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()0+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：