二叉树遍历

二叉树遍历

树的遍历是树的一种重要的运算。所谓遍历是指对树中所有结点的信息的访问，即依次对树中每个结点访问一次且仅访问一次，我们把这种对所有节点的访问称为遍历（traversal）。那么树的两种重要的遍历模式是深度优先遍历和广度优先遍历,深度优先一般用递归，广度优先一般用队列。一般情况下能用递归实现的算法大部分也能用堆栈来实现。

深度优先遍历

对于一颗二叉树，深度优先搜索(Depth First Search)是沿着树的深度遍历树的节点，尽可能深的搜索树的分支。
那么深度遍历有重要的三种方法。这三种方式常被用于访问树的节点，它们之间的不同在于访问每个节点的次序不同。这三种遍历分别叫做先序遍历（preorder），中序遍历（inorder）和后序遍历（postorder）。我们来给出它们的详细定义，然后举例看看它们的应用。

• 先序遍历 在先序遍历中，我们先访问根节点，然后递归使用先序遍历访问左子树，再递归使用先序遍历访问右子树
  根节点->左子树->右子树

"""
Definition of TreeNode:
class TreeNode:
    def __init__(self, val):
        self.val = val
        self.left, self.right = None, None
"""

class Solution:
    """
    @param root: The root of binary tree.
    @return: Postorder in ArrayList which contains node values.
    """
    result = []
    def preorderTraversal(self, root):
        # write your code here
        if root is None:
            return []
        stack = []
        seq = [] #记录先序访问序列
        while ((root!=None) | (len(stack)!=0)):
            if root!=None:
                seq.append(root.val)   #先访问根节点
                stack.append(root)  
                root = root.left   
            else:
                root = stack.pop() #回溯至父节点
                root = root.right
        return seq     

• 中序遍历 在中序遍历中，我们递归使用中序遍历访问左子树，然后访问根节点，最后再递归使用中序遍历访问右子树

　　　左子树->根节点->右子树

"""
Definition of TreeNode:
class TreeNode:
    def __init__(self, val):
        self.val = val
        self.left, self.right = None, None
"""

class Solution:
    """
    @param root: The root of binary tree.
    @return: Postorder in ArrayList which contains node values.
    """
    result = []
    def inorderTraversal(self, root):
        # write your code here
        if root is None:
            return []
        stack = []
        seq = []
        output = []
        while ((root!=None) | (len(stack)!=0)):
            if root!=None:
                stack.append(root)
                root = root.left
            else:
                root = stack.pop()
                seq.append(root.val) # 左孩子先pop出来，再pop根节点
                root = root.right
         
        return seq     

• 后序遍历 在后序遍历中，我们先递归使用后序遍历访问左子树和右子树，最后访问根节点
  左子树->右子树->根节点

"""
Definition of TreeNode:
class TreeNode:
    def __init__(self, val):
        self.val = val
        self.left, self.right = None, None
"""

class Solution:
    """
    @param root: The root of binary tree.
    @return: Postorder in ArrayList which contains node values.
    """
    result = []
    def postorderTraversal(self, root):
        # write your code here
        if root is None:
            return []
        stack = []
        seq = []
        output = []
        while ((root!=None) | (len(stack)!=0)):
            if root!=None:
                seq.append(root.val)
                stack.append(root)
                root = root.right  # 这从left变成了 right
            else:
                root = stack.pop()
                root = root.left # 这从right变成了 left
                
        while seq:  # 后序遍历 是 将先序遍历的反过来
            output.append(seq.pop())

        return output                    

广度优先遍历(层次遍历)

 从树的root开始，从上到下从从左到右遍历整个树的节点

 

"""
Definition of TreeNode:
class TreeNode:
    def __init__(self, val):
        self.val = val
        self.left, self.right = None, None
"""

class Solution:
    """
    @param root: The root of binary tree.
    @return: Postorder in ArrayList which contains node values.
    """
    def BFS(self, root):  # 层次遍历核心代码
        if root == None:
            return
        queue = []
        res = []
        queue.append(root)

        while queue:
            now_node = queue.pop(0)
            res.append(now_node.val)

            if now_node.left != None:
                queue.append(now_node.left)

            if now_node.right != None:
                queue.append(now_node.right)

        return res