Heap sort Python implementation

问题:

def heap_sort(nos):
    global size
    size = len(nos)
    print "the size of the List is : %d " %size
    Build_heap(size,nos)
    for i in range(size-1,0,-1):
        nums[0],nums[i] = nums[i],nums[0]
        size = size-1
        print "\n", nums
        heapify(nos,i,size)
    print "heap sort array:" ,nums

def left_child(i):
    return 2*i+1

def right_child(i):
    return 2*i+2

def heapify(nums,i,size):
    l = left_child(i)
    r = right_child(i)
    if l <= size and r <= size:
        if r != size:
            if nums[l] >= nums[r]:
                max = nums[l]
                max_index = l
            elif nums[l] <= nums[r]:
                max = nums[r]
                max_index = r
            if nums[i] >= max:
                print nums
                return
            elif nums[i] <= max:
                nums[i],nums[max_index] = max,nums[i]
                heapify(nums,max_index,size)
        else:
            nums[i],nums[l] = nums[l],nums[i]
            print nums

# build a heap A from an unsorted array          
def Build_heap(size,elements):
    iterate = size//2-1
    for i in range(iterate,-1,-1):
        print "In %d iteration" %i
        heapify(elements,i,size)
    print "heapified array is : " ,elements


if __name__ == '__main__':
    #get input from user
    nums = [6,9,3,2,4,1,7,5,10]
    #sort the list
    heap_sort(nums)

Output which I get is something like this:

the size of the List is : 9 
In 3 iteration
[6, 9, 3, 10, 4, 1, 7, 5, 2]
In 2 iteration
[6, 9, 7, 10, 4, 1, 3, 5, 2]
In 1 iteration
[6, 10, 7, 9, 4, 1, 3, 5, 2]
[6, 10, 7, 9, 4, 1, 3, 5, 2]
In 0 iteration
[10, 6, 7, 9, 4, 1, 3, 5, 2]
[10, 9, 7, 6, 4, 1, 3, 5, 2]
[10, 9, 7, 6, 4, 1, 3, 5, 2]
heapified array is :  [10, 9, 7, 6, 4, 1, 3, 5, 2]
heap sort array: 
[9, 7, 6, 4, 1, 3, 5, 2, 10]

I tried implementing a heap sort algorithm in python. The final output is not sorted. There is something wrong in the heapify operation which I tried to figure out, but I couldn't find it.

Can someone point out what's wrong in my code and propose a solution for it?

回答1:

The first item(0) was swaped with the last item. To keep max-heap invairant, you should call heapify with 0.

def heap_sort(nos):
    size = len(nos)
    build_heap(size,nos)
    for i in range(size-1,0,-1):
        nums[0],nums[i] = nums[i],nums[0]
        size -= 1
        heapify(nos, 0, size) # <--- i -> 0

回答2:

The following is my PYTHON implementation. If the program is "heapsort.py", an example to run it is "python heapsort.py 10", to sort 10 randomly generated numbers.

The validation code is near the end of the program, to verify the correctness of the function, heapsort().

#!/bin/python
#
# TH @stackoverflow, 2016-01-20, HeapSort
#
import sys, random


def pushdown( A, root, size_of_A ):
    M = root * 2
    if(M <= size_of_A):
        if(size_of_A > M):
            if(A[M - 1] < A[M]):
                M += 1

        if(A[root - 1] < A[M - 1]):
            A[root - 1], A[M - 1] = A[M - 1], A[root - 1]
            pushdown(A, M, size_of_A)


def heapsort( H ):
    for i in range(len(H)/2, 0, -1):
        pushdown(H, i, len(H))

    for i in range(len(H) - 1, 0, -1):
        H[i], H[0] = H[0], H[i]
        pushdown(H, 1, i)

    return H


number_to_numbers = int(sys.argv[1])
X = [ random.randint(0, number_to_numbers) for i in range(number_to_numbers) ]
Y = X
print Y
print heapsort(X)
print sorted(Y)