Python堆排序实现解释
Python heapsort implementation explanation
这是堆排序的 python3 实现,其中 n 是堆的大小。
def heapify(arr, n, i):
largest = i
l = 2 * i + 1 # left = 2*i + 1
r = 2 * i + 2 # right = 2*i + 2
# See if left child of root exists and is
# greater than root
if l < n and arr[i] < arr[l]:
largest = l
# See if right child of root exists and is
# greater than root
if r < n and arr[largest] < arr[r]:
largest = r
# Change root, if needed
if largest != i:
arr[i],arr[largest] = arr[largest],arr[i] # swap
# Heapify the root.
heapify(arr, n, largest)
# The main function to sort an array of given size
def heapSort(arr):
n = len(arr)
# Build a maxheap.
for i in range(n, -1, -1):
heapify(arr, n, i)
# One by one extract elements
for i in range(n-1, 0, -1):
arr[i], arr[0] = arr[0], arr[i] # swap
heapify(arr, i, 0)
我了解 heapify 函数及其作用。不过,我在最大堆中看到了一个问题:
for i in range(n, -1, -1):
根据我的研究,我认为我只需要在非叶节点上构建最大堆,它应该是 0 ... n/2。那么这里的范围是否正确?
我也很难理解最后一部分:
for i in range(n-1, 0, -1):
arr[i], arr[0] = arr[0], arr[i] # swap
heapify(arr, i, 0)
这里从 n-1 ... 0 到步长 =-1 的范围如何工作?
GeeksforGeeks 在 c++ 中的 HeapSort 代码
// Build heap (rearrange array)
for (int i = n / 2 - 1; i >= 0; i--)
heapify(arr, n, i);
参考:-
CLRS 书中的 Heapsort 伪代码
BUILD-MAX-HEAP(A)
heap-size[A] ← length[A]
for i ← length[A]/2 downto 1
do MAX-HEAPIFY(A, i)
所以是的,你是对的。 Heapfying 仅 非叶节点 就足够了。
关于你的第二个问题:-
伪代码
1.MaxHeapify(Array)
2.So the Array[0] has the maximum element
3.Now exchange Array[0] and Array[n-1] and decrement the size of heap by 1.
4.So we now have a heap of size n-1 and we again repeat the steps 1,2 and 3 till the index is 0.
这是堆排序的 python3 实现,其中 n 是堆的大小。
def heapify(arr, n, i):
largest = i
l = 2 * i + 1 # left = 2*i + 1
r = 2 * i + 2 # right = 2*i + 2
# See if left child of root exists and is
# greater than root
if l < n and arr[i] < arr[l]:
largest = l
# See if right child of root exists and is
# greater than root
if r < n and arr[largest] < arr[r]:
largest = r
# Change root, if needed
if largest != i:
arr[i],arr[largest] = arr[largest],arr[i] # swap
# Heapify the root.
heapify(arr, n, largest)
# The main function to sort an array of given size
def heapSort(arr):
n = len(arr)
# Build a maxheap.
for i in range(n, -1, -1):
heapify(arr, n, i)
# One by one extract elements
for i in range(n-1, 0, -1):
arr[i], arr[0] = arr[0], arr[i] # swap
heapify(arr, i, 0)
我了解 heapify 函数及其作用。不过,我在最大堆中看到了一个问题:
for i in range(n, -1, -1):
根据我的研究,我认为我只需要在非叶节点上构建最大堆,它应该是 0 ... n/2。那么这里的范围是否正确?
我也很难理解最后一部分:
for i in range(n-1, 0, -1):
arr[i], arr[0] = arr[0], arr[i] # swap
heapify(arr, i, 0)
这里从 n-1 ... 0 到步长 =-1 的范围如何工作?
GeeksforGeeks 在 c++ 中的 HeapSort 代码
// Build heap (rearrange array)
for (int i = n / 2 - 1; i >= 0; i--)
heapify(arr, n, i);
参考:-
CLRS 书中的 Heapsort 伪代码
BUILD-MAX-HEAP(A)
heap-size[A] ← length[A]
for i ← length[A]/2 downto 1
do MAX-HEAPIFY(A, i)
所以是的,你是对的。 Heapfying 仅 非叶节点 就足够了。
关于你的第二个问题:-
伪代码
1.MaxHeapify(Array)
2.So the Array[0] has the maximum element
3.Now exchange Array[0] and Array[n-1] and decrement the size of heap by 1.
4.So we now have a heap of size n-1 and we again repeat the steps 1,2 and 3 till the index is 0.