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最新推荐文章于 2025-08-15 18:53:39 发布

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最新推荐文章于 2025-08-15 18:53:39 发布

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分类专栏： Practice 文章标签： c++ 数据结构二叉树

本文链接：https://blog.youkuaiyun.com/u010774000/article/details/39011647

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本文介绍了一种通过给定的二叉树前序和中序遍历序列来构造二叉树的方法，并实现了相应的C++程序。此外，还介绍了如何通过后序和中序遍历来构造二叉树，最后展示了如何进行前序、中序和后序遍历。

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数据结构经常会考：由二叉树前序+中序判断后序或后序+中序判断前序。

下面编程实现作为练习：

#include<iostream>
#include<string>
#include<queue>
using namespace std;
struct Node{
	char data;
	Node *pleft;
	Node *pright;
	Node():pleft(NULL),pright(NULL){}
};
typedef Node* pNode;
class bTree{
public:
	bTree(char* pr, char* mid, char* post):m_pr(pr),m_mid(mid),m_post(post),m_Btree(NULL){};
	pNode m_Btree;
	void pr_mid(pNode& tree,int i,int j,int len);//已知前序和中序
	void post_mid(pNode& tree, int i, int j, int len);//已知后序和中序

	static void print_post(pNode node){
		if (!node)
			return;
		print_post(node->pleft);
		print_post(node->pright);
		cout << node->data;
	}
	static void print_pr(pNode node){
		if (!node)
			return;
		cout << node->data;
		print_pr(node->pleft);
		print_pr(node->pright);
	}
	static void free(pNode node){
		if (!node)
			return;
		free(node->pleft);
		free(node->pright);
		delete node;
	}
	void print_tree(){
		queue<pNode> s1,s2;
		s1.push(m_Btree);
		while (!s1.empty() || !s2.empty()){
			if (s1.empty()){
				while (!s2.empty()){
					pNode temp = s2.front();
					s2.pop();
					cout << temp->data;
					if (temp->pleft)
						s1.push(temp->pleft);
					if (temp->pright)
						s1.push(temp->pright);
				}
			}
			else{
				while (!s1.empty()){
					pNode temp = s1.front();
					s1.pop();
					cout << temp->data;
					if (temp->pleft)
						s2.push(temp->pleft);
					if (temp->pright)
						s2.push(temp->pright);
				}
			
			}
			cout << endl;
		}
	}
private:
	int loc_in_mid(char ch){
		return string(m_mid, m_mid + strlen(m_mid)).find_first_of(ch);
	}
	char *m_pr;//前序
	char *m_mid;//中序
	char *m_post;//后序
	
};
void bTree::pr_mid(pNode& tree, int i, int j, int len){//i为子树第一个元素在前序的位置，j为子树第一个元素在中序的位置，len为序列长度
	if (len == 0)
		return;
	tree = new Node;
	tree->data = m_pr[i];
	int loc = loc_in_mid(tree->data);
	pr_mid(tree->pleft, i + 1, j, loc - j);
	pr_mid(tree->pright, i + (loc - j) + 1, loc + 1, len - (loc - j + 1));
}
void bTree::post_mid(pNode& tree, int i, int j, int len){//i为子树第一个元素在后序的位置，j为子树第一个元素在中序的位置，len为序列长度
	if (len == 0)
		return;
	tree = new Node;
	tree->data = m_post[i+len-1];
	int loc = loc_in_mid(tree->data);
	post_mid(tree->pleft, i, j, loc - j);
	post_mid(tree->pright, i + (loc - j), loc + 1, len - (loc - j + 1));
}
int main(){
	char *pr="ABDHLEKCFG";
	char *mid = "HLDBEKAFCG";
	char *post = "LHDKEBFGCA";
	bTree bt(pr,mid,NULL);//已知前序，中序
	bt.pr_mid(bt.m_Btree,0,0,strlen(pr));
	bt.print_tree();
	cout << "Post: ";
	bTree::print_post(bt.m_Btree);
	cout << endl;
	bTree::free(bt.m_Btree);

	bt = bTree(NULL, mid, post);//已知后序，中序
	bt.post_mid(bt.m_Btree,0, 0, strlen(pr));
	cout << "Pr: ";
	bTree::print_pr(bt.m_Btree);
	bTree::free(bt.m_Btree);

}