关于eager binomial heaps的内容详见算法设计搬运(3)——Heaps，更多细节在后面的Lazy Binomial Heaps也有。比较懒用的双向链表写的。双向链表可以实现

的 decreaseKey 和 deleteMin，可以参考石溪的ppt，尽管它是用array来存heap指针。有的ppt就错得离谱，单向链表decreaseKey就不只是在树的一个路径上比较了，没法

找它的left。

资源已上传，新手上路，就只当为熟悉python指针练手...

# author: zyx

# eager binomial heaps

# merge,insert,find_min,extractMin

class Binomial_Heap():

def __init__(self):

self.head = None

self.min = None

def merge(self,H2):

if not self.min:

self.min = H2.min

elif not H2.min:

return

else:

if self.min.data > H2.min.data:

self.min = H2.min

h1 = self.head

h2 = H2.head

unique_order_heap = Binomial_Heap()

c = unique_order_heap.head

while h1 and h2:

if h1.order == h2.order:

if h1.data <= h2.data:

h1.order+=1

h2.pre = None

d = h2

h2 = h2.sibling

d.sibling = h1.Lchild

d.parent = h1

h1.Lchild = d

if unique_order_heap.head == None:

unique_order_heap.head = h1

c = h1

h1.pre = None

h1 = h1.sibling

else:

h1.pre = c

c.sibling = h1

h1 = h1.sibling

c = c.sibling

else:

h2.order += 1

h1.pre = None

d = h1

h1 = h1.sibling

d.sibling = h2.Lchild

d.parent = h2

h2.Lchild = d

if unique_order_heap.head == None:

unique_order_heap.head = h2

c = h2

h2.pre = None

h2 = h2.sibling

else:

h2.pre = c

c.sibling = h2

h2 = h2.sibling

c = c.sibling

elif h1.order < h2.order:

if unique_order_heap.head == None:

unique_order_heap.head = h1

c = unique_order_heap.head

h1.pre = None

h1 = h1.sibling

else:

if h1.order == c.order:

if c.data <= h1.data:

c.order += 1

d = h1

h1.pre = None

h1 = h1.sibling

d.sibling = c.Lchild

c.Lchild = d

d.parent = c

else:

if c.pre == None: # single B

unique_order_heap.head = h1

h1.pre = None

else:

c.pre.sibling = h1

h1.pre = c.pre

h1.order += 1

c.sibling = h1.Lchild

h1.Lchild = c

c.parent = h1

c = h1

h1 = h1.sibling

else:

c.sibling = h1

h1.pre = c

h1 = h1.sibling

c = c.sibling

else:

if unique_order_heap.head == None:

unique_order_heap.head = h2

c = unique_order_heap.head

h2.pre = None

h2 = h2.sibling

else:

if h2.order == c.order:

if c.data <= h2.data:

d = h2

c.order += 1

h2 = h2.sibling

d.sibling = c.Lchild

c.Lchild = d

d.parent = c

else:

if c.pre == None: # single B

unique_order_heap.head = h2

h2.pre = None

else:

c.pre.sibling = h2

h2.pre = c.pre

h2.order += 1

c.sibling = h2.Lchild

h2.Lchild = c

c.parent = h2

c = h2

h2 = h2.sibling

else:

c.sibling = h2

h2.pre = c

h2 = h2.sibling

c = c.sibling

if c:

c.sibling = None

while h1:

if c:

if h1.order == c.order:

if c.data <= h1.data:

c.order += 1

d = h1

h1.pre = None

h1 = h1.sibling

d.sibling = c.Lchild

c.Lchild = d

d.parent = c

else:

if c.pre == None: # single B

unique_order_heap.head = h1

h1.pre = None

else:

c.pre.sibling = h1

h1.pre = c.pre

h1.order += 1

c.sibling = h1.Lchild

h1.Lchild = c

c.parent = h1

c = h1

h1 = h1.sibling

else:

c.sibling = h1

h1.pre = c

break

else:

unique_order_heap.head = h1

h1.pre = None

break

while h2:

if c:

if h2.order == c.order:

if c.data <= h2.data:

d = h2

c.order += 1

h2 = h2.sibling

d.sibling = c.Lchild

c.Lchild = d

d.parent = c

else:

if c.pre == None: # single B

unique_order_heap.head = h2

h2.pre = None

else:

c.pre.sibling = h2

h2.pre = c.pre

h2.order += 1

c.sibling = h2.Lchild

h2.Lchild = c

c.parent = h2

c = h2

h2 = h2.sibling

else:

c.sibling = h2

h2.pre = c

break

else:

unique_order_heap.head = h2

h2.pre = None

break

self.head = unique_order_heap.head

def find_Min(self):

return self.min

def insert(self,item):

node = Binomial_Trees(item)

H2 = Binomial_Heap()

H2.head = node

H2.min = node

self.merge(H2)

def extractMin(self):

m = self.min

if m.pre:

m.pre.sibling = m.sibling

else:

self.head = m.sibling

if m.sibling:

m.sibling.pre = m.pre

new_heap = Binomial_Heap()

to_transform = m.Lchild

minimum = to_transform

while to_transform:

if minimum.data > to_transform.data:

minimum = to_transform

to_transform.parent = None

if not new_heap.head:

new_heap.head = to_transform

to_transform = to_transform.sibling

new_heap.head.sibling = None

else:

d = to_transform

to_transform = to_transform.sibling

d.sibling = new_heap.head

new_heap.head.pre = d

new_heap.head = d

new_heap.min = minimum

cur = self.head

minimum = self.head

while cur:

if minimum.data < cur.data:

minimum = cur

cur = cur.sibling

self.min = minimum

self.merge(new_heap)

return m.data

class Binomial_Trees():

def __init__(self,item):

self.order = 0

self.parent = None

self.sibling = None

self.Lchild = None

self.data = item

self.pre = None

if __name__ == '__main__':

a = Binomial_Heap()

a.insert(1)

a.insert(2)

a.insert(3)

a.insert(4)

a.insert(-1)

a.extractMin()

a.extractMin()

b = Binomial_Heap()

b.insert(2)

b.insert(5)

b.insert(0)

b.insert(3)

a.merge(b)

a.insert(-1)