03-樹3 Tree Traversals Again （25 point(s)）

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:

6
Push 1
Push 2
Push 3
Pop
Pop
Push 4
Pop
Pop
Push 5
Push 6
Pop
Pop
 

Sample Output:

3 4 2 6 5 1

#include<iostream>
#include<stdio.h>
#include<string>
#include<sstream>
#include<vector>
#include<stack>
using namespace std;
int N, cur=0;
vector<int>preorder;
vector<int>inorder;
typedef struct TreeNode *Node;
struct TreeNode
{
	int num;
	Node left;
	Node right;
	TreeNode() {
		left = NULL;
		right = NULL;
	}
};
int findrootindex(int rootnum)
{
	for (int i = 0; i < N; i++)
	{
		if (inorder[i]==rootnum)
		{
			return i;
		}
	}
	return -1;
}
Node createtree(int left, int right) {
	if (left>right)
	{
		return NULL;
	}
	int root = preorder[cur];
	cur++;
	int rootindex = findrootindex(root);
	Node T = new TreeNode();
	T->num = root;
	if (left!=right)
	{
		T->left = createtree(left, rootindex-1);
		T->right = createtree(rootindex + 1, right);
	}
	return T;
}
bool FLAG = true;
void postfix(Node T)
{
	if (!T)
	{
		return;
	}
	postfix(T->left);
	postfix(T->right);
	if (FLAG)
	{
		cout << T->num;
		FLAG = false;
	}
	else
	{
		cout <<' '<<T->num;
	}
}
int main()
{
	stringstream ss;
	string INPUT,Nstr;
	getline(cin, Nstr);
	ss << Nstr;
	ss >> N;
	ss.clear();
	stack<int>stk;
	int value;
	for (int i = 0; i <N*2; i++)
	{
		getline(cin, INPUT);
		if (INPUT[1]=='u')
		{
			string num = INPUT.substr(5);
			ss << num;
			ss >> value;
			ss.clear();
			stk.push(value);
			preorder.push_back(value);
		}
		else
		{
			value = stk.top();
			stk.pop();
			inorder.push_back(value);
		}
	}
	Node T =createtree(0,N-1) ;
	postfix(T);
	return 0;
}