求二叉树高度（更新：用C++14编写）

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因为树是递归定义的，所以用递归算法很方便。

#define _CRT_SECURE_NO_WARNINGS#include <iostream>#include <cstdio>using namespace std;struct Node {char data;Node *lchild;Node *rchild;};void High(Node *T, int &h){if (T == NULL)h = 0;else {int left_h;High(T->lchild, left_h);int right_h;High(T->rchild, right_h);h = 1 + max(left_h, right_h);}}Node *CreateBiTree(Node *&T) {  // 算法6.4// 按先序次序输入二叉树中结点的值（一个字符），空格字符表示空树，// 构造二叉链表表示的二叉树T。char ch;cin >> ch;if (ch == '#')T = NULL;else {if (!(T = (Node *)malloc(sizeof(Node))))return 0;T->data = ch;              // 生成根结点CreateBiTree(T->lchild);   // 构造左子树CreateBiTree(T->rchild);   // 构造右子树}return T;} // CreateBiTreevoid Free(Node *&T){if (T == NULL)return;Free(T->lchild);//T->lchild = NULL;Free(T->rchild);//T->rchild = NULL;free(T);T = NULL;}int main(int argc, char **argv){freopen("cin.txt", "r", stdin);Node *T = NULL;CreateBiTree(T);int height;High(T, height);cout << height << endl;Free(T);return 0;}/* cin.txt:ABC##DE#G##F###*/

构造的树：

输出为5。

2015.06.03更新

下面用 C++14 标准重写了程序，定义了 Node 和 Tree 两个类。

#ifndef TREE_H#define TREE_H#include <memory>template <class DataType>class Node {private:DataType data_;std::shared_ptr<Node> left_;std::shared_ptr<Node> right_;public:Node(const DataType &data = DataType(),const std::shared_ptr<Node> &left = nullptr,const std::shared_ptr<Node> &right = nullptr): data_(data), left_(left), right_(right) {}auto data() const {return data_;}/* * deep copy */std::shared_ptr<Node> copy() const {auto left = (left_ == nullptr ? nullptr : left_->copy());auto right = (right_ == nullptr ? nullptr : right_->copy());return std::make_shared<Node>(data_, left, right);}};template <class DataType>class Tree {private:std::shared_ptr<Node<DataType>> root_;public:Tree(const std::shared_ptr<Node<DataType>> &root = nullptr) : root_(root) {}/* * deep copy */Tree(const Tree &that) : root_(that.root_->copy()) {}/* * deep assignment */Tree & operator=(const Tree &that) {if (this != &that) {root_ = that.root_->copy();}return *this;}auto root() const {return root_;}};#endif

下面是测试程序。

#include <iostream>#include "tree.h"int main() {auto pnode = std::make_shared<Node<int>>(2, nullptr, nullptr);auto pnode2 = pnode->copy();std::cout << pnode->data() << std::endl;std::cout << pnode2->data() << std::endl;Tree<int> t(pnode);auto t2 = t;std::cout << t2.root()->data() << std::endl;std::cout << t.root()->data() << std::endl;return 0;}