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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