二叉树遍历：递归+非递归+逐层遍历

1. 数据结构及遍历方法定义

/* * binarytree.h */#ifndef BINARYTREE_H_#define BINARYTREE_H_// 二叉树几点包含的实体数据类型typedef char elementType;// 定义而二叉树节点数据结构struct BinaryTreeNode {    elementType data;    BinaryTreeNode* left; // left child    BinaryTreeNode* right; // right child};// 二叉树及节点typedef BinaryTreeNode btNode;// 二叉树（root节点）typedef BinaryTreeNode btree;// 递归先序遍历void rpre_order(btree*);// 递归后续遍历void rpost_order(btree*);// 递归中序遍历void rin_order(btree*);// 非递归前序遍历void pre_order(btree*);// 非递归后续遍历void post_order(btree*);// 非递归中序遍历void in_order(btree*);// 广度优先遍历void bfs_order(btree*);// 销毁树void destory_btree(btree*);#endif /* BINARYTREE_H_ */

2. 遍历方法实现

2.1 递归遍历

/* * BinaryTree.cpp */#include "binarytree.h"#include <iostream>#include <malloc.h>#include <stack>#include <queue>using namespace std;//--------------------------------------------------// 递归先序遍历void rpre_order(btree* tree) {btNode * p = tree;if (NULL == p) {return;}cout << p->data << "  ";rpre_order(p->left);rpre_order(p->right);}// 递归后续遍历void rpost_order(btree* tree) {btNode* p = tree;if (NULL == p)return;rpost_order(p->left);rpost_order(p->right);cout << p->data << "  ";}// 递归中序遍历void rin_order(btree* tree) {btNode* p = tree;if (NULL == p)return;rin_order(p->left);cout << p->data << "  ";rin_order(p->right);}

2.2  消除递归

//--------------------------------------------------// 非递归前序遍历void pre_order(btree* tree) {btNode * p = tree;if (NULL == p)return;stack<btNode*>* st = new stack<btNode*>();st->push(p);while (!st->empty()) {p = st->top();st->pop();cout << p->data << "  ";if (NULL != p->right) {st->push(p->right);}if (NULL != p->left) {st->push(p->left);}}delete st;}// 非递归后续遍历//需要注意的是 : 非递归后序遍历方法相对实现比较困难，主要原因就在于父子节点访问缺乏连续//              解决思路是将前一个访问节点记忆下来，并判断和当前节点之间的关系再做处理void post_order(btree* tree) {btNode* curr = tree;  // 记录当前执行的节点btNode* prev = NULL; // 记录前一个访问的节点if (NULL == curr) {return;}stack<btNode*>* st = new stack<btNode*>();st->push(curr);while (!st->empty()) {curr = st->top();// 如果该节点没有孩子节点则可以直接访问if (NULL == curr->left && NULL == curr->right) {cout << curr->data << "  ";st->pop();prev = curr;continue;}// 如果该节点的孩子节点已经被访问过了，也可直接访问if (NULL != prev && (prev == curr->right || prev == curr->left)) {cout << curr->data << "  ";st->pop();prev = curr;continue;}// 除了上述情况则需要将孩子节点入栈if (NULL != curr->right) {st->push(curr->right);}if (NULL != curr->left) {st->push(curr->left);}}delete st;}// 非递归中序遍历void in_order(btree* tree) {btNode* p = tree;if (NULL == p)return;stack<btNode*>* st = new stack<btNode*>();while (NULL != p || !st->empty()) {while (NULL != p) {st->push(p);p = p->left;}if (!st->empty()) {p = st->top();st->pop();cout << p->data << "  ";p = p->right;}}delete st;}

2.3 逐层遍历

//--------------------------------------------------// 广度优先void bfs_order(btree* tree) {btNode* p = tree;if (NULL == p) {return;}queue<btNode*> * qu = new queue<btNode*>();qu->push(p);while (!qu->empty()) {p = qu->front();qu->pop();cout << p->data << "  ";if (NULL != p->left) {qu->push(p->left);}if (NULL != p->right) {qu->push(p->right);}}delete qu;}//--------------------------------------------------// 销毁二叉树void destory_btree(btree* tree) {btNode* p = tree;if (NULL == p) {return;}queue<btNode*> * qu = new queue<btNode*>();qu->push(p);while (!qu->empty()) {p = qu->front();qu->pop();if (NULL != p->left) {qu->push(p->left);}if (NULL != p->right) {qu->push(p->right);}free(p);}delete qu;}

3. 测试

//============================================================================// Name        : main.cpp//============================================================================#include <iostream>#include "binarytree.h"#include <malloc.h>using namespace std;btNode* init_tree() {btNode* a = (btNode *) malloc(sizeof(btNode));a->data = 'A';a->left = a->right = NULL;btNode* b = (btNode *) malloc(sizeof(btNode));b->data = 'B';b->left = b->right = NULL;btNode* c = (btNode *) malloc(sizeof(btNode));c->data = 'C';c->left = c->right = NULL;btNode* d = (btNode *) malloc(sizeof(btNode));d->data = 'D';d->left = d->right = NULL;btNode* e = (btNode *) malloc(sizeof(btNode));e->data = 'E';e->left = e->right = NULL;btNode* f = (btNode *) malloc(sizeof(btNode));f->data = 'F';f->left = f->right = NULL;btNode* g = (btNode *) malloc(sizeof(btNode));g->data = 'G';g->left = g->right = NULL;btNode* h = (btNode *) malloc(sizeof(btNode));h->data = 'H';h->left = h->right = NULL;btNode* i = (btNode *) malloc(sizeof(btNode));i->data = 'I';i->left = i->right = NULL;a->left = b;a->right = c;b->right = d;c->left = e;d->left = f;d->right = g;e->left = h;e->right = i;return a;}int main() {cout << "Binary Tree Test" << endl; // prints Binary Tree Test// init treebtree * tree = init_tree();cout << "Pre order" << endl;rpre_order(tree);cout << endl;pre_order(tree);cout << endl;cout << "Post order" << endl;rpost_order(tree);cout << endl;post_order(tree);cout << endl;cout << "In order" << endl;rin_order(tree);cout << endl;in_order(tree);cout << endl;cout << "BFS order" << endl;bfs_order(tree);cout << endl;//destory_btree(tree);return 0;}

测试结果如下：

Binary Tree TestPre orderA  B  D  F  G  C  E  H  I  A  B  D  F  G  C  E  H  I  Post orderF  G  D  B  H  I  E  C  A  F  G  D  B  H  I  E  C  A  In orderB  F  D  G  A  H  E  I  C  B  F  D  G  A  H  E  I  C  BFS orderA  B  C  D  E  F  G  H  I