1086 Tree Traversals Again

Statement

Metadata

作者: CHEN, Yue
单位: 浙江大学
代码长度限制: 16 KB
时间限制: 400 ms
内存限制: 64 MB

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

Last update: May 4, 2022