PTA3.3 Tree Traversals Again

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 $N$ ($\le 30$) 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 <stack>
#include <iostream>
#include <fstream>
#include <sstream>
using namespace std;

#define Empty (-1)

template<class T>
struct TreeNode
{
	T data;
	TreeNode<T> *left;
	TreeNode<T> *right;
	TreeNode(const T d = T(-1)) :data(d), left(nullptr), right(nullptr) {}
};

template<class T>
TreeNode<T>* createTree()
{
	fstream file("data.txt");
	int nodeNum = 0;
	file >> nodeNum;
	if (nodeNum == 0)
		return nullptr;

	stack<TreeNode<T>*> stack;
	TreeNode<T> *root = nullptr;
	TreeNode<T> *cur = nullptr;
	bool lastActionIsPop = false; //記錄上一次操作是否是POP

	for (int i = 0; i < nodeNum *2; i++)
	{
		string action;
		file >> action;
		if (action == "Push")
		{
			T item;
			file >> item;
			if (root == nullptr)
			{
				root = new TreeNode<T>(item);
				cur = root;
				stack.push(cur);
			}
			else
			{
				TreeNode<T> *tmp = new TreeNode<T>(item);
				if (lastActionIsPop)
					cur->right = tmp;
				else
					cur->left = tmp;
				cur = tmp;
				stack.push(cur);
			}
			lastActionIsPop = false;
		}
		else if (action == "Pop")
		{
			cur = stack.top(); //return reference in the top
			stack.pop(); //none retval
			lastActionIsPop = true;
		}
	}

	file.close();
	return root;
}

template<class T>
void postorderTraversal(TreeNode<T> *root, string &res)
{
	if (root == nullptr) return;

	postorderTraversal(root->left, res);
	postorderTraversal(root->right, res);
	
	stringstream os;
	os << root->data;
	res += (os.str() + " ");
}

int main()
{
	string res = "";
	TreeNode<char> *root = createTree<char>();
	postorderTraversal<char>(root, res);
	cout << res.substr(0, res.size() - 1); //不輸出最後面的空格

	system("pause");
	return 0;
}