有序表查找:折半查找、插值查找
二叉排序树的查找、插入、删除
1. 折半查找
def zhebanfind(list, key):
if not list:
return False
low = 0
high = len(list) - 1
while(low < high):
if (high - low) == 1:
if list[low] == key:
return low
elif list[high] == key:
return high
else:
return False
mid = (low + high)//2
if list[mid] < key:
low = mid + 1
elif list[mid] > key:
high = mid - 1
else:
return mid
2. 插值查找
def chazhifind(list, key):
if not list or list[-1] < key or list[0] > key:
return False
low = 0
high = len(list) - 1
while(low < high):
if (high - low) == 1:
if list[low] == key:
return low
elif list[high] == key:
return high
else:
return False
mid = low + (key - list[low])*(high - low)//(list[high] - list[low])
if mid == low: mid += 1
if mid == high: mid -= 1
if list[mid] < key:
low = mid + 1
elif list[mid] > key:
high = mid - 1
else:
return mid
print(chazhifind([1,2,4,7,9], 7))
3. 二叉排序树
这个比较难写,自己参考别的博客:
#!/usr/bin/env python
# -*- coding:utf-8 -*-
# Author: Liu Jiang
# Python 3.5
class BSTNode:
"""
定义一个二叉树节点类。
以讨论算法为主,忽略了一些诸如对数据类型进行判断的问题。
"""
def __init__(self, data, left=None, right=None):
"""
初始化
:param data: 节点储存的数据
:param left: 节点左子树
:param right: 节点右子树
"""
self.data = data
self.left = left
self.right = right
class BinarySortTree:
"""
基于BSTNode类的二叉排序树。维护一个根节点的指针。
"""
def __init__(self):
self._root = None
def is_empty(self):
return self._root is None
def search(self, key):
"""
关键码检索
:param key: 关键码
:return: 查询节点或None
"""
bt = self._root
while bt:
entry = bt.data
if key < entry:
bt = bt.left
elif key > entry:
bt = bt.right
else:
return entry
return None
def insert(self, key):
"""
插入操作
:param key:关键码
:return: 布尔值
"""
bt = self._root
if not bt:
self._root = BSTNode(key)
return
while True:
entry = bt.data
if key < entry:
if bt.left is None:
bt.left = BSTNode(key)
return
bt = bt.left
elif key > entry:
if bt.right is None:
bt.right = BSTNode(key)
return
bt = bt.right
else:
bt.data = key
return
def delete(self, key):
"""
二叉排序树最复杂的方法
:param key: 关键码
:return: 布尔值
"""
p, q = None, self._root # 维持p为q的父节点,用于后面的链接操作
if not q:
print("空树!")
return
while q and q.data != key:
p = q
if key < q.data:
q = q.left
else:
q = q.right
if not q: # 当树中没有关键码key时,结束退出。
return
# 上面已将找到了要删除的节点,用q引用。而p则是q的父节点或者None(q为根节点时)。
if not q.left:
if p is None:
self._root = q.right
elif q is p.left:
p.left = q.right
else:
p.right = q.right
return
# 查找节点q的左子树的最右节点,将q的右子树链接为该节点的右子树
# 该方法可能会增大树的深度,效率并不算高。可以设计其它的方法。
r = q.left
while r.right:
r = r.right
r.right = q.right
if p is None:
self._root = q.left
elif p.left is q:
p.left = q.left
else:
p.right = q.left
def __iter__(self):
"""
实现二叉树的中序遍历算法,
展示我们创建的二叉排序树.
直接使用python内置的列表作为一个栈。
:return: data
"""
stack = []
node = self._root
while node or stack:
while node:
stack.append(node)
node = node.left
node = stack.pop()
yield node.data
node = node.right
if __name__ == '__main__':
lis = [62, 58, 88, 48, 73, 99, 35, 51, 93, 29, 37, 49, 56, 36, 50]
bs_tree = BinarySortTree()
for i in range(len(lis)):
bs_tree.insert(lis[i])
# bs_tree.insert(100)
bs_tree.delete(58)
for i in bs_tree:
print(i, end=" ")
# print("\n", bs_tree.search(4))