PAT A 1086. Tree Traversals Again (25)

题目

An inorder binary tree traversal can be implemented in a non-recursive way with a stack.  For example, suppose that when a 6-node binary tree (with the keys numbered from 1 to 6) is traversed, the stack operations are: push(1); push(2); push(3); pop(); pop(); push(4); pop(); pop(); push(5); push(6); pop(); pop().  Then a unique binary tree (shown in Figure 1) can be generated from this sequence of operations.  Your task is to give the postorder traversal sequence of this tree.

Figure 1

Input Specification:

Each input file contains one test case.  For each case, the first line contains a positive integer N (<=30) which is the total number of nodes in a tree (and hence the nodes are numbered from 1 to N).  Then 2N lines follow, each describes a stack operation in the format: "Push X" where X is the index of the node being pushed onto the stack; or "Pop" meaning to pop one node from the stack.

Output Specification:

For each test case, print the postorder traversal sequence of the corresponding tree in one line.  A solution is guaranteed to exist.  All the numbers must be separated by exactly one space, and there must be no extra space at the end of the line.

Sample Input:

6Push 1Push 2Push 3PopPopPush 4PopPopPush 5Push 6PopPop

Sample Output:

3 4 2 6 5 1

 

先构造树，然后后续遍历

 

代码：

#include <iostream>#include <string>using namespace std;struct node//点{int key;node *left,*right;node(int k):key(k),left(NULL),right(NULL){};};node* buildtree();//构造树void postorder(node* p,node* root);//后续遍历int n,num_t=0;//n，已经执行的指令数string ins;//指令int key;//输入的值int main(){node *root=NULL;cin>>n;root=buildtree();postorder(root,root);return 0;}node* buildtree()//根据堆栈信息构造树，递归{node* r=NULL;if(num_t<2*n){cin>>ins;if(ins=="Push")//压入，依次处理左右子树{num_t++;cin>>key;r=new node(key);r->left=buildtree();r->right=buildtree();}else//弹出{num_t++;return NULL;}}return r;}void postorder(node* p,node* root)//后续遍历{if(p->left!=NULL)postorder(p->left,root);if(p->right!=NULL)postorder(p->right,root);cout<<p->key;if(p!=root)cout<<" ";}