问题

  1945年,现代计算机之父冯·诺伊曼提出归并排序.

   归并排序算法：无论最好还是最坏时间复杂度均为:O(nlgn); 空间复杂度为 O(n); 是一种稳定的排序算法.

方法一:使用递归(分而治之)

def merge_sort(arr):
    
    if len(arr) == 1:# 首先是递归.需要找出终止条件
        return arr

    middle = len(arr)//2 # 向下取整.
    left = arr[:middle]
    right = arr[middle:]
    return merge(merge_sort(left),merge_sort(right))


def merge(left,right):
    result = []

    while len(left)>0 and len(right)>0:

        if left[0] <= right[0]:
            result.append(left.pop(0))
        else:
            result.append(right.pop(0))
    
    result += left
    result += right
    return result




print(merge_sort([79,84,21,6]))
print(merge_sort([11, 99, 33 , 69, 77, 88, 55, 11, 33, 36,39, 66, 44, 22]))

  画一遍图就会对这个算法明晰了.
  分解为子问题 : merge_sort([79,84,21,6]) = > merge_sort([79,84]) merge_sort([21,6]) => merge_sort([79]) merge_sort([84]) merge_sort([21]) merge_sort([6])

  子问题得出最优解并合并为主问题的最优解: merge_sort([79]) merge_sort([84]) merge_sort([21]) merge_sort([6]) => merge_sort([79,84]) merge_sort([6,21]) => return [6,21,79,84]

方法二:使用循环

  待学习~

参考

• 归并可视化