归并排序
概述
归并排序是典型的分而治之策略的应用。主要是把一个数组分成若干个子数组进行从小到大的归并直至有序。下面所说的归并排序默认为2路归并排序。
递归算法思想
1）将数组平分为2等份，对这两个子数组进行从小大到有序归并。 2）递归对左半部分进行2路归并 3）递归对右半部分进行2路归并
//一趟归并
void Merge(int* data,int* tmp,int left,int right,int rightend)
{
int leftend = right-1;
int size = rightend-left+1;
int cnt = left;
while(left <= leftend && right <= rightend){
if(data[left] < data[right]){
tmp[cnt++] = data[left++];
}else{
tmp[cnt++] = data[right++];
}
}
while(left <= leftend){
tmp[cnt++] = data[left++];
}
while(right <= rightend){
tmp[cnt++] = data[right++];
}
for(int i = 0 ; i < size ; i++,rightend--){
data[rightend] = tmp[rightend];
}
}
//归并排序
void Msort(int* data,int* tmp,int left,int rightend)
{
if(left < rightend){
int mid = (left+rightend)/2;
Msort(data,tmp,left,mid);
Msort(data,tmp,mid+1,rightend);
Merge(data,tmp,left,mid+1,rightend);
}
}
//归并排序(递归版本)
void Merge_Sort(int* data,int size)
{
int* tmp = new int[size];
if(tmp != NULL){
Msort(data,tmp,0,size-1);
}
}非递归算法思想
1）首先构造一个与原数组大小一样的临时数组 2）设置归并长度length = 1，从头开始堆两个length长度的数组进行归并到tmp直至倒数第二组。由于原数组长度与length布置时候能整除，如果能整除，那么把最后一组归并到数组了，若不能，那么就直接导入tmp数组。 3）更新length，使之翻倍，重复上述2）操作，只不过是把tmp的数组归并到原数组。 4）重复上述2）与3）操作，直至length大于数组长度。
//一趟归并
void Merge(int* data,int* tmp,int left,int right,int rightend)
{
int leftend = right-1;
int size = rightend-left+1;
int cnt = left;
while(left <= leftend && right <= rightend){
if(data[left] < data[right]){
tmp[cnt++] = data[left++];
}else{
tmp[cnt++] = data[right++];
}
}
while(left <= leftend){
tmp[cnt++] = data[left++];
}
while(right <= rightend){
tmp[cnt++] = data[right++];
}
for(int i = 0 ; i < size ; i++,rightend--){
data[rightend] = tmp[rightend];
}
}
//一趟归并排序
void Merge_Pass(int* data,int* tmp,int size,int length)
{
int i;
for(i = 0 ; i <= size-2*length ; i += 2*length){
Merge(data,tmp,i,i+length,i+2*length-1);
}
if(i+length < size){//归并最后两个子序列
Merge(data,tmp,i,i+length,size-1);
}else{//归并最后一个子序列
for(int j = i ; j < size ; j++){
tmp[j] = data[j];
}
}
}
//归并排序(非递归排序)
void Merge_Sort1(int* data,int size)
{
int* tmp = new int[size];
int length = 1;
if(tmp != NULL){
while(length < size){
Merge_Pass(data,tmp,size,length);
length*=2;
Merge_Pass(tmp,data,size,length);
length*=2;
}
delete tmp;
}
}全部代码
#include <iostream>
#include <cstdlib>
#include <ctime>
using namespace std;
//初始化数组
void SetArray(int* data,int size)
{
//srand(time(0));
cout<<"随机初始化"<<size<<"个数"<<endl;
for(int i = 0 ; i < size ; i++){
data[i] =rand()%100+1;
}
}
//打印函数
void Print(int* data ,int size)
{
for(int i = 0 ; i < size ; i++){
cout<<data[i]<<" ";
}
cout<<endl;
}
//一趟归并
void Merge(int* data,int* tmp,int left,int right,int rightend)
{
int leftend = right-1;
int size = rightend-left+1;
int cnt = left;
while(left <= leftend && right <= rightend){
if(data[left] < data[right]){
tmp[cnt++] = data[left++];
}else{
tmp[cnt++] = data[right++];
}
}
while(left <= leftend){
tmp[cnt++] = data[left++];
}
while(right <= rightend){
tmp[cnt++] = data[right++];
}
for(int i = 0 ; i < size ; i++,rightend--){
data[rightend] = tmp[rightend];
}
}
//归并排序
void Msort(int* data,int* tmp,int left,int rightend)
{
if(left < rightend){
int mid = (left+rightend)/2;
Msort(data,tmp,left,mid);//递归归并排序左半部分
Msort(data,tmp,mid+1,rightend);//递归归并排序右半部分
Merge(data,tmp,left,mid+1,rightend);//对左右部分进行有序归并
}
}
//归并排序(递归版本)
void Merge_Sort(int* data,int size)
{
int* tmp = new int[size];
if(tmp != NULL){
Msort(data,tmp,0,size-1);
}
}
//一趟归并排序
void Merge_Pass(int* data,int* tmp,int size,int length)
{
int i;
for(i = 0 ; i <= size-2*length ; i += 2*length){
Merge(data,tmp,i,i+length,i+2*length-1);
}
if(i+length < size){//归并最后两个子序列
Merge(data,tmp,i,i+length,size-1);
}else{//归并最后一个子序列
for(int j = i ; j < size ; j++){
tmp[j] = data[j];
}
}
}
//归并排序(非递归排序)
void Merge_Sort1(int* data,int size)
{
int* tmp = new int[size];
int length = 1;
if(tmp != NULL){
while(length < size){
Merge_Pass(data,tmp,size,length);
length*=2;
Merge_Pass(tmp,data,size,length);
length*=2;
}
delete tmp;
}
}
int main()
{
cout<<"请输入数组长度:"<<endl;
int size,*data;
cin>>size;
data = new int[size];
SetArray(data,size);
cout<<"归并排序（递归版本）前："<<endl;
Print(data,size);
cout<<"归并排序（递归版本）后："<<endl;
Merge_Sort(data,size);
Print(data,size);
SetArray(data,size);
cout<<"归并排序（非递归版本）前："<<endl;
Print(data,size);
cout<<"归并排序（非递归版本）后："<<endl;
Merge_Sort1(data,size);
Print(data,size);
return 0;
} 截图：
这里写图片描述
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