一颗完全二叉树，求其结点个数

网上看了很多人的答案，都说最优解是o(n），想到了一种更快的算法，复杂度是O(lgn的平方），就是对左右子树进行二分，找最后一层的最右边那个结点即可：

#include <iostream>#include <cmath>#include <stdlib.h>using namespace std;struct Node {  Node* left;  Node* right;  ~Node() {    if (left) {      delete left;      left = NULL;    }    if (right) {      delete right;      right = NULL;    }  }};int GetDepth(Node* root) {  int depth = 0;  while (root) {    depth++;    root = root->left;  }  return depth;}void GetMostRightDepthAndIndex(Node* root, int* depth, int* index) {  while (root) {    if (root->right) {      root = root->right;      *index = (*index - 1) * 2;      *index += 2;      *depth += 1;    } else if (root->left) {      root = root->left;      *index = (*index - 1) * 2;      *index += 1;      *depth += 1;    } else {      return;    }  }}void GetMostLeftDepthAndIndex(Node* root, int* depth, int* index) {  while (root) {    if (root->left) {      root = root->left;      *index = (*index - 1) * 2;      *index += 1;      *depth += 1;    }    else if (root->left) {      root = root->right;      *index = (*index - 1) * 2;      *index += 2;      *depth += 1;    } else {      return;    }  }}void GetNodeNum(Node* root, int cur_depth, int cur_index,    int* node_num, int max_depth) {  if (!root->left) {    if (cur_depth - 1 >= 1) {      *node_num += pow(2, cur_depth - 1) - 1;    }    *node_num += cur_index;    return;  }  int ml_depth = root->left ? cur_depth + 1 : cur_depth;  int ml_index = (cur_index - 1) * 2 + 1;  int mr_depth = root->right ? cur_depth + 1 : cur_depth;  int mr_index = (cur_index - 1) * 2 + 2;  GetMostRightDepthAndIndex(root->left, &ml_depth, &ml_index);  GetMostLeftDepthAndIndex(root->right, &mr_depth, &mr_index);  if (ml_depth == mr_depth) {    if (ml_depth == max_depth) {      GetNodeNum(root->right, cur_depth + 1, (cur_index - 1) * 2 + 2,          node_num, max_depth);    } else if (ml_depth < max_depth) {      GetNodeNum(root->left, cur_depth + 1, (cur_index - 1) * 2 + 1,          node_num, max_depth);    } else {      std::cout << "illegal tree";      exit(1);    }  } else if (ml_depth > mr_depth) {    if (ml_depth == max_depth && mr_depth == max_depth - 1) {      *node_num = pow(2, ml_depth - 1) - 1 + ml_index;    }  } else {    std::cout << "illegal tree";    exit(1);  }}int main() {  /* Input: create a  */  // depth 1  Node* root = new Node();  // depth 2  root->left = new Node();  root->right = new Node();  // depth 3  root->left->left = new Node();  root->left->right = new Node();  root->right->left = new Node();  root->right->right = new Node();  // depth 4  root->left->left->left = new Node();  root->left->left->right= new Node();  root->left->right->left = new Node();  root->left->right->right = new Node();  root->right->left->left = new Node();  root->right->left->right = new Node();  root->right->right->left = new Node();  root->right->right->right = new Node();  // depth 5  root->left->left->left->left = new Node();  int root_depth = 1;  int root_index = 1;  int max_depth = GetDepth(root);  int node_num = 0;  GetNodeNum(root, root_depth, root_index, &node_num, max_depth);  std::cout << "node_num = " << node_num << endl;  delete root;}