# Merge sort

Merge sort is a very typical application of divide and conquer method . The idea of merging and sorting is to recursively decompose arrays first , Recombine arrays .

After decomposing the array to the minimum , Then merge two ordered arrays , The basic idea is to compare the first two arrays , Take the first one who is small , After taking the corresponding pointer, move it back one bit . Then compare , Until an array is empty , Finally, copy the rest of another array .

## Analysis of merge sort ```def merge_sort(alist):
if len(alist) <= 1:
return alist
# Dichotomy
num = len(alist)/2
left = merge_sort(alist[:num])
right = merge_sort(alist[num:])
# Merge
return merge(left,right)
def merge(left, right):
''' Merge operation , Put two ordered arrays left[] and right[] Merge into a large ordered array '''
#left And right The subscript pointer to
l, r = 0, 0
result = []
while l<len(left) and r<len(right):
if left[l] < right[r]:
result.append(left[l])
l += 1
else:
result.append(right[r])
r += 1
result += left[l:]
result += right[r:]
return result
alist = [54,26,93,17,77,31,44,55,20]
sorted_alist = mergeSort(alist)
print(sorted_alist)```

### Time complexity

• Optimal time complexity ：O(nlogn)
• Worst time complexity ：O(nlogn)
• stability ： Stable

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