三个月算法进阶--day40
目录
堆的性质
父节点大于子节点
堆排序
构建大根堆
def heap_adjust(L, start, end):
temp = L[start]
i = start
j = 2 * i
while j <= end:
if j < end and L[j] < L[j + 1]:
j += 1
if temp < L[j]:
L[i] = L[j]
i = j
j = 2 * i
else:
break
L[i] = temp
L = collections.deque([50, 15, 7, 80, 2])
L.appendleft(0)
L_length = len(L) - 1
first_sort_count = L_length // 2
for i in range(first_sort_count):
heap_adjust(L, first_sort_count - i, L_length)
def heapify(arr, n, i):
largest = i
l = 2 * i + 1
r = 2 * i + 2
# 找到父节点与两个子节点的最大值
if l < n and arr[i] < arr[l]:
largest = 1
if r < n and arr[largest] < arr[r]:
largest = r
if largest != i:
arr[i], arr[largest] = arr[largest], arr[i] # 下溯
heapify(arr, n, largest)
arr = [50, 15, 7, 80, 2]
n = len(arr)
for i in range(n, -1, -1):
heapify(arr, n, i)
大顶堆实现升序排序
for i in range(L_length - 1):
L[1], L[L_length - i] = L[L_length - i], L[1]
heap_adjust(L, 1, L_length - i - 1)
for i in range(n-1, 0, -1):
arr[i], arr[0] = arr[0], arr[i]
heapify(arr, i, 0)
堆顶执行下溯,最底端元素执行上溯
pop与push
完全二叉树
将array的#0元素保留(或设为无限大值或无限小值),那么完全二叉树中的某个节点位于array的i处时,其左子节点位于array的2i处,其右子节点位于array的2i+1处,其父节点位于i/2
python的链表结构
from collections import deque
appendleft, extendleft, popleft