# 【python刷题】二叉堆-优先级队列

1、二叉堆是一棵完全二叉树；
2、可以构造大顶堆和小顶堆；
3、二叉堆构建优先级队列，以大顶堆为例，每次出队列的值都是当前队列中的最大值；

class MaxPQ:
def __init__(self):
self.n = 0  # 当前优先级队列中的元素，优先级队列：插入或删除元素的时候，元素会自动排序
self.pq = [0]  # 存储数组，0索引位置不用

def parent(self, root):
return root // 2

def left(self, root):
return root * 2

def right(self, root):
return root * 2 + 1

def getMax(self):
return self.pq[1]

def insert(self, x):
self.n += 1
self.pq.append(x)
self.up(self.n)

def delMax(self):
m = self.pq[1]
self.swap(1, self.n)
self.pq.pop()
self.n -= 1
self.down(1)
return m

def maxChildInd(self, x):
# 如果右孩子为空，返回左孩子的索引
if self.right(x) > self.n:
return self.left(x)
else:
if self.less(self.left(x), self.right(x)):
return self.right(x)
else:
return self.left(x)

# 上浮第x个元素
def up(self, x):
while self.parent(x) > 0:
# 如果新节点小于父节点
if self.pq[x] > self.pq[self.parent(x)]:
self.swap(self.parent(x), x)
x = self.parent(x)

# 下浮第x个元素
def down(self, x):
while self.left(x) <= self.n:
# 返回值较大的那个的索引
tmp = self.maxChildInd(x)
if self.pq[tmp] > self.pq[x]:
self.swap(tmp, x)
x = tmp

# 交换两个元素
def swap(self, i, j):
self.pq[i],self.pq[j] = self.pq[j],self.pq[i]

# pq[i]是否比pq[j]小
def less(self, i, j):
return self.pq[i] < self.pq[j]

def buildHeap(self, alist):
self.pq = self.pq + alist
self.n = len(alist)
ind = self.n // 2
while ind > 0:
self.down(ind)
ind -= 1

maxPQ = MaxPQ()
maxPQ.buildHeap([78, 83, 82, 80, 79, 65, 84])
print("初始的pq：", maxPQ.pq)
print(maxPQ.delMax())
print(maxPQ.pq)
print(maxPQ.delMax())
print(maxPQ.pq)
print(maxPQ.delMax())
print(maxPQ.pq)
print(maxPQ.delMax())
print(maxPQ.pq)
print(maxPQ.delMax())
print(maxPQ.pq)
maxPQ.insert(67)
print("插入67之后的pq：", maxPQ.pq)
print(maxPQ.delMax())
print(maxPQ.pq)
maxPQ.insert(66)
print("插入66之后的pq：", maxPQ.pq)
print(maxPQ.delMax())
print(maxPQ.pq)


84
[0, 83, 80, 82, 78, 79, 65]
83
[0, 82, 80, 65, 78, 79]
82
[0, 80, 79, 65, 78]
80
[0, 79, 78, 65]
79
[0, 78, 65]

78
[0, 67, 65]

67
[0, 66, 65]

posted @ 2021-02-01 19:20  西西嘛呦  阅读(100)  评论(0编辑  收藏  举报