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