Leetcode** 222. Count Complete Tree Nodes

Description: Given the root of a complete binary tree, return the number of the nodes in the tree.

According to Wikipedia, every level, except possibly the last, is completely filled in a complete binary tree, and all nodes in the last level are as far left as possible. It can have between 1 and 2h nodes inclusive at the last level h.

Link: 222. Count Complete Tree Nodes

Examples:

Example 1:

Input: root = [1,2,3,4,5,6]
Output: 6

Example 2:
Input: root = []
Output: 0

Example 3:
Input: root = [1]
Output: 1

思路: 从头遍历一次，O(n). 怎样才能更快呢？

class Solution(object):
    def countNodes(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        if not root: return 0
        return 1 + self.countNodes(root.left) + self.countNodes(root.right)

class Solution(object):
    def countNodes(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        self.res = 0
        if not root: return 0
        self.res += 1
        if root.left:
            self.res += self.countNodes(root.left)
        if root.right:
            self.res += self.countNodes(root.right)
        return self.res

深度为 h 的满二叉树，节点个数为 2 ^ h - 1. 完全二叉树的最后一层节点不一定满，从左到右填充。

首先计算左子树的深度l. 右子树的深度r; 如果 l == r，说明左子树是满二叉树，右子树是完全二叉树，总节点数 = 2 ** l -1 + 1 (root node) + countNodes(root.right)如果l > r，说明右子树是满二叉树，左子树是完全二叉树, 总节点数 = 2 ** r -1 + 1 (root node) + countNodes(root.left)。计算深度时，因为是完全二叉树，从左边排起，只要一直向下数做节点就好。

class Solution(object):
    def countNodes(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        if not root: return 0
        leftdepth = self.getdepth(root.left)
        rightdepth = self.getdepth(root.right)
        if leftdepth == rightdepth:
            return pow(2,leftdepth) + self.countNodes(root.right)
        else:
            return pow(2,rightdepth) + self.countNodes(root.left)
    
    def getdepth(self, root):
        depth = 0
        while root:
            depth += 1
            root = root.left
        return depth
        
    # def getdepth(self, root):
    #     if not root:
    #         return 0
    #     return 1 + self.getdepth(root.left)

Reference: https://blog.csdn.net/fuxuemingzhu/article/details/80781666

日期: 2021-04-15 生活总不会让人太难