歸併排序

原理

分治算法：分解、解決、合併

設計

分解：分解函數merge_sort(A,l,r)
解決：判斷交換順序
合併：合併函數merge(A,l,m,r)

僞代碼

merge_sort(A,l,r)
	if l < r
		m = (l+r)/2
		merge_sort(A,l,m)
		merge_sort(A,m+1,r)
		merge(A,l,m,r)

merge(A,l,m,r)
	n1=m-l+1
	n2=r-m
	i = l
	j = m+1
	k=0
	for i<= m && j<= r 
		if A[i] < A[j]
			B[k] = A[i]
			i = i + 1
		else
			B[k] = A[j]
			j = j + 1
		k = k + 1
	for i to m
		B[k] = A[i]
		i=i+1
		k=k+1
	for j to r
		B[k]=A[j]
		j=j+1
		k=k+1
k=0
for l to r
	A[l]=B[k]
	k=k+1
	l=l+1

C++源碼

#include<iostream>
using namespace std;
void merge(int *a,int l,int mid,int r)//合併
{
 int i=l,j=mid+1,k=0;
 int *b=new int[r-l+1];
 while(i<=mid&&j<=r)
 {
  if(a[i]<a[j])
   b[k++] = a[i++];
  else
   b[k++] = a[j++];
 }
 while(i<=mid) b[k++]=a[i++];
 while(j<=r) b[k++]=a[j++];
 k=0;
 while(l<=r) a[l++]=b[k++];
}
void merge_sort(int *a,int l,int r)//歸併排序
{
 if(l<r)
 {
  int mid=(l+r)/2; 
  merge_sort(a,l,mid);
  merge_sort(a,mid+1,r);
  merge(a,l,mid,r);
 }
}
int main()
{
 int i,n,*a;
 cout<<"請輸入數組元素個數：";
 cin>>n;
 a=new int[n];
 cout<<"請輸入數組元素"<<endl;
 for(i=0;i<n;i++)
  cin>>a[i];
 merge_sort(a,0,n-1);
 cout<<"排序後數組爲"<<endl;
 for(i=0;i<n;i++)
  cout<<a[i]<<" ";
 cout<<endl;
 return 0;
}