右孩子存在 右孩子>左孩子
//不能这么写 if (a[child + 1] > a[chid] && child + 1 < n )
//这样写会有越界的风险 因为是先访问了数组中的元素 再去比较右孩子是否存在
{
++child;
}
//child就是大的那个孩子
//不关心到底是左孩子还是右孩子
if (a[child] > a[parent])
{
Swap(&a[child], &a[parent]);
parent = child;
child = parent * 2 + 1;//默认又算的是左孩子
}
else
{
break;
}
}
}
//堆排序
void HeapSort(int* a, int n)
{
//建堆------向下调整建堆
int i = 0;
for (i = (n - 1 - 1) / 2; i >= 0; i--)
{
AdjustDown(a, n, i);
}
//升序------建大堆
int end = n - 1;
while (end > 0)
{
Swap(&a[0], &a[end]);
AdjustDown(a, end, 0);
--end;
}
}
//三数取中
int GetMidIndex(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 right;
}
else
{
return left;
}
}
else // a[left] > a[mid]
{
if (a[mid] > a[right])
{
return mid;
}
else if (a[left] > a[right])
{
return right;
}
else
{
return left;
}
}
}
// hoare
// [left, right]
int PartSort1(int* a, int left, int right)
{
int midi = GetMidIndex(a, left, right);
Swap(&a[left], &a[midi]);
int keyi = left;
while (left < right)
{
// 右边找小
while (left < right && a[right] >= a[keyi])
{
--right;
}
// 左边找大
while (left < right && a[left] <= a[keyi])
{
++left;
}
Swap(&a[left], &a[right]);
}
Swap(&a[keyi], &a[left]);
return left;
}
**挖坑法
left, right
//int PartSort2(int* a, int left, int right)
//{
// int midi = GetMidIndex(a, left, right);
// Swap(&a[left], &a[midi]);
//
// int key = a[left];
// int hole = left;
// while (left < right)
// {
// // 右边找小
// while (left < right && a[right] >= key)
// {
// --right;
// }
//
// a[hole] = a[right];
// hole = right;
//
// // 左边找大
// while (left < right && a[left] <= key)
// {
// ++left;
// }
//
// a[hole] = a[left];
// hole = left;
// }
//
// a[hole] = key;
//
// return hole;
//}
//
前后指针法
left, right
//int PartSort3(int* a, int left, int right)
//{
// int midi = GetMidIndex(a, left, right);
// Swap(&a[left], &a[midi]);
//
// int prev = left;
// int cur = left + 1;
// int keyi = left;
// while (cur <= right)
// {
// if (a[cur] < a[keyi] && ++prev != cur)
// {
// Swap(&a[prev], &a[cur]);
// }
//
// ++cur;
// }
//
// Swap(&a[prev], &a[keyi]);
// keyi = prev;
// return keyi;
//}
//快速排序
void QuickSort(int* a, int begin, int end)
{
if (begin >= end)
{
return;
}
int keyi = PartSort1(a, begin, end);
//[begin,keyi-1] keyi [keyi+1,end]
QuickSort(a, begin, keyi - 1);
QuickSort(a, keyi + 1, end);
}**
//快速排序非递归
void QuickSortNonR(int* a, int begin, int end)
{
Stack st;
StackInit(&st);
StackPush(&st, end);
StackPush(&st, begin);
while (!StackEmpty(&st))
{
int left = StackTop(&st);
StackPop(&st);
void _MergeSort(int* a, int begin, int end, int* tmp)
{
if (begin >= end)
{
return;
}
int mid = (begin + end) / 2;
//[begin,mid] [mid+1,end]
_MergeSort(a, begin, mid, tmp);
_MergeSort(a, mid + 1, end, tmp);
//归并两个区间
int begin1 = begin;
int begin2 = mid + 1;
int end1 = mid;
int end2 = end;
int i = begin;
while (begin1 <= end1 && begin2 <= end2)
{
if (a[begin1] < a[begin2])
{
tmp[i++] = a[begin1++];
}
else
{
tmp[i++] = a[begin2++];
}
}
while (begin1 <= end1)
{
tmp[i++] = a[begin1++];
}
while (begin2 <= end2)
{
tmp[i++] = a[begin2++];
}
memcpy(a + begin, tmp + begin, sizeof(int) * (end - begin + 1));
}
//归并排序
void MergeSort(int* a, int n)
{
int* tmp = (int*)malloc(sizeof(int) * n);
if (tmp == NULL)
{
perror("malloc失败!!!");
return;
}
_MergeSort(a, 0, n - 1, tmp);
free(tmp);
}
//归并排序非递归
void MergeSortNonR(int* a, int n)
{
int* tmp = (int*)malloc(sizeof(int) * n);
// 1 2 4 ....
int gap = 1;
while (gap < n)
{
int j = 0;
for (int i = 0; i < n; i += 2 * gap)
{
// 每组的合并数据
int begin1 = i, end1 = i + gap - 1;
int begin2 = i + gap, end2 = i + 2 * gap - 1;
