我有一个关于递归合并排序的Python版本的问题。我完成了基本版本,它只由数组引用,现在正在处理索引版本。我会陷入无休止的循环,但我不确定哪里做错了。你介意分享一些想法吗?先谢谢你
成功的非索引版本:
def mergesort(x):
# The base case is when the array contains less than 1 observation.
length = len(x)
if length < 2:
return x
else:
# Recursive case:merge sort on the lower subarray, and the upper subarray.
mid = (length) // 2
lower = mergesort(x[:mid])
upper = mergesort(x[mid:])
# merge two subarrays.
x_sorted = merge(lower, upper)
return (x_sorted)
def merge(lower, upper):
nlower = len(lower)
nupper = len(upper)
i, j, k = 0, 0, 0
# create a temp array to store the sorted results
temp = [0] * (nlower + nupper)
# as the lower and upper are sorted, since the base case is the single observation.
# now we compare the smallest element in each sorted array, and store the smaller one to the temp array
# repeat this process until one array is completed moved to the temp array
# store the other array to the end of the temp array
while i < nlower and j < nupper:
if lower[i] <= upper[j]:
temp[k] = lower[i]
i += 1
k += 1
else:
temp[k] = upper[j]
j += 1
k += 1
if i == nlower:
temp[i+j:] = upper[j:]
else:
temp[i+j:] = lower[i:]
return temp
预期结果如下:
x = random.sample(range(0, 30), 15)
mergesort(x)
[0, 1, 3, 6, 9, 10, 11, 13, 14, 17, 18, 20, 25, 27, 29]
但我将陷入索引版本的无休止循环:
def ms(x, left, right):
# the base case: right == left as a single-element array
if left < right:
mid = (left + right) // 2
ms(x, left, mid)
ms(x, mid, right + 1)
m(x, left, mid, right)
return m
def m(x, left, mid, right):
nlower = mid - left
nupper = right - mid + 1
temp = [0] * (nlower + nupper)
ilower, iupper, k = left, mid, 0
while ilower < mid and iupper < right + 1:
if x[ilower] <= x[iupper]:
temp[k] = x[ilower]
ilower += 1
k += 1
else:
temp[k] = x[iupper]
iupper += 1
k += 1
if ilower == mid:
temp[k:] = x[iupper:right+1]
else:
temp[k:] = x[ilower:mid]
x[left:right+1] = temp
return x
试验数据如下所示:
x = random.sample(range(0, 30), 15)
ms(x, 0, 14)
---------------------------------------------------------------------------
RecursionError Traceback (most recent call last)
<ipython-input-59-39859c9eae4a> in <module>
1 x = random.sample(range(0, 30), 15)
----> 2 ms(x, 0, 14)
... last 2 frames repeated, from the frame below ...
<ipython-input-57-854342dcdefb> in ms(x, left, right)
3 if left < right:
4 mid = (left + right)//2
----> 5 ms(x, left, mid)
6 ms(x, mid, right+1)
7 m(x, left, mid, right)
RecursionError: maximum recursion depth exceeded in comparison
你介意提供一些见解吗?谢谢
索引版本使用了一种混乱的约定,即
left
是切片中第一个元素的索引,right
是最后一个元素的索引。此约定需要易于出错的+1
/-1
调整。你的问题是:^ {< CD5> }是左半部分中最后一个元素的索引,但是你认为^ {CD5}}是右半部分的第一个元素:2个元素的一个片段被分成0个,2个一个,因此无限递归。您可以通过将ms(x, mid, right+1)
更改为ms(x, mid+1, right)
等来解决此问题此外,从函数
ms
重新调整m
没有任何意义。如果有任何问题,您应该返回x
与Python中的范围说明符一样,将
right
作为超过最后一个元素的索引是不容易出错的。这样就不会有令人困惑的+1
/-1
调整以下是修改版本:
您将作为以下内容调用:
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