python - 在 Python 中进行 Introsort，有人可以指出我的错误吗？

Question

尝试使用 Python 实现 Introsort。

给出的伪代码是:

1 n ←|A| 
2 if n ≤ 1 
3 return 
4 elseif d = 0 
5 Heap-Sort(A) 
6 else 
7 p ← Partition(A) // Partitions A and returns pivot position 
8 Intro-Sort(A[0:p],d−1) 
9 Intro-Sort(A[p+1:n],d−1)

我的源代码是:

import math

def introSort(a,d):
    n = len(a)
    if n <= 1:
        return
    elif d == 0:
        heapSort(a)
    else:
        p = partition(a)
        a1 = a[0:p]
        a2 = a[p+1:n]
        introSort(a1, d-1)
        introSort(a2, d-1)
        a = a1 + [a[p]] + a2

def heapSort (a):
    END = len(a)
    for k in range (math.floor(END/2) - 1, -1, -1):
        heapify(a, END, k)

    for k in range(END, 1, -1):
        swap(a, 0, k-1)
        heapify(a, k-1, 0)

def partition(a):
    x = a[len(a) - 1]
    i = -1
    for j in range(0, len(a) - 2):
        if a[j] <= x:
            i = i + 1
            swap(a, i, j)
    swap(a, i + 1, len(a) - 1)
    return i + 1

def swap(a, i, j):
    tmp = a[i]
    a[i] = a[j]
    a[j] = tmp

def heapify(a,iEnd,iRoot):
    iL = 2*iRoot + 1
    iR = 2*iRoot + 2
    if iR < iEnd:
        if (a[iRoot] >= a[iL] and a[iRoot] >= a[iR]):
            return

        else:
            if(a[iL] > a[iR]):
                j = iL
            else: 
                j = iR
            swap(a, iRoot, j)
            heapify(a, iEnd, j)

    elif iL < iEnd:
        if (a[iRoot] >= a[iL]):
            return
        else:
            swap(a, iRoot, iL)
            heapify(a,iEnd,iL)

    else: 
        return

a = [3,5,6,1,23,521,6243,632,123,53,62,421,15,672,7,435,21]

introSort(a,2)

print(a)

给出的结果是错误的:

>python introsort.py
[3, 5, 6, 1, 15, 7, 21, 632, 123, 53, 62, 421, 23, 672, 521, 435, 6243]

似乎它在分区后立即停止并且子列表上的排序不起作用。很明显，21 是枢轴，分区工作得很好。

有人能指出我的错误吗？非常感谢!

Answer 1

实际上，我通过使用对列表的一部分调用堆排序的辅助函数来修复此问题。我没有通过修改 heapsort 函数来做到这一点，而是在一个单独的副本中这样做，并将排序后的元素更新回原始列表中。代码显示为:

import math

def introSort(a, d, start, end):
    n = end - start
    if n <= 1:
        return
    elif d == 0:
        introHS(a, start, end)
    else:
        p = partition(a, start, end)
        introSort(a, d-1, start, p)
        introSort(a, d-1, p+1, end)

def introHS (a, start, end):
    b = a[start:end]
    heapSort(b)
    for i in range(0,len(b)):
        a[start+i] = b[i]

def heapSort (a):
    END = len(a)
    for k in range (math.floor(END/2) - 1, -1, -1):
        heapify(a, END, k)

    for k in range(END, 1, -1):
        swap(a, 0, k-1)
        heapify(a, k-1, 0)

def partition(a, start, end):
    x = a[end-1]
    i = start-1
    for j in range(start, end-1):
        if a[j] <= x:
            i=i+1
            swap(a, i, j)
    swap(a, i+1, end-1)
    return i+1

def swap(a, i, j):
    tmp = a[i]
    a[i] = a[j]
    a[j] = tmp

def heapify(a,iEnd,iRoot):
    iL = 2*iRoot + 1
    iR = 2*iRoot + 2
    if iR < iEnd:
        if (a[iRoot] >= a[iL] and a[iRoot] >= a[iR]):
            return

        else:
            if(a[iL] > a[iR]):
                j = iL
            else: 
                j = iR
            swap(a, iRoot, j)
            heapify(a, iEnd, j)

    elif iL < iEnd:
        if (a[iRoot] >= a[iL]):
            return
        else:
            swap(a, iRoot, iL)
            heapify(a,iEnd,iL)

    else: 
        return

通过测试它工作正常:

a = [3,5,6,1,23,521,6243,632,123,53,62,421,15,672,7,435,21,123,41,52,6234,11,55,6345,324,58,46,2,123,152,6156,46,34,3426,5341,16,3314,34,73416,345]
print("Original:")
print(a)
for i in range(0,15):
    introSort(a,i,0,len(a))
    print("d=" + str(i))
    print(a)

给予:

>Original:
>[3, 5, 6, 1, 23, 521, 6243, 632, 123, 53, 62, 421, 15, 672, 7, 435, 21, 123, 41, 52, 6234, 11, 55, 6345, 324, 58, 46, 2, 123, 152, 6156, 46, 34, 3426, 5341, 16, 3314, 34, 73416, 345]
>d=0
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=1
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=2
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=3
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=4
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=5
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=6
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=7
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=8
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=9
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=10
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=11
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=12
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=13
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]
>d=14
>[1, 2, 3, 5, 6, 7, 11, 15, 16, 21, 23, 34, 34, 41, 46, 46, 52, 53, 55, 58, 62, 123, 123, 123, 152, 324, 345, 421, 435, 521, 632, 672, 3314, 3426, 5341, 6156, 6234, 6243, 6345, 73416]