1162 Postfix Expression

Statement

Metadata

• 作者: 陈越
• 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

Given a syntax tree (binary), you are supposed to output the corresponding postfix expression, with parentheses reflecting the precedences of the operators.

Input Specification

Each input file contains one test case. For each case, the first line gives a positive integer N ( 20) which is the total number of nodes in the syntax tree. Then N lines follow, each gives the information of a node (the -th line corresponds to the -th node) in the format:

data left_child right_child

where data is a string of no more than 10 characters, left_child and right_child are the indices of this node's left and right children, respectively. The nodes are indexed from 1 to N. The NULL link is represented by . The figures 1 and 2 correspond to the samples 1 and 2, respectively.

Figure 1	Figure 2

Output Specification

For each case, print in a line the postfix expression, with parentheses reflecting the precedences of the operators.There must be no space between any symbols.

Sample Input 1

8
* 8 7
a -1 -1
* 4 1
+ 2 5
b -1 -1
d -1 -1
- -1 6
c -1 -1

Sample Output 1

(((a)(b)+)((c)(-(d))*)*)

Sample Input 2

8
2.35 -1 -1
* 6 1
- -1 4
% 7 8
+ 2 3
a -1 -1
str -1 -1
871 -1 -1

Sample Output 2

(((a)(2.35)*)(-((str)(871)%))+)

---

Last update: May 4, 2022