創建堆(python)

創建最大（小）堆

二叉堆本質上是一種完全二叉樹，存儲方式並不是鏈式存儲，而是順序存儲

• 堆操作：插入（葉子節點上調），刪除（堆頂元素下沉）

• 堆創建：非葉子節點下沉（從最后一個非葉子節點開始）

  • 最小堆：

    最小堆任何一個父節點的值，都小於等於它左右孩子節點的值

    創建過程：如果非葉子節點值大於其子節點，將其下沉

  • 最大堆：

    最大堆任何一個父節點的值，都大於等於它左右孩子節點的值。

    創建過程：如果非葉子節點值小於其子節點，將其下沉

#最小堆
def upadjust(nums):
    childindex = len(nums)-1
    parentindex = (childindex-1)//2
    temp = nums[childindex] #插入的葉子節點值
    while childindex>0 and temp<nums[parentindex]:#子節點小於父節點，上調子節點
        nums[childindex] = nums[parentindex]
        childindex = parentindex
        parentindex = (parentindex-1)//2
    nums[childindex] = temp

def downadjust(nums,parentindex):
    temp = nums[parentindex]
    childindex = 2*parentindex + 1
    while childindex < len(nums):
        #右孩子值小於左孩子，父節點和小的交換
        if childindex +1 <len(nums) and nums[childindex+1] < nums[childindex]:
            childindex += 1
        if temp < nums[childindex]:    #父節點小於子節點，不用調整
            break
        nums[parentindex] = nums[childindex]
        parentindex = childindex
        childindex = childindex*2+1
    nums[parentindex] = temp

def buildMinHeap(nums):
    for i in range((len(nums)-1)//2,-1,-1):
        downadjust(nums,i)

>>> nums = [5,8,6,3,9,2,1,7,0]
>>> buildMinHeap(nums)
>>> nums
[0, 3, 1, 5, 9, 2, 6, 7, 8]

#最大堆
#非葉子節點小值下沉
def downadjust(nums,parentindex):
    temp = nums[parentindex]
    childindex = 2*parentindex + 1
    while childindex < len(nums):
        if childindex +1 <len(nums) and nums[childindex+1] > nums[childindex]:#右孩子值大於左孩子,父節點和大的交換
            childindex += 1
        if temp > nums[childindex]:    #父節點大於子節點，不用調整
            break
        nums[parentindex] = nums[childindex]
        parentindex = childindex
        childindex = childindex*2+1
    nums[parentindex] = temp

def buildMaxHeap(nums):
    for i in range((len(nums)-1)//2,-1,-1):
        downadjust(nums,i)

>>> nums = [5,8,6,3,9,2,1,7,0]
>>> buildMaxHeap(nums)
>>> nums
[9, 8, 6, 7, 5, 2, 1, 3, 0]

python自帶堆模塊

>>> import heapq
#默認最小堆
>>> nums = [5,8,6,3,9,2,1,7,0]
>>> heapq.heapify(nums)
>>> nums
[0, 3, 1, 5, 9, 2, 6, 7, 8]