Question

我试图通过仅使用一个1个辅助数组来实现合并排序，而不是在递归例程中为左右创建一个新数组。因为这可能会导致额外的阵列创建成本。而且有时您会看到Mergesort由于该错误而表现不佳。

我正在尝试实现此处本课程所述的合并排序- https://www.coursera.org/learn/algorithms-part1/lecture/ARWDq/mergesort （第7 -10分钟）。

我当前正面临RecursionError

我已经用python编写了代码（在该社区其他人的大力帮助下）。这是-

class merge_sort:

    aux_array = []                               

    def __init__(self, data):
        self.data = data
        self.aux_array = [0 for i in range(len(data))]  

    def merge(self, low, mid, high):             

        for k in range(low, high):
            self.aux_array[k] = self.data[k]            

        if( low == high):
            self.data[low] = self.aux_array[low]
            return


        i = low
        j = mid + 1
        for k in range(low, high):
            if(i > mid):
                self.data[k] = self.aux_array[j]        
                j = j + 1
            elif(j > high):
                self.data[k] = self.aux_array[i]        
                i = i + 1
            elif(self.aux_array[i] < self.aux_array[j]):
                self.data[k] = self.aux_array[i]        
                i = i + 1
            else:
                self.data[k] = self.aux_array[j]        
                j = j + 1

        return

    def mergesort(self,low, high):

        if(low < high):
            mid = (high - low)//2
            self.mergesort(low, mid)              
            self.mergesort(mid+1, high)           
            self.merge(low, mid, high)            
        else:
            return

    def start_sort(self):
        high = len(self.data) - 1
        self.mergesort(0, high)


arr = [10, 2, 30, 0, 4]

arr1 = merge_sort(arr)
arr1.start_sort()
print(arr1)

这是确切的错误-

Traceback (most recent call last):
  File "new_sorting.py", line 55, in <module>
    arr1.start_sort()
  File "new_sorting.py", line 49, in start_sort
    self.mergesort(0, high)
  File "new_sorting.py", line 42, in mergesort
    self.mergesort(mid+1, high)
  File "new_sorting.py", line 42, in mergesort
    self.mergesort(mid+1, high)
  File "new_sorting.py", line 42, in mergesort
    self.mergesort(mid+1, high)
  [Previous line repeated 993 more times]
  File "new_sorting.py", line 41, in mergesort
    self.mergesort(low, mid)
  File "new_sorting.py", line 39, in mergesort
    if(low < high):
RecursionError: maximum recursion depth exceeded in comparison

Answer 1

数学错误：

mid = (high - low)//2

中点实际上是两个数字的平均值：

mid = (high + low)//2

还在high = low + 1

时检查边界条件

Answer 2

修正了评论中提到的问题：

class merge_sort:

    def __init__(self, data):
        self.data = data                            # reference to data
        self.aux_array = [0] * len(data)            # allocate aux_array

    def merge(self, low, mid, high):
        for k in range(low, high+1):                # fix (high+1)
            self.aux_array[k] = self.data[k]
        i = low
        j = mid + 1
        for k in range(low, high+1):                # fix (high+1)
            if(i > mid):
                self.data[k] = self.aux_array[j]
                j = j + 1
            elif(j > high):
                self.data[k] = self.aux_array[i]
                i = i + 1
            elif(self.aux_array[i] < self.aux_array[j]):
                self.data[k] = self.aux_array[i]
                i = i + 1
            else:
                self.data[k] = self.aux_array[j]
                j = j + 1

    def mergesort(self, low, high):
        if(low >= high):
            return
        mid = low + (high - low)//2                 # fix (low + )
        self.mergesort(low, mid)
        self.mergesort(mid+1, high)
        self.merge(low, mid, high)

    def start_sort(self):
        high = len(self.data) - 1
        self.mergesort(0, high)

arr = [10, 2, 30, 0, 4]
#arr1.data will be a reference to arr
arr1 = merge_sort(arr)
arr1.start_sort()
print(arr)                                          # fix (arr not arr1)

如何解决合并排序中的此递归错误？

2 个答案: