python使用递归的方式建立二叉树

树和图的数据结构,就很有意思啦。

# coding = utf-8

class BinaryTree:

def __init__(self, root_obj):

self.key = root_obj

self.left_child = None

self.right_child = None

def insert_left(self, new_node):

node = BinaryTree(new_node)

if self.left_child is None:

self.left_child = node

else:

node.left_child = self.left_child

self.left_child = node

def insert_right(self, new_node):

node = BinaryTree(new_node)

if self.right_child is None:

self.right_child = node

else:

node.right_child = self.right_child

self.right_child = node

def get_right_child(self):

return self.right_child

def get_left_child(self):

return self.left_child

def set_root_val(self, obj):

self.key = obj

def get_root_val(self):

return self.key

root = BinaryTree('a')

print(root.get_root_val())

print(root.get_left_child())

root.insert_left('b')

print(root.get_left_child())

print(root.get_left_child().get_root_val())

root.insert_right('c')

print(root.get_right_child())

print(root.get_right_child().get_root_val())

root.get_right_child().set_root_val('hello')

print(root.get_right_child().get_root_val())

C:\Users\Sahara\.virtualenvs\test\Scripts\python.exe C:/Users/Sahara/PycharmProjects/test/python_search.py

a

None

<__main__.BinaryTree object at 0x00000000024139B0>

b

<__main__.BinaryTree object at 0x00000000024139E8>

c

hello

Process finished with exit code 0

Python实现二叉树遍历的递归和非递归算法

前序遍历

# -----------前序遍历 ------------

# 递归算法

def pre_order_recursive(self, T):

if T == None:

return

print(T.root, end=' ')

self.pre_order_recursive(T.lchild)

self.pre_order_recursive(T.rchild)

# 非递归算法

def pre_order_non_recursive(self, T):

"""借助栈实现前驱遍历

"""

if T == None:

return

stack = []

while T or len(stack) > 0:

if T:

stack.append(T)

print(T.root, end=' ')

T = T.lchild

else:

T = stack[-1]

stack.pop()

T = T.rchild

中序遍历

# -----------中序遍历 ------------

# 递归算法

def mid_order_recursive(self, T):

if T == None:

return

self.mid_order_recursive(T.lchild)

print(T.root, end=' ')

self.mid_order_recursive(T.rchild)

# 非递归算法

def mid_order_non_recursive(self, T):

"""借助栈实现中序遍历

"""

if T == None:

return

stack = []

while T or len(stack) > 0:

if T:

stack.append(T)

T = T.lchild

else:

T = stack.pop()

print(T.root, end=' ')

T = T.rchild

后序遍历

# -----------后序遍历 ------------

# 递归算法

def post_order_recursive(self, T):

if T == None:

return

self.post_order_recursive(T.lchild)

self.post_order_recursive(T.rchild)

print(T.root, end=' ')

# 非递归算法

def post_order_non_recursive(self, T):

"""借助两个栈实现后序遍历

"""

if T == None:

return

stack1 = []

stack2 = []

stack1.append(T)

while stack1:

node = stack1.pop()

if node.lchild:

stack1.append(node.lchild)

if node.rchild:

stack1.append(node.rchild)

stack2.append(node)

while stack2:

print(stack2.pop().root, end=' ')

return

层次遍历

# -----------层次遍历 ------------

def level_order(self, T):

"""借助队列(其实还是一个栈)实现层次遍历

"""

if T == None:

return

stack = []

stack.append(T)

while stack:

node = stack.pop(0) # 实现先进先出

print(node.root, end=' ')

if node.lchild:

stack.append(node.lchild)

if node.rchild:

stack.append(node.rchild)

完整代码

class NodeTree:

def __init__(self, root=None, lchild=None, rchild=None):

"""创建二叉树

Argument:

lchild: BinTree

左子树

rchild: BinTree

右子树

Return:

Tree

"""

self.root = root

self.lchild = lchild

self.rchild = rchild

class BinTree:

# -----------前序遍历 ------------

# 递归算法

def pre_order_recursive(self, T):

if T == None:

return

print(T.root, end=' ')

self.pre_order_recursive(T.lchild)

self.pre_order_recursive(T.rchild)

# 非递归算法

def pre_order_non_recursive(self, T):

"""借助栈实现前驱遍历

"""

if T == None:

return

stack = []

while T or len(stack) > 0:

if T:

stack.append(T)

print(T.root, end=' ')

T = T.lchild

else:

T = stack[-1]

stack.pop()

T = T.rchild

# -----------中序遍历 ------------

# 递归算法

def mid_order_recursive(self, T):

if T == None:

return

self.mid_order_recursive(T.lchild)

print(T.root, end=' ')

self.mid_order_recursive(T.rchild)

# 非递归算法

def mid_order_non_recursive(self, T):

"""借助栈实现中序遍历

"""

if T == None:

return

stack = []

while T or len(stack) > 0:

if T:

stack.append(T)

T = T.lchild

else:

T = stack.pop()

print(T.root, end=' ')

T = T.rchild

# -----------后序遍历 ------------

# 递归算法

def post_order_recursive(self, T):

if T == None:

return

self.post_order_recursive(T.lchild)

self.post_order_recursive(T.rchild)

print(T.root, end=' ')

# 非递归算法

def post_order_non_recursive(self, T):

"""借助两个栈实现后序遍历

"""

if T == None:

return

stack1 = []

stack2 = []

stack1.append(T)

while stack1:

node = stack1.pop()

if node.lchild:

stack1.append(node.lchild)

if node.rchild:

stack1.append(node.rchild)

stack2.append(node)

while stack2:

print(stack2.pop().root, end=' ')

return

# -----------层次遍历 ------------

def level_order(self, T):

"""借助队列(其实还是一个栈)实现层次遍历

"""

if T == None:

return

stack = []

stack.append(T)

while stack:

node = stack.pop(0) # 实现先进先出

print(node.root, end=' ')

if node.lchild:

stack.append(node.lchild)

if node.rchild:

stack.append(node.rchild)

# ----------- 前序遍历序列、中序遍历序列 —> 重构二叉树 ------------

def tree_by_pre_mid(self, pre, mid):

if len(pre) != len(mid) or len(pre) == 0 or len(mid) == 0:

return

T = NodeTree(pre[0])

index = mid.index(pre[0])

T.lchild = self.tree_by_pre_mid(pre[1:index + 1], mid[:index])

T.rchild = self.tree_by_pre_mid(pre[index + 1:], mid[index + 1:])

return T

# ----------- 后序遍历序列、中序遍历序列 —> 重构二叉树 ------------

def tree_by_post_mid(self, post, mid):

if len(post) != len(mid) or len(post) == 0 or len(mid) == 0:

return

T = NodeTree(post[-1])

index = mid.index(post[-1])

T.lchild = self.tree_by_post_mid(post[:index], mid[:index])

T.rchild = self.tree_by_post_mid(post[index:-1], mid[index + 1:])

return T

if __name__ == '__main__':

# ----------- 测试:前序、中序、后序、层次遍历 -----------

# 创建二叉树

nodeTree = NodeTree(1,

lchild=NodeTree(2,

lchild=NodeTree(4,

rchild=NodeTree(7))),

rchild=NodeTree(3,

lchild=NodeTree(5),

rchild=NodeTree(6)))

T = BinTree()

print('前序遍历递归\t')

T.pre_order_recursive(nodeTree) # 前序遍历-递归

print('\n')

print('前序遍历非递归\t')

T.pre_order_non_recursive(nodeTree) # 前序遍历-非递归

print('\n')

print('中序遍历递归\t')

T.mid_order_recursive(nodeTree) # 中序遍历-递归

print('\n')

print('中序遍历非递归\t')

T.mid_order_non_recursive(nodeTree) # 中序遍历-非递归

print('\n')

print('后序遍历递归\t')

T.post_order_recursive(nodeTree) # 后序遍历-递归

print('\n')

print('后序遍历非递归\t')

T.post_order_non_recursive(nodeTree) # 后序遍历-非递归

print('\n')

print('层次遍历\t')

T.level_order(nodeTree) # 层次遍历

print('\n')

print('==========================================================================')

# ----------- 测试:由遍历序列构造二叉树 -----------

T = BinTree()

pre = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I']

mid = ['B', 'C', 'A', 'E', 'D', 'G', 'H', 'F', 'I']

post = ['C', 'B', 'E', 'H', 'G', 'I', 'F', 'D', 'A']

newT_pre_mid = T.tree_by_pre_mid(pre, mid) # 由前序序列、中序序列构造二叉树

T.post_order_recursive(newT_pre_mid) # 获取后序序列

print('\n')

newT_post_mid = T.tree_by_post_mid(post, mid) # 由后序序列、中序序列构造二叉树

T.pre_order_recursive(newT_post_mid) # 获取前序序列

运行结果

前序遍历递归 

1 2 4 7 3 5 6

前序遍历非递归 

1 2 4 7 3 5 6

中序遍历递归 

4 7 2 1 5 3 6

中序遍历非递归 

4 7 2 1 5 3 6

后序遍历递归 

7 4 2 5 6 3 1

后序遍历非递归 

7 4 2 5 6 3 1

层次遍历 

1 2 3 4 5 6 7

==========================================================================

C B E H G I F D A

A B C D E F G H I

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