数据结构和算法系列（1）——二叉树常用算法总结（python）

二叉树的递归思想很重要，还有递归的复杂度分析

- [1.1 二叉树的初始化](#11-二叉树的初始化)
- [1.2 创建一个二叉树](#12-创建一个二叉树)
- [1.3 前序遍历](#13-前序遍历)
- [1.4 中序遍历](#14-中序遍历)
- [1.5 后序遍历](#15-后序遍历)
- [1.6 层序遍历](#16-层序遍历)
- [1.7 计算节点数](#17-计算节点数)
- [1.8 计算树的深度](#18-计算树的深度)
- [1.9 计算树的叶子树](#19-计算树的叶子树)
- [1.10 获取第K层节点数](#110-获取第k层节点数)
- [1.11 判断两颗二叉树是否相同](#111-判断两颗二叉树是否相同)
- [1.12 二叉树的镜像](#112-二叉树的镜像)
- [1.13 找最低公共祖先节点](#113-找最低公共祖先节点)
- [1.14 获取两个节点的距离](#114-获取两个节点的距离)
- [1.15 找一个节点的所有祖宗节点](#115-找一个节点的所有祖宗节点)

# 1.1 二叉树的初始化

#initial of BinaryTree
class BinaryTree:
    def __init__(self,rootObj):
        self.val = rootObj
        self.left = None
        self.right = None

    def insertLeft(self,newNode):
        if self.left == None:
            self.left = BinaryTree(newNode)
        else:
            t = BinaryTree(newNode)
            t.left = self.left
            self.left = t

    def insertRight(self,newNode):
        if self.right == None:
            self.right = BinaryTree(newNode)
        else:
            t = BinaryTree(newNode)
            t.right = self.right
            self.right = t

# 1.2 创建一个二叉树

#create a BinaryTree [18,7,11,3,4,5,6,#,#,#,#,1,3,2,4]
#  18
# 7  11
#3 4 5 6
#   1 3 2 4

root = BinaryTree(18)
root.left = BinaryTree(7)
root.right = BinaryTree(11)
root.left.left = BinaryTree(3)
root.left.right = BinaryTree(4)
root.right.left = BinaryTree(5)
root.right.right = BinaryTree(6)
root.right.left.left = BinaryTree(1)
root.right.left.right = BinaryTree(3)
root.right.right.left = BinaryTree(2)
root.right.right.right = BinaryTree(4)

# 1.3 前序遍历

#递归版本
def PreOrder(self, node):
    if node:
        print(node.val)
        self.PreOrder(node.left)
        self.PreOrder(node.right)
#循环版本
def PreOrderLoop(self, node):
    if node == None:
        return
    stack =[]
    print(node.val)
    stack.append(node)
    node = node.left
    while stack!=[] or node:
        while node:
            print(node.val)
            stack.append(node)
            node = node.left
        node = stack[-1].right
        stack.pop()

#ouput: 18 7 3 4 11 5 1 3 6 2 4 

# 1.4 中序遍历

#递归版本
def InOrder(self, node):
    if node:
        self.InOrder(node.left)
        print(node.val)
        self.InOrder(node.right)
#循环版本
def InOrderLoop(self, node):
    if node == None:
        return None
    stack = []
    stack.append(node)
    node = node.left
    while stack!=[] or node:
        while node:
            stack.append(node)
            node = node.left
        print(stack[-1].val)
        node = stack[-1].right
        stack.pop()
#output：3 7 4 18 1 5 3 11 2 6 4

# 1.5 后序遍历

#递归
def PostOrder(self, node):
    if node:
        self.PostOrder(node.left)
        self.PostOrder(node.right)
        print(node.val)
#非递归
def PostOrderLoop(self, node):
    if node == None:
        return
    stack =[]
    stack.append(node)
    pre = None
    while stack!=[]:
        node = stack[-1]
        if ((node.left==None and node.right==None) or
                (pre and (pre == node.left or pre ==node.right))):
            print(node.val)
            pre = node
            stack.pop()
        else:
            if node.right:
                stack.append(node.right)
            if node.left:
                stack.append(node.left)
#output:3 4 7 1 3 5 2 4 6 11 18

# 1.6 层序遍历

def LevelOrder(self, node):
    if node == None:
        return
    stack = []
    stack.append(node)
    while stack!=[]:
        node = stack[0]
        if node.left:
            stack.append(node.left)
        if node.right:
            stack.append(node.right)
        print(node.val)
        stack.pop(0)
output: 18 7 11 3 4 5 6 1 3 2 4

# 1.7 计算节点数

#递归版本
def CountNode(self, root):
    if root == None:
        return 0
    return self.CountNode(root.left) + self.CountNode(root.right) + 1
#非递归版本
def CountNodeNotRev(self, root):
    if root == None:
        return 0
    stack = []
    stack.append(root)
    index = 0
    while index<len(stack):
        if stack[index].left:
            stack.append(stack[index].left)
        if stack[index].right:
            stack.append(stack[index].right)
        index += 1
    print(len(stack))
output: 11

# 1.8 计算树的深度

def getTreeDepth(self, root):
    if root == None:
        return 0
    left = self.getTreeDepth(root.left) + 1
    right = self.getTreeDepth(root.right) + 1
    return left if left>right else right

# 1.9 计算树的叶子树

def countLeaves(self, root):
    if root == None:
        return 0
    if root.left==None and root.right==None:
        return 1
    return self.countLeaves(root.left)+self.countLeaves(root.right)
```
# 1.10 获取第K层节点数
```
def getKLevel(self, root, K):
    if root == None: return 0
    if K == 1: return 1
    return self.getKLevel(root.left, K-1)+self.getKLevel(root.right, K-1)

# 1.11 判断两颗二叉树是否相同

def StrucCmp(self, root1, root2):
    if root1 == None and root2 == None: return True
    elif root1 ==None or root2 == None: return False
    return self.StrucCmp(root1.left, root2.left) and self.StrucCmp(root1.right, root2.right)

# 1.12 二叉树的镜像

def Mirror(self, root):
    if root == None: return
    tmp = root.left
    root.left = root.right
    root.right = tmp
    self.Mirror(root.left)
    self.Mirror(root.right)

# 1.13 找最低公共祖先节点

def findLCA(self, root, node1, node2):
    if root == None: return
    if root == node1 or root == node2: return root
    left = self.findLCA(root.left, node1, node2)
    right = self.findLCA(root.right, node1, node2)
    if left and right:
        return root
    return left if left else right

# 1.14 获取两个节点的距离

def getDist(self, root, node1, node2):
    lca = self.findLCA(root, node1, node2) #找最低公共祖宗节点
    level1 = self.FindLevel(lca, node1) #祖节点到两个节点的距离
    level2 = self.FindLevel(lca, node2)
    return level1+level2
def FindLevel(self, node, target):
    if node == None: return -1
    if node == target: return 0
    level = self.FindLevel(node.left, target)
    if level == -1: level = self.FindLevel(node.right, target)
    if level != -1: return level + 1
    return -1

# 1.15 找一个节点的所有祖宗节点

def findAllAncestor(self, root, target):
    if root == None: return False
    if root == target: return True
    if self.findAllAncestor(root.left, target) or self.findAllAncestor(root.right, target):
        print(root.val)
        return True
    return False