使用 python 构建最大堆我遇到了错误的 output

Question

i'm trying to build max heap in python i have done but after heapify the list output is not satisfy the max heap property. Can any one help to fix this issue

def max_heapify(arr,i):
    left = 2 *i 
    right = 2 * i + 1
    length = len(arr)-1
    largest = i
    if length > left and arr[largest] < arr[left]:
        largest = left
    if length > right and arr[largest] < arr[right]:
        largest = right
    if largest != i:
        arr[largest],arr[i] = arr[i],arr[largest]
        max_heapify(arr,largest)
def build_max_heap(arr):
    for i in reversed(range(len(arr)//2)):
        max_heapify(arr,i)
    return arr

arr = [1,12,9,5,6,10]
print(build_max_heap(arr))

i'm getting out put [12, 9, 6, 5, 1, 10] which is not satisfy max heap property

Answer 1

There are two issues:

• First, the heap is 0-based (the root is at index zero), so the children of node 0 will be 1 and 2, and hence the children of node i will be 2*i+1 and 2*i+2
• Your code compared the two children before swapping, but it has not compared the larger child with the parent, and it should only swap if the child is larger than the parent

def max_heapify(arr,i):
    left = 2 *i + 1
    right = 2 * i + 2
    length = len(arr)
    largest = i
    if length > left and arr[largest] < arr[left]:
        largest = left
    if length > right and arr[largest] < arr[right]:
        largest = right
    if arr[largest] > arr[i]:
        arr[largest], arr[i] = arr[i],arr[largest]
        max_heapify(arr,largest)

def build_max_heap(arr):
    N = len(arr)
    for i in reversed(range(len(arr)//2)):
        max_heapify(arr,i)
    return arr

arr = [1,12,9,5,6,10]
print(build_max_heap(arr))

arr = [1,12,9,5,6,10,13]
print(build_max_heap(arr))


output:
[12, 6, 10, 5, 1, 9]                                                                                                                                                               
[13, 12, 10, 5, 6, 1, 9]