leetcode_c++:树:Count Complete Tree Nodes（222 )

Given a complete binary tree, count the number of nodes.

Definition of a complete binary tree from Wikipedia:
In a complete binary tree every level, except possibly the last, is completely filled, 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.

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算法

求一个完全二叉树的大小。

这题的本质就是要找最深层有几个节点。那么要如何定位最后的那个节点呢。看到之前递归算法写的 getDepth 方法，发现可以 O(logn) 去我得到 depth，那就可以获取左右的路径的深度，然后进行处理了：如果一样的话，这个子树就是满的，可以直接得到大小，如果不是一样的话，就分别求左右子树的大小。

O(lognlogn)

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class Solution {public:    int countNodes(TreeNode* root) {        if (root == NULL) return 0;        int left_depth = getLeftDepth(root);        int right_depth = getRightDepth(root);        if (left_depth == right_depth) {            return (1 << left_depth) - 1;        } else {            return countNodes(root->left) + countNodes(root->right) + 1;        }    }private:    int getRightDepth(TreeNode* root) {        if (root) return getRightDepth(root->right) + 1;        return 0;    }    int getLeftDepth(TreeNode* root) {        if (root) return getLeftDepth(root->left) + 1;        return 0;    }};