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#问题

Python中的二叉树查找算法模块

#思路说明

二叉树查找算法,在开发实践中,会经常用到。按照惯例,对于这么一个常用的东西,Python一定会提供轮子的。是的,python就是这样,一定会让开发者省心,降低开发者的工作压力。

python中的二叉树模块内容:

  • BinaryTree:非平衡二叉树
  • AVLTree:平衡的AVL树
  • RBTree:平衡的红黑树

以上是用python写的,相面的模块是用c写的,并且可以做为Cython的包。

  • FastBinaryTree
  • FastAVLTree
  • FastRBTree

特别需要说明的是:树往往要比python内置的dict类慢一些,但是它中的所有数据都是按照某个关键词进行排序的,故在某些情况下是必须使用的。

#安装和使用

##安装方法

###安装环境:

ubuntu12.04, python 2.7.6

###安装方法

安装成功,ok!下面就看如何使用了。

###应用

bintrees提供了丰富的API,涵盖了通常的多种应用。下面逐条说明其应用。

  • 引用

如果按照一般模块的思路,输入下面的命令引入上述模块

>>> import bintrees

错了,这是错的,出现如下警告:(×××不可用,用×××)

Warning: FastBinaryTree not available, using Python version BinaryTree.
Warning: FastAVLTree not available, using Python version AVLTree.
Warning: FastRBTree not available, using Python version RBTree.

正确的引入方式是:

>>> from bintrees import BinaryTree     #只引入了BinartTree
>>> from bintrees import *              #三个模块都引入了
  • 实例化

看例子:

>>> btree = BinaryTree()
>>> btree
BinaryTree({})
>>> type(btree)
<class 'bintrees.bintree.BinaryTree'>
  • 逐个增加键值对:.setitem(k,v) .复杂度O(log(n))(后续说明中,都会有复杂度标示,为了简单,直接标明:O(log(n)).)

看例子:

>>> btree.__setitem__("Tom","headmaster")
>>> btree
BinaryTree({'Tom': 'headmaster'})
>>> btree.__setitem__("blog","http://blog.csdn.net/qiwsir")
>>> btree
BinaryTree({'Tom': 'headmaster', 'blog': 'http://blog.csdn.net/qiwsir'})
  • 批量添加:.update(E) E是dict/iterable,将E批量更新入btree. O(E*log(n))

看例子:

>>> adict = [(2,"phone"),(5,"tea"),(9,"scree"),(7,"computer")]
>>> btree.update(adict)
>>> btree
BinaryTree({2: 'phone', 5: 'tea', 7: 'computer', 9: 'scree', 'Tom': 'headmaster', 'blog': 'http://blog.csdn.net/qiwsir'})
  • 查找某个key是否存在:.contains(k) 如果含有键k,则返回True,否则返回False. O(log(n))

看例子:

>>> btree
BinaryTree({2: 'phone', 5: 'tea', 7: 'computer', 9: 'scree', 'Tom': 'headmaster', 'blog': 'http://blog.csdn.net/qiwsir'})
>>> btree.__contains__(5)
True
>>> btree.__contains__("blog")
True
>>> btree.__contains__("qiwsir")
False
>>> btree.__contains__(1)
False
  • 根据key删除某个key-value:.delitem(key), O(log(n))

看例子:

>>> btree
BinaryTree({2: 'phone', 5: 'tea', 7: 'computer', 9: 'scree', 'Tom': 'headmaster', 'blog': 'http://blog.csdn.net/qiwsir'})
>>> btree.__delitem__(5)        #删除key=5的key-value,即:5:'tea' 被删除.
>>> btree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree', 'Tom': 'headmaster', 'blog': 'http://blog.csdn.net/qiwsir'})
  • 根据key值得到该kye的value:.getitem(key)

看例子:

>>> btree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree', 'Tom': 'headmaster', 'blog': 'http://blog.csdn.net/qiwsir'})
>>> btree.__getitem__("blog")
'http://blog.csdn.net/qiwsir'
>>> btree.__getitem__(7)
'computer'
>>> btree._getitem__(5)         #在btree中没有key=5,于是报错。
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
AttributeError: 'BinaryTree' object has no attribute '_getitem__'
  • 迭代器:.iter()

看例子:

>>> btree        
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree', 'Tom': 'headmaster', 'blog': 'http://blog.csdn.net/qiwsir'})
>>> aiter = btree.__iter__()
>>> aiter
<generator object <genexpr> at 0xb7416dec>
>>> aiter.next()        #注意:next()一个之后,该值从list中删除
2
>>> aiter.next()
7
>>> list(aiter)
[9, 'Tom', 'blog']
>>> list(aiter)         #结果是空
[]
>>> bool(aiter)         #but,is True
True
  • 数的数据长度:.len(),返回btree的长度。O(1)

看例子:

>>> btree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree', 'Tom': 'headmaster', 'blog': 'http://blog.csdn.net/qiwsir'})
>>> btree.__len__()
5
  • 找出key最大的k-v对:.max(),按照key排列,返回key最大的键值对。

  • 找出key最小的键值对:.min()

看例子:

>>> btree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree'})
>>> btree.__max__()
(9, 'scree')
>>> btree.__min__()
(2, 'phone')
  • 两棵树的关系运算

看例子:

>>> other = [(3,'http://blog.csdn.net/qiwsir'),(7,'qiwsir')]
>>> bother = BinaryTree()       #再建一个树
>>> bother.update(other)        #加入数据

>>> bother
BinaryTree({3: 'http://blog.csdn.net/qiwsir', 7: 'qiwsir'})
>>> btree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree'})

>>> btree.__and__(bother)       #重叠部分部分
BinaryTree({7: 'computer'})

>>> btree.__or__(bother)        #全部
BinaryTree({2: 'phone', 3: 'http://blog.csdn.net/qiwsir', 7: 'computer', 9: 'scree'})

>>> btree.__sub__(bother)       #btree不与bother重叠的部分
BinaryTree({2: 'phone', 9: 'scree'})

>>> btree.__xor__(bother)       #两者非重叠部分
BinaryTree({2: 'phone', 3: 'http://blog.csdn.net/qiwsir', 9: 'scree'})
  • 输出字符串模样,注意仅仅是输出的模样罢了:.repr()

看例子:

>>> btree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree'})
>>> btree.__repr__()
"BinaryTree({2: 'phone', 7: 'computer', 9: 'scree'})"
  • 清空树中的所有数据:.clear(),O(log(n))

看例子:

>>> bother   
BinaryTree({3: 'http://blog.csdn.net/qiwsir', 7: 'qiwsir'})
>>> bother.clear()
>>> bother
BinaryTree({})
>>> bool(bother)
False
  • 浅拷贝:.copy(),官方文档上说是浅拷贝,但是我做了操作实现,是下面所示,还不是很理解其“浅”的含义。O(n*log(n))

看例子:

>>> btree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree'})
>>> ctree = btree.copy()
>>> ctree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree'})

>>> btree.__setitem__("github","qiwsir")    #增加btree的数据
>>> btree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree', 'github': 'qiwsir'})
>>> ctree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree'})     #这是不是在说明属于深拷贝呢?

>>> ctree.__delitem__(7)    #删除ctree的一个数据
>>> ctree
BinaryTree({2: 'phone', 9: 'scree'})
>>> btree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree', 'github': 'qiwsir'})
  • 移除树中的一个数据:.discard(key),这个功能与.delitem(key)类似.两者都不反悔值。O(log(n))

看例子:

>>> ctree
BinaryTree({2: 'phone', 9: 'scree'})
>>> ctree.discard(2)    #删除后,不返回值,或者返回None
>>> ctree
BinaryTree({9: 'scree'})
>>> ctree.discard(2)    #如果删除的key不存在,也返回None
>>> ctree.discard(3)
>>> ctree.__delitem__(3) #但是,.__delitem__(key)则不同,如果key不存在,会报错。
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/local/lib/python2.7/site-packages/bintrees/abctree.py", line 264, in __delitem__
  self.remove(key)
  File "/usr/local/lib/python2.7/site-packages/bintrees/bintree.py", line 124, in remove
  raise KeyError(str(key))
  KeyError: '3'
  • 根据key查找,并返回或返回备用值:.get(key[,d])。如果key在树中存在,则返回value,否则如果有d,则返回d值。O(log(n))

看例子:

>>> btree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree', 'github': 'qiwsir'})
>>> btree.get(2,"algorithm")
'phone'
>>> btree.get("python","algorithm") #没有key='python'的值,返回'algorithm'
'algorithm'
>>> btree.get("python")     #如果不指定第二个参数,若查不到,则返回None
>>> 
  • 判断树是否为空:is_empty().根据树数据的长度,如果数据长度为0,则为空。O(1)

看例子:

>>> ctree
BinaryTree({9: 'scree'})
>>> ctree.clear()   #清空数据
>>> ctree
BinaryTree({})
>>> ctree.is_empty()
True
>>> btree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree', 'github': 'qiwsir'})
>>> btree.is_empty()
False
  • 根据key、value循环从树中取值:

.items([reverse])--按照(key,value)结构取值; .keys([reverse])--key .values([reverse])--value. O(n) .iter_items(s,e[,reverse]--s,e是key的范围,也就是生成在某个范围内的key的迭代器 O(n)

看例子:

>>> btree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree', 'github': 'qiwsir'})
>>> for (k,v) in btree.items():
...     print k,v
... 
2 phone
7 computer
9 scree
github qiwsir
>>> for k in btree.keys():
...     print k
... 
2
7
9
github
>>> for v in btree.values():
...     print v
... 
phone
computer
scree
qiwsir
>>> for (k,v) in btree.items(reverse=True):  #反序
...     print k,v
... 
github qiwsir
9 scree
7 computer
2 phone

>>> btree
BinaryTree({2: 'phone', 5: None, 7: 'computer', 8: 'eight', 9: 'scree', 'github': 'qiwsir'})
>>> for (k,v) in btree.iter_items(6,9):  #要求迭代6<=key<9的键值对数据
...     print k,v
... 
7 computer
8 eight
>>> 
  • 删除数据并返回该值:

.pop(key[,d]), 根据key删除树的数据,并返回该value,但是如果没有,并也指定了备选返回的d,则返回d,如果没有d,则报错; .pop_item(),在树中随机选择(key,value)删除,并返回。

看例子:

>>> ctree = btree.copy()
>>> ctree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree', 'github': 'qiwsir'})

>>> ctree.pop(2)    #删除key=2的数据,返回其value
'phone'
>>> ctree.pop(2)    #删除一个不存在的key,报错
Traceback (most recent call last):
    File "<stdin>", line 1, in <module>
    File "/usr/local/lib/python2.7/site-packages/bintrees/abctree.py", line 350, in pop
    value = self.get_value(key)
    File "/usr/local/lib/python2.7/site-packages/bintrees/abctree.py", line 557, in get_value
    raise KeyError(str(key))
    KeyError: '2'

>>> ctree.pop_item()   #随机返回一个(key,value),并已删除之
(7, 'computer')
>>> ctree
BinaryTree({9: 'scree', 'github': 'qiwsir'})

>>> ctree.pop(7,"sing")    #如果没有,可以返回指定值
'sing'
  • 查找数据,并返回value:.set_default(key[,d]),在树的数据中查找key,如果存在,则返回该value。如果不存在,当指定了d,则将该(key,d)添加到树内;当不指定d的时候,添加(key,None). O(log(n))

看例子:

>>> btree
BinaryTree({2: 'phone', 7: 'computer', 9: 'scree', 'github': 'qiwsir'})
>>> btree.set_default(7)    #存在则返回
'computer'

>>> btree.set_default(8,"eight")  #不存在,则返回后备指定值,并加入到树
'eight'
>>> btree
BinaryTree({2: 'phone', 7: 'computer', 8: 'eight', 9: 'scree', 'github': 'qiwsir'})

>>> btree.set_default(5)    #如果不指定值,则会加入None
>>> btree
BinaryTree({2: 'phone', 5: None, 7: 'computer', 8: 'eight', 9: 'scree', 'github': 'qiwsir'})

>>> btree.get(2)        #注意,.get(key)与.set_default(key[,d])的区别
'phone'
>>> btree.get(3,"mobile")   #不存在的 key,返回但不增加到树
'mobile'
>>> btree
BinaryTree({2: 'phone', 7: 'computer', 8: 'eight', 9: 'scree', 'github': 'qiwsir'})
  • 根据key删除值

.remove(key),删除(key,value) .remove_items(keys),keys是一个key组成的list,逐个删除树中的对应数据

看例子:

>>> ctree
BinaryTree({2: 'phone', 5: None, 7: 'computer', 8: 'eight', 9: 'scree', 'github': 'qiwsir'})
>>> ctree.remove_items([5,6])       #key=6,不存在,报错
Traceback (most recent call last):
    File "<stdin>", line 1, in <module>
    File "/usr/local/lib/python2.7/site-packages/bintrees/abctree.py", line 271, in remove_items
    self.remove(key)
    File "/usr/local/lib/python2.7/site-packages/bintrees/bintree.py", line 124, in remove
    raise KeyError(str(key))
    KeyError: '6'

>>> ctree
BinaryTree({2: 'phone', 7: 'computer', 8: 'eight', 9: 'scree', 'github': 'qiwsir'})
>>> ctree.remove_items([2,7,'github'])  #按照 列表中顺序逐个删除
>>> ctree
BinaryTree({8: 'eight', 9: 'scree'})

###以上只是入门的基本方法啦,还有更多内容,请移到文章开头的官方网站。