归并排序（Merge Sort）

 

基本思想：

归并（Merge）排序法是将两个（或两个以上）有序表合并成一个新的有序表，即把待排序序列分为若干个子序列，每个子序列是有序的。然后再把有序子序列合并为整体有序序列。

归并排序示例：

 

 

合并方法：

若i>m 或j>n，转⑷ //其中一个子表已合并完，比较选取结束

• //选取r[i]和r[j]较小的存入辅助数组rf
  如果r[i]<r[j]，rf[k]=r[i]； i++； k++； 转⑵
  否则，rf[k]=r[j]； j++； k++； 转⑵
• //将尚未处理完的子表中元素存入rf
  如果i<=m，将r[i…m]存入rf[k…n] //前一子表非空
  如果j<=n ,  将r[j…n] 存入rf[k…n] //后一子表非空
• 合并结束。

 

//将r[i…m]和r[m +1 …n]归并到辅助数组rf[i…n]
void Merge(ElemType *r,ElemType *rf, int i, int m, int n)
{
	int j,k;
	for(j=m+1,k=i; i<=m && j <=n ; ++k){
		if(r[j] < r[i]) rf[k] = r[j++];
		else rf[k] = r[i++];
	}
	while(i <= m)  rf[k++] = r[i++];
	while(j <= n)  rf[k++] = r[j++];
}

 

归并的迭代算法

 

1 个元素的表总是有序的。所以对n 个元素的待排序列，每个元素可看成1 个有序子表。对子表两两合并生成n/2个子表，所得子表除最后一个子表长度可能为1 外，其余子表长度均为2。再进行两两合并，直到生成n 个元素按关键码有序的表。

 

void print(int a[], int n){
	for(int j= 0; j<n; j++){
		cout<<a[j] <<"  ";
	}
	cout<<endl;
}

//将r[i…m]和r[m +1 …n]归并到辅助数组rf[i…n]
void Merge(ElemType *r,ElemType *rf, int i, int m, int n)
{
	int j,k;
	for(j=m+1,k=i; i<=m && j <=n ; ++k){
		if(r[j] < r[i]) rf[k] = r[j++];
		else rf[k] = r[i++];
	}
	while(i <= m)  rf[k++] = r[i++];
	while(j <= n)  rf[k++] = r[j++];
	print(rf,n+1);
}

void MergeSort(ElemType *r, ElemType *rf, int lenght)
{ 
	int len = 1;
	ElemType *q = r ;
	ElemType *tmp ;
	while(len < lenght) {
		int s = len;
		len = 2 * s ;
		int i = 0;
		while(i+ len <lenght){
			Merge(q, rf,  i, i+ s-1, i+ len-1 ); //对等长的两个子表合并
			i = i+ len;
		}
		if(i + s < lenght){
			Merge(q, rf,  i, i+ s -1, lenght -1); //对不等长的两个子表合并
		}
		tmp = q; q = rf; rf = tmp; //交换q,rf，以保证下一趟归并时，仍从q 归并到rf
	}
}


int main(){
	int a[10] = {3,1,5,7,2,4,9,6,10,8};
	int b[10];
	MergeSort(a, b, 10);
	print(b,10);
	cout<<"结果：";
	print(a,10);

}
两路归并的递归算法

?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

<span class="kwd">void</span><span class="pln"> </span><span class="typ">MSort</span><span class="pun">(</span><span class="typ">ElemType</span><span class="pln"> </span><span class="pun">*</span><span class="pln">r</span><span class="pun">,</span><span class="pln"> </span><span class="typ">ElemType</span><span class="pln"> </span><span class="pun">*</span><span class="pln">rf</span><span class="pun">,</span><span class="kwd">int</span><span class="pln"> s</span><span class="pun">,</span><span class="pln"> </span><span class="kwd">int</span><span class="pln"> t</span><span class="pun">)</span><span class="pln">  </span><span class="lit">2.</span><span class="pun">{</span><span class="pln">   </span><span class="lit">3.</span><span class="pln">    </span><span class="typ">ElemType</span><span class="pln"> </span><span class="pun">*</span><span class="pln">rf2</span><span class="pun">;</span><span class="pln">  </span><span class="lit">4.</span><span class="pln">    </span><span class="kwd">if</span><span class="pun">(</span><span class="pln">s</span><span class="pun">==</span><span class="pln">t</span><span class="pun">)</span><span class="pln"> r</span><span class="pun">[</span><span class="pln">s</span><span class="pun">]</span><span class="pln"> </span><span class="pun">=</span><span class="pln"> rf</span><span class="pun">[</span><span class="pln">s</span><span class="pun">];</span><span class="pln">  </span><span class="lit">5.</span><span class="pln">    </span><span class="kwd">else</span><span class="pln">  </span><span class="lit">6.</span><span class="pln">    </span><span class="pun">{</span><span class="pln">   </span><span class="lit">7.</span><span class="pln">        </span><span class="kwd">int</span><span class="pln"> m</span><span class="pun">=(</span><span class="pln">s</span><span class="pun">+</span><span class="pln">t</span><span class="pun">)/</span><span class="lit">2</span><span class="pun">;</span><span class="pln">          </span><span class="com">/*平分*p 表*/</span><span class="pln">  </span><span class="lit">8.</span><span class="pln">        </span><span class="typ">MSort</span><span class="pun">(</span><span class="pln">r</span><span class="pun">,</span><span class="pln"> rf2</span><span class="pun">,</span><span class="pln"> s</span><span class="pun">,</span><span class="pln"> m</span><span class="pun">);</span><span class="pln">        </span><span class="com">/*递归地将p[s…m]归并为有序的p2[s…m]*/</span><span class="pln">  </span><span class="lit">9.</span><span class="pln">        </span><span class="typ">MSort</span><span class="pun">(</span><span class="pln">r</span><span class="pun">,</span><span class="pln"> rf2</span><span class="pun">,</span><span class="pln"> m</span><span class="pun">+</span><span class="lit">1</span><span class="pun">,</span><span class="pln"> t</span><span class="pun">);</span><span class="pln">      </span><span class="com">/*递归地将p[m+1…t]归并为有序的p2[m+1…t]*/</span><span class="pln">  </span><span class="lit">10.</span><span class="pln">        </span><span class="typ">Merge</span><span class="pun">(</span><span class="pln">rf2</span><span class="pun">,</span><span class="pln"> rf</span><span class="pun">,</span><span class="pln"> s</span><span class="pun">,</span><span class="pln"> m</span><span class="pun">+</span><span class="lit">1</span><span class="pun">,</span><span class="pln">t</span><span class="pun">);</span><span class="pln">   </span><span class="com">/*将p2[s…m]和p2[m+1…t]归并到p1[s…t]*/</span><span class="pln">  </span><span class="lit">11.</span><span class="pln">    </span><span class="pun">}</span><span class="pln">  </span><span class="lit">12.</span><span class="pun">}</span><span class="pln">  </span><span class="lit">13.void</span><span class="pln"> </span><span class="typ">MergeSort_recursive</span><span class="pun">(</span><span class="typ">ElemType</span><span class="pln"> </span><span class="pun">*</span><span class="pln">r</span><span class="pun">,</span><span class="pln"> </span><span class="typ">ElemType</span><span class="pln"> </span><span class="pun">*</span><span class="pln">rf</span><span class="pun">,</span><span class="pln"> </span><span class="kwd">int</span><span class="pln"> n</span><span class="pun">)</span><span class="pln">  </span><span class="lit">14.</span><span class="pun">{</span><span class="pln">   </span><span class="com">/*对顺序表*p 作归并排序*/</span><span class="pln">  </span><span class="lit">15.</span><span class="pln">    </span><span class="typ">MSort</span><span class="pun">(</span><span class="pln">r</span><span class="pun">,</span><span class="pln"> rf</span><span class="pun">,</span><span class="lit">0</span><span class="pun">,</span><span class="pln"> n</span><span class="pun">-</span><span class="lit">1</span><span class="pun">);</span><span class="pln">  </span><span class="lit">16.</span><span class="pun">}</span><span class="pln">  </span>