歸併排序是一種穩定的排序，採用分而治之策略，可以用於順序儲存結構，也易於在連結串列上實現。其原理如下圖：

    演算法時間複雜度為  O（nlogn），空間複雜度為 O（n）。

1 在陣列上實現

def mergesort(seq):  
    if len(seq)<=1:  
        return seq  
    mid=int(len(seq)/2)  
    left=mergesort(seq[:mid])  
    right=mergesort(seq[mid:])
    
    return merge(left,right)  

def merge(left,right):  
    result=[]  
    i,j=0,0  
    while i<len(left) and j<len(right):  
        if left[i]<=right[j]:  
            result.append(left[i])  
            i+=1  
        else:  
            result.append(right[j])  
            j+=1  
    result+=left[i:]  
    result+=right[j:]  
    
    return result  

if __name__=='__main__':  
    seq=[6,5,8,7]  
    print(mergesort(seq))
 

輸出：

[5, 6, 7, 8]

2 在連結串列上實現

# Definition of ListNode
class ListNode(object):
    def __init__(self, val, next=None):
        self.val = val
        self.next = next


class Solution:
    """
    @param: head: The head of linked list.
    @return: You should return the head of the sorted linked list, using constant space complexity.
    """
    # 歸併法
    def sortList(self, head):
        # write your code here
        if head is None or head.next is None:
            return head
        pre = head
        slow = head               # 使用快慢指標來確定中點
        fast = head
        while fast and fast.next:
            pre = slow
            slow = slow.next
            fast = fast.next.next
        
        left = head  
        right = pre.next  
        pre.next = None           # 從中間打斷連結串列
        left = self.sortList(left)  
        right = self.sortList(right)  
        return self.merge(left,right)
        
    def merge(self, left, right):
        pre = ListNode(-1)
        first = pre
        while left and right:
            if left.val < right.val:
                pre.next = left
                pre = left
                left = left.next
            else:
                pre.next = right
                pre = right
                right = right.next
        if left:
            pre.next = left
        else:
            pre.next = right
                
        return first.next
 

node1 = ListNode(4)  
node2 = ListNode(3)  
node3 = ListNode(2)  
node4 = ListNode(1)  
  
node1.next = node2  
node2.next = node3  
node3.next = node4  
  
s = Solution()  
result = s.sortList(node1)  

while (result != None):  
    print(result.val)  
    result = result.next 

輸出：

1
2
3
4