【数据结构】二叉树的遍历

二叉树是每个结点最多有两个子树的有序树。通常子树的根被称作“左子树”（left subtree）和“右子树”（right subtree）。二叉树常被用作二叉查找树和二叉堆或是二叉排序树。二叉树的每个结点至多只有二棵子树(不存在度大于2的结点)，二叉树的子树有左右之分，次序不能颠倒。

 

二叉树的遍历包括深度优先和宽度优先，深度优先又有前序，中序遍历和后序遍历三种。

对于深度优先遍历，递归遍历方法直观而简洁，如果要使用非递归方法，一般要借用栈结构；

宽度优先则常使用队列来实现。

 

#include 
 using namespace std;
 
 template
 class TreeNode
 {
 protected:
     TreeNode* left;
     TreeNode* right;
 public:
     T data;
 
     TreeNode (const T& item, TreeNode *lptr,TreeNode *rptr):
         data(item), left(lptr), right(rptr)    {}
     virtual ~TreeNode() {}
     TreeNode* Left() const    {
         return left;
     }
     TreeNode* Right() const {
         return right;
     }
 
     //递归遍历
     void Preorder(TreeNode *const node )const ;
     void Inorder(TreeNode  *const node )const ;
     void Postorder(TreeNode *const node)const;
 
     void Preorder() {
         Preorder(this);
     }
     void Inorder() {
         Preorder(this);
     }
     void Postorder() {
         Preorder(this);
     }
     //非递归遍历
     void PreTraverse(TreeNode *const node )const ;
     void InTraverse(TreeNode  *const node )const ;
     void PostTraverse(TreeNode *const node)const;
 
     void PreTraverse() {
         PreTraverse(this);
     }
     void InTraverse() {
         InTraverse(this);
     }
     void PostTraverse() {
         PostTraverse(this);
     }
 };
 
 // preorder recursive scan of the nodes in a tree
 template 
 void TreeNode::Preorder (TreeNode *const t) const
 {
     if (t != NULL) {
         cout << t->data << " "; // visit the node
         Preorder (t->Left());   // descend left
         Preorder (t->Right());  // descend right
     }
 }
 
 // inorder recursive scan of the nodes in a tree
 template 
 void TreeNode::Inorder (TreeNode*const t) const
 {
     if (t != NULL) {
         Inorder (t->Left());    // descend left
         cout << t->data << " ";                        // visit the node
         Inorder (t->Right());  // descend right
     }
 }
 
 // postorder recursive scan of the nodes in a tree
 template 
 void TreeNode::Postorder (TreeNode *const t) const
 {
     if (t != NULL) {
         Postorder (t->Left());  // descend left
         Postorder(t->Right()); // descend right
         cout << t->data << " "; // visit the node
     }
 }
 
 template
 void TreeNode::PreTraverse(TreeNode *const node ) const
 {
     if (node == NULL)
         return;
     TreeNode *t = node;
     stack< TreeNode* > s;
     s.push(t);
     while (! s.empty()) {
         t = s.top();
         s.pop();
         cout << t->data << " ";
         if(t->right != NULL)
             s.push(t->right);
         if(t->left != NULL)
             s.push(t->left);
     }
 }
 template
 void TreeNode::InTraverse(TreeNode *const node ) const
 {
     if (node == NULL)
         return;
     TreeNode *t = node;
     stack< TreeNode* > s;
     do {
         while(t != NULL) {
             s.push(t);
             t = t->left;
         }
         t = s.top();
         s.pop();
         cout << t->data << " ";
         t = t->right;
     } while (!s.empty()|| t!=NULL);
 }
 template
 void TreeNode::PostTraverse(TreeNode *const node ) const
 {
     stack<TreeNode* > s;
     stack sf;
     TreeNode *t = node;
     int flag;
     while (!s.empty() || t!=NULL){
         while (t!=NULL){
             s.push(t);
             sf.push(0);
             t = t->left;
         }
         t = s.top(),s.pop();
         flag = sf.top(),sf.pop();
         if (flag == 0) {
             s.push(t);
             sf.push(1);
             t =  t->right;
         }else {
             cout << t->data << " ";
             t = NULL;
         }
     }
 }一个简单的测试程序

 1 int main()
 2 {
 3     TreeNode<int> n1(10,NULL,NULL);
 4     TreeNode<int> n2(9,NULL,NULL);
 5     TreeNode<int> n3(6,&n1,&n2);
 6     TreeNode<int> n4(7,NULL,NULL);
 7     TreeNode<int> n5(8,NULL,NULL);
 8     TreeNode<int> n6(3,&n4,&n5);
 9     TreeNode<int> n7(1,&n3,&n6); 
10 
11     n7.PreTraverse(); cout << endl; 
12     n7.InTraverse();  cout << endl; 
13     n7.PostTraverse();cout << endl;  
14 
15     system("pause");
16     return 0;
17 }